Vol. 33, No. 3, May–June 2014, pp. 382–400ISSN 0732-2399 (print) � ISSN 1526-548X (online) http://dx.doi.org/10.1287/mksc.2013.0826

© 2014 INFORMS

Persuasive PufferyArchishman Chakraborty

Syms School of Business, Yeshiva University, New York, New York 10033, archishman@yu.edu

Rick HarbaughKelley School of Business, Indiana University, Bloomington, Indiana 47405, riharbau@indiana.edu

Sellers often make claims about product strengths without providing evidence. Even though such claims aremere puffery, we show that they can be credible because talking up any one strength comes at the implicit

trade-off of not talking up another potential strength. Puffery pulls in some buyers who value product attributesthat are talked up or emphasized while pushing away other buyers who infer that the attributes they valueare relative weaknesses. When the initial probability of making a sale is low, there are more potential buyersto pull in than to push away, so puffery is persuasive overall. This persuasiveness requires that buyers havesome privacy about their preferences so that the seller does not completely pander to them. More generally, theresults show how comparative cheap talk by an expert to a decision maker can be credible and persuasive instandard discrete choice models used throughout marketing, economics, and other disciplines.

Keywords : cheap talk; sales talk; comparative advertising; negative advertising; unique selling point; targeting;privacy; pandering

History : Received: October 2, 2012; accepted: September 14, 2013; Preyas Desai served as the editor-in-chiefand Miguel Villas-Boas served as associate editor for this article. Published online in Articles in AdvanceMarch 24, 2014.

[“Puffery” is] frequently used to denote the exaggerationsreasonably to be expected of a seller as to the degree of qual-ity of his product, the truth or falsity of which cannot beprecisely determined. —Federal Trade Commission1

1. IntroductionMuch of seller communication is mere “puffery”that makes vague or subjective claims about prod-uct strengths that are difficult or impossible to verify.Salespeople assure customers that a tie “looks great”or that a car “drives well.” Advertisements claimthat a pizza has “better ingredients” or that a painmedicine offers “fast, fast, fast relief.”2 Even moresubjectively, sellers emphasize a product’s stylish-ness or sportiness or try to make other favorableassociations that help position the product. Stud-ies find that most advertisements contain subjec-tive claims and that many advertisements contain noobjective facts (Stewart and Furse 1986, Abernethyand Franke 1996).3

1 Better Living, Inc., et al. 54 F.T.C. 648 (1957), aff’d, 259 F.2d 271 (3rdCir. 1958).2 The former claim by Papa John’s was ruled to be permissiblepuffery by the 5th U.S. Circuit Court of Appeals in 2000, whereasthe latter claim by Anacin was apparently never challenged.3 Stewart and Furse (1986) find that 58% of a sample of 1,000 tele-vision ads contain puffery. Abernethy and Franke (1996) find thatacross multiple studies, only 70% of television ads contain anyobjective information and only 34% contain more than one piece ofsuch information.

It is often argued that puffery by salespeople andadvertisers is only useful to the seller if it successfullydupes a credulous buyer (e.g., Preston 1996, Hoffman2006). However, the argument that puffery is unam-biguously bad seems at odds with the right to engagein puffery being supported by both common law andnearly a century of regulatory law.4 Moreover, somepuffery is so extreme that even a credulous buyeris unlikely to take it seriously—stores proclaim that“our service can’t be beat” and salespeople insist thata shirt “looks perfect.” When seller claims are nottaken at face value, might they still communicate use-ful information to buyers?

To gain insight into long-standing questions aboutthe effects of puffery, we analyze seller commu-nication about unverifiable product attributes. Wedevelop a discrete choice model where the buyer hasprivate information about her preferences and theseller has private information about his product thatcan help the buyer make a better decision. The infor-mation is subjective (or otherwise unverifiable), sothere is no way to directly prove the information tothe buyer. We show how puffery can be informa-tive in that it credibly communicates useful informa-tion on product attributes that would otherwise be

4 The Federal Trade Commission (FTC) 1987 Policy Statement onDeception confirmed the regulatory policy to not pursue claimsdesignated as puffery, and in 2008, the U.S. Court of Appeals, 9thCircuit, in Newcal Industries v. Ikon Office Solution (No. 05-16208 (9thCir. January 23, 2008)) found that puffery is legally nonactionable.

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difficult to communicate, and we show how it canbe persuasive in that it induces rational buyers tobe more likely to buy a product.5 Hence, despite thepotential for misleading some credulous buyers, wefind that puffery can benefit both buyers and sellers.

Consistent with the legal definition of puffery asclaims about subjective features of a product, wemodel puffery as “cheap talk” (Crawford and Sobel1982), rather than as verifiable messages (Milgrom1981) or costly signals (Spence 1973, Nelson 1974).In particular, we model puffery as a form of “com-parative cheap talk” that provides implicit informa-tion to buyers (e.g., Chakraborty and Harbaugh 2007,2010). Therefore, we assume that buyers are nei-ther completely naive nor completely skeptical aboutpuffery but rather treat unsupported claims as pro-viding potentially useful comparative information.For instance, even if a customer does not believethat a store has unbeatable service, the store’s servicemight still be its relative strength, and even if a shirtdoes not really look perfect, it might be better-lookingthan it is durable. When buyers treat claims in thisway, talking up one attribute of a product comes atthe implicit cost of not talking up a different attribute.Hence, even though puffery is unverifiable cheap talk,it can still be credible.

Puffery makes buyers who value the talked-up orfeatured attribute(s) more willing to buy the productand makes buyers who value the other attribute(s)less willing to buy the product. Is there any neteffect on the likelihood of a purchase, and if so,are more buyers pulled in by puffery or are morebuyers pushed away? We consider a standard dis-crete choice model in which buyer utility is linearin the attributes, so it may seem that there shouldbe no net effect. However, when buyers have privateinformation about their preferences, i.e., the buyer’sweights on the different attributes are uncertain as ina random coefficients model, we show that pufferyincreases the variation in buyer valuations, whichhelps the seller when the probability of a purchase isconvex. Such convexity holds when the prior prob-ability of a purchase is low so that there are morebuyers to pull in and fewer buyers to push away.

Puffery can highlight the strengths of a seller’sproduct, and it can also highlight the weaknesses of acompetitor’s product. We find that negative puffery,such as a negative advertisement or a salespersontalking down a competing product, is also credibleand that it helps the seller when the competitor’s

5 Following the terminology of sender–receiver games, communi-cation in our model is “informative” in that it provides real infor-mation and may be “persuasive” in that the information induces arational receiver to act in a way that the sender prefers. The earlyeconomics and marketing literatures define communication as per-suasive if it somehow alters buyer preferences.

probability of making a sale is sufficiently large. Suchpuffery scares away customers who were initiallyleaning toward the competitor’s product but whovalue attributes that are portrayed as weaknesses,and some of them go to the seller instead. It alsopushes some customers to the competitor’s productwho value attributes that have not been criticized.Although credible and effective, it may seem thathighlighting a competitor’s weaknesses would be lesseffective than highlighting one’s own strengths, andthis is true in our numerical example of a standardlogit model with symmetric preferences.

Combining the case of puffery about one’s ownproduct with that of negative puffery about acompetitor’s product, we then consider puffery thathighlights the comparative advantage of a firm’sproduct, i.e., that highlights which attribute is best rel-ative to that of a competitor. Such comparative advan-tage puffery, which could be verbal communicationby a salesperson or a form of comparative advertis-ing, can be doubly powerful in that it pulls in cus-tomers who value one attribute while simultaneouslypushing them away from the competitor. We showthat it helps the seller when the competitor’s probabil-ity of making a sale is sufficiently large (or the seller’sprobability of making a sale is sufficiently small). Forinstance, the classic “We try harder” ad campaign ofAvis is an example of comparative advertising by asmaller firm that is about a service attribute of theproduct.

Our assumption of random coefficients is appro-priate if the seller is communicating to multiplebuyers at once or if the seller is communicatingto one buyer whose type is unknown.6 If hetero-geneity in consumer preferences disappears becausethe seller can learn the exact type of individualbuyers and communicate to them separately, thenthe seller has an incentive to emphasize whateverattribute each buyer values more. Such “pandering”is completely discounted by buyers so that in equi-librium there is no net effect from seller communi-cation on the buyer’s probability of purchasing theproduct.7 Hence, greater information about a buyer’spreferences, or better ability to target communica-tion to different buyers with different preferences, canparadoxically hurt the seller by undermining the per-suasiveness of communication.

We focus on puffery of particular productattributes, but sellers may also engage in “product

6 Our results build on the early idea that simultaneous cheap talk tomultiple audiences can often facilitate communication (Farrell andGibbons 1989).7 The negative effects of pandering on credibility are analyzed byChe et al. (2013) in the related context of recommendations amongmultiple actions, e.g., a seller’s recommendation to buy one goodover another.

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puffery,” which highlights the overall strength of aproduct. As previously shown in the literature, ifthe seller has at least two products, there can bean equilibrium trade-off where pushing one prod-uct increases the probability that it is sold but alsodecreases the probability that another of the seller’sproducts is sold (Chakraborty and Harbaugh 2007,2010; Inderst and Ottaviani 2012; Che et al. 2013).From this perspective, product puffery can be seen asan implicit recommendation. For instance, a restau-rant’s claim to have “the world’s best hotdogs” mightnot convince people that its hotdogs are really thebest, but it can credibly convey that its hotdogs arenot as bad as its hamburgers. By decreasing the prob-ability that a potential diner fails to stop for eitherhotdogs or hamburgers, product puffery can increaseseller profits.8

If communication via puffery (cheap talk) helps aseller, it may seem that communication based on veri-fiable statements (“disclosure” or “persuasion”) mustbe even better, but this is not the case. First, commu-nication via puffery has a favorable impact on buyerimpressions of one attribute and a negative impacton impressions of another attribute, whereas commu-nication of verifiable information sometimes revealsbad information on both attributes. By the unravel-ing argument for verifiable information, sellers willoften feel compelled to reveal all verifiable informa-tion in equilibrium (e.g., Milgrom 1981, Koessler andRenault 2012). Therefore, seller types with bad infor-mation on both attributes would be hurt by disclo-sure of verifiable information but can still benefit frompuffery. Second, puffery sometimes strikes the rightbalance between revealing some information but nottoo much information so that it is better on averagefor the seller than full disclosure of information. Weillustrate this in §5.3 in an example that links attributepuffery with product recommendations.

This paper provides the first results on cheap talkabout choice attributes in standard discrete choicemodels such as the logit and probit. Beyond the par-ticular issue of seller puffery, the results apply moregenerally to discrete choice models in a wide rangeof areas such as managerial decision making, voting,and lobbying. We find that cheap talk can be credibleand persuasive even in the environment that mightseem least conducive to it—when the expert is push-ing one particular choice regardless of the benefit tothe decision maker and when the decision maker’sutility is linear in the choice attributes. In the follow-ing sections, we review the related literature, outline asimple example of how puffery is persuasive, provide

8 This situation can be modeled as a nested discrete choice problemwhere hotdogs and hamburgers are two attributes of the restaurant,as done in §5.3.

results on the shape of the choice probability functionin discrete choice models, analyze our main model ofpuffery, and then extend the model in a number ofdirections.

2. Literature ReviewA rapidly growing literature analyzes how sellerscan provide information about product attributes thatfacilitates a better match between buyers and prod-ucts (e.g., Anderson and Renault 2006, 2009; Johnsonand Myatt 2006; Sun 2011; Anand and Shachar 2009,2011; Gu and Xie 2013). We contribute to this litera-ture by showing how communication of unverifiablesoft information rather than just disclosure of veri-fiable hard information can improve such matching.Hence, the results from this literature focusing on ver-ifiable information are more general than previouslyrecognized.

The idea that puffery of one attribute might be per-suasive when puffery of every attribute is not per-suasive was examined by Kamins and Marks (1987).They consider puffery as part of a “two-sided argu-ment” in which one product attribute is explicitly con-ceded to be weak in order to increase the credibilityof claims regarding the featured attribute.9 They findthat such puffery is believed by experimental sub-jects and interpret the result as evidence that pufferycan be successful at deceiving consumers. We modelthe same insight that puffery about one of multipleattributes can be persuasive, but in our model ratio-nal consumers receive useful information from theseller’s decision to push a particular attribute.

Puffery of an attribute in our model can be counter-balanced by an explicit concession as in the two-sidedarguments literature, or it can be counterbalanced byan implicit concession whereby buyers correctly inferthat unmentioned attributes are not the product’s rel-ative strength.10 This implicit trade-off is consistentwith the long-recognized “discount effect” in whichconsumers often make negative inferences about thevalues of unmentioned attributes (e.g., see Meyer1981, Johnson and Levin 1985, and the survey by

9 Two-sided arguments were first studied regarding propagandastrategies (Hovland et al. 1949). The marketing literature hasemphasized that a buyer is less likely to attribute a seller’s inten-tions to that of just making a sale when some negative informationis provided. Our results show that credibility is still possible evenwhen the buyer thinks the seller’s only intention is to make a sale.10 Note that the seller still faces a trade-off from pushing oneattribute or another even if some credulous buyers maintain theirprior quality estimates for unmentioned attributes. However, ourconclusions that puffery helps buyers make a better decision andthat puffery is counterproductive when the probability of a sale ishigh depend on enough buyers updating rationally. Credulity isanalyzed in related contexts by Inderst and Ottaviani (2012) andHoffman et al. (2013).

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Kardes et al. 2004). In our cheap talk model, pufferythat raises the updated estimate of one attribute abovethe prior must, in equilibrium, lower the updated esti-mate of the other attribute below the prior. Hence,even when the underlying attributes are positivelycorrelated, the updated equilibrium estimates are neg-atively correlated.11

The result that communication benefits a firm whena sale is unlikely is consistent with anecdotal evidencethat puffery is most common by firms with weak mar-ket position (Preston 1996) and with the finding thatcomparative advertising is most useful for new andsmall firms rather than market leaders (Pechmannand Stewart 1991, Grewal et al. 1997). It is also consis-tent with long-standing experimental results that two-sided arguments increase purchase intent only whenpurchase intentions are initially weak (e.g., Crowleyand Hoyer 1994). The underlying mechanism thathigher variation in buyer valuations helps when val-uations are low also fits the findings by Sun (2012)that higher variance of product reviews helps whena product’s average ratings are low. In our modelwith multiple product attributes, if a product is strongon one dimension and weak on another dimension,then buyer valuations will vary more, and some buy-ers will buy the product even if overall valuationsare low.12

A recent theoretical literature considers compar-ative advertising when information is verifiable orpotentially so. Anderson and Renault (2009) ana-lyze comparative information that must be accurate,Barigozzi et al. (2009) analyze comparative informa-tion that a competitor can challenge or not in court,and Emons and Fluet (2012) analyze comparativeinformation for both the verifiable case and the casewhere exaggerations are costly in that they might bepenalized. Our cheap talk approach shows that theinsights from these models can often be extended tothe case where information is not verifiable. In par-ticular, Anderson and Renault (2009) show that smallfirms have the strongest incentive to reveal informa-tion about a competitor, and we find the same resultin our setting.13 As long as there are at least two

11 If there is verifiable rather than unverifiable information on mul-tiple attributes, a skeptical buyer should also make a negative infer-ence about an unmentioned attribute. By the unraveling argument,such skepticism should lead all but the very worst information oneach attribute to be disclosed in equilibrium.12 Johnson and Myatt (2006) examine how revealing informationincreases dispersion in buyer valuations and leads to a rotation inthe demand curve. They show how a seller with a niche rather thanmass-market strategy prefers to reveal information, but in theirmodel, the effect is driven by the ability to raise prices.13 In their model, prices are endogenous, so there is the extra con-sideration of how the equilibrium of the pricing game changes withcomparative advertising.

attributes, even if they are both vertical attributesvalued to some extent by all buyers, sales can risebecause of disclosure of comparative information bypure puffery.

Our analysis of comparative advantage pufferyadds to the understanding of how firms can create a“unique selling proposition” that differentiates a keyattribute of the product from that of the competition(Reeves 1961). Every firm must have a comparativeadvantage in some attribute relative to another firmthat it can credibly use puffery to highlight even ifthe advantage cannot be directly proven. Just as tradebased on comparative advantage helps both sides, wefind that comparative advertising based on a uniqueselling proposition for one firm can implicitly high-light the comparative advantage of the competingfirm to the benefit of firms and buyers.

That sellers can credibly communicate soft informa-tion is important in view of debates in the empiricalliterature on the content of advertising. The standardResnik and Stern (1977) methodology for measuringadvertising content includes any information aboutobjective product attributes even if it is not supportedby evidence but excludes subjective information. Thispaper’s results support the idea that even cheap talkabout objective information can be credible and infor-mative but also imply that excluding subjective infor-mation can underestimate the amount of informationin advertisements. In fact, the results imply that themere choice to focus on one aspect of a product suchas its popularity or its convenience can provide realinformation.14

We show how information about the relativequality of different product attributes can be commu-nicated through puffery when buyer attribute prefer-ences are uncertain. The prior literature on cheap talkin advertising has shown how a connection betweenperceived quality and pricing can make seller state-ments about overall quality credible. Bagwell andRamey (1993) find that cheap talk claims of high qual-ity can be credible when a seller of a low-qualitygood does not want to scare away low-income buyerswho correctly anticipate that high quality will implya high price. Gardete (2013) extends this analysis toallow for a range of different qualities and finds thatlow-quality firms will often pool with slightly betterfirms so that their quality claims are to some extentexaggerated. In these models, and in Chakrabortyand Harbaugh (2010, Section II.D), cheap talk is onlyinfluential if it is transmitted before the price and

14 Relatedly, the literature on targeted advertising has shown thatthe choice to focus advertisements on one consumer segment oranother, such as by choosing media that reach different typesof consumers, reveals information about a product (Anand andShachar 2009).

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if the price is expected to vary with quality. In ourapproach, we show that cheap talk is influential evenif prices are fixed.15

As long recognized in the literature, reputationalconcerns can provide a break on seller incentives tomislead. The reputational costs of lying in a cheaptalk model can be captured implicitly by a limitedbias as in Crawford and Sobel (1982) or by preferencecomplementarities as in Chakraborty and Harbaugh(2007), by explicit treatment of reputation over multi-ple interactions as in Sobel (1985), by a reduced-formfuture cost from current exaggerations as in Ottavianiand Sørensen (2006) and Inderst and Ottaviani (2009),or by incorporation of lying costs as in Kartik (2009).In our model, the seller does not face implicit orexplicit future costs from being caught lying butinstead faces an immediate opportunity cost of push-ing one attribute rather than another.

Chakraborty and Harbaugh (2010) providesufficient conditions for comparative cheap talk withstate-independent expert (seller) preferences to becredible; we use these in this paper. The sufficientconditions from that paper for cheap talk to bepersuasive cannot be applied directly to our randomcoefficients environment because of the interactionbetween the seller’s private information on attributequality and the buyers’ private information ontheir attribute preferences. However, we establishalternative conditions for persuasiveness that canbe applied in this environment, thereby extendingthe applicability of comparative cheap talk to linearrandom coefficient models.

3. ExampleFollowing a standard linear discrete choice model,suppose a buyer is considering product i at price piwith value Vi + �i, where Vi = �1�i1 + �2�i2 − pi. Theseller knows the product attribute qualities 4�i11 �i25and the buyer knows their own attribute preferences4�11�25. Suppose for now i = 1, and the only choice isto buy the product or not. The value to not buying isV0 + �0, where V0 = 0 and the independent and iden-tically distributed (i.i.d.) additive shocks �i and �0 areknown only to the buyer.

For simplicity, suppose that it is equally likely thateither the first or second attribute is the strength ofthe product and that it is equally likely that the buyeris a type who values the first or second attribute

15 We endogenize the price in §5.2. Note that endogenous priceswith multiple goods are considered by Chakraborty and Harbaugh(2003), where communication is by the buyer; by Chakraborty et al.(2006), where prices are set in auctions by competing buyers aftercommunication by the seller; and by Inderst and Ottaviani (2012),where prices are set by competing manufacturers and communica-tion is by a salesperson.

more. In particular, suppose that 4�111 �125 is 43115 or41135 with equal chance and, independently, 4�11�25is 43115 or 41135 with equal chance. The attributesare “vertical” quality measures because each attributeis valued positively, yet there is a “horizontal” fitcomponent because different buyer types value theattributes differently. The price is fixed at p1 = 10.

Letting v1 be the buyer’s expectation of V1, with-out any communication from the seller, E6�117 =

E6�127 = 2; so for the first type of buyer v1 = 3425 +

1425 − 10 = −2, and for the second type of buyerv1 = 1425+ 3425− 10 = −2. If the seller indicates thatattribute 1 is better, then these expected values for thetwo types are, respectively, v1 = 3435 + 1415 − 10 = 0and v1 = 1435+ 3415− 10 = −4, and if the seller indi-cates that attribute 2 is better, they are, respectively,v1 = 3415+1435−10 = −4 and v1 = 3435+ 1415− 10 = 0.Notice that from the seller’s perspective it has thesame effect to indicate that either attribute is better.Hence, even without reputational or other factors thatare likely to give an extra incentive for honesty, theseller has no incentive to lie and claim that the worseattribute is really the product’s strength, so puffing upone attribute at the expense of the other is credible.

Now consider when puffery is persuasive in thatit raises the likelihood of making a sale. Because V1

is linear in the seller’s information, it might seemthat good news on one attribute will raise the pur-chase probability just as much as bad news on anotherattribute will lower it, so that there is no impact frompushing an attribute as the strength of the product.However, this ignores the nonlinearities induced bythe distributions of �1 and �0. Assuming that theyfollow Gumbel distributions as in the logit model,the purchase probability is P1 = Pr6v1 + �1 > �07 =

ev1/41 + ev15, which has the familiar S shape inFigure 1. In particular, for this case of two choices4¡2/¡v2

15P14v15= 41 − 2P1541 −P15P1, so P1 is convex forP1 ≤ 1/2 and concave for P1 ≥ 1/2.

Communication of which attribute is the product’sstrength increases the variation in buyer valuationsbecause some buyer types like the product more andothers like it less than their prior expectations. There-fore, by application of Jensen’s inequality, this vari-ation helps the seller when the purchase probabilityis in the lower convex region. In this example, ifthere is no communication, then P1 = e−241 + e−25 =

00119, which is in the convex region. With pufferyof one attribute, the type of buyer who cares moreabout that attribute has an expected value of v1 =

0 and thus buys with probability P1 = e0/41 + e05 =

005, whereas the type of buyer who cares more aboutthe other attribute has an expected value of v1 = −4and thus buys with probability P1 = e−4/41 + e−45 =

00024. Therefore, the expected purchase probability is

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Figure 1 Effect of Puffery on Purchase Probability

42

P1(�1)

�1

0–2–4

0.024

0.119

0.262

0.5

1.0

4005 + 000245/2 = 00262, which is over twice the prob-ability without communication.

Since P1 is concave for higher ranges of v1, com-munication that increases variation in v1 hurts ratherthan helps the seller. In this case, the consumer isalready likely to buy a product, so the seller is betteroff remaining silent rather than risk losing the sale.For instance, if consumers have stronger preferencesfor the product attributes (the ranges of �1 and �2 arehigher) or if the attributes are more likely to be ofhigh quality (the ranges of �1 and �2 are higher), thenthis is the case. If the cost of production is low so thatthe price p1 is low, then this is also the case.16

Because the probability of making a sale can also beinterpreted as the share of potential buyers who buythe product, the convex–concave shape of the logitmodel captures the intuition that when market shareis low there is a large pool of potential buyers who arenot currently buying and might be enticed by goodnews about one of the attributes, while there are notmany current buyers who are buying and might bepushed away by bad news about the other attribute.In contrast, when market share is high, good newsabout an attribute pulls in fewer buyers than badnews about the other attribute pushes away. So theseller benefits from puffery when market share is low,but the seller is hurt when market share is high.

This example imposes the simplifying assumptionsthat the coefficients and attributes have symmetrictwo-point distributions, that each buyer type valueseach attribute positively, that there is only one prod-uct the buyer is considering, that the price is fixed,

16 In this example, setting p = 10 is optimal with puffery for amarginal cost of c = 8. Note that without puffery, a lower price ofapproximately 902 is optimal. We endogenize the price in §5.2.

and that the noise parameters are consistent with thelogit model. In our following analysis, these assump-tions are relaxed. Some attributes might be moreimportant than others, buyers might already expectone attribute to be stronger than the other, the twoattribute qualities might be positively correlated orhave any other dependent distribution, some buyertypes might place negative weight on some attributes,there might be multiple goods under consideration,the seller might choose to adjust the price in light ofcommunication possibilities, and the noise parame-ters may follow any log-concave distribution. Never-theless, the same result holds—puffery is credible andpersuasive as long as there are at least two attributes:the buyer’s preferences � are not perfectly known bythe seller and the probability of making a sale is low.

4. The ModelBuilding on the discrete choice model introducedabove, suppose that buyer utility from product isold by seller i is Vi + �i. Let Vi = ��i, where �i =

4�i11 0 0 0 1 �iN 5 represents the N attributes of product i =11 0 0 0 1n and � = 4�11 0 0 0 1�N 5 specifies the marginalutilities (buyer preferences) of the different attributes.The vector �i includes at least two uncertain qual-ity attributes and also known attributes, including theproduct price pi. The value of the no purchase optionis normalized to V0 = 0. Although our proofs are moregeneral, for concreteness, we will focus the presenta-tion on the case of two firms, n= 2, and two uncertainquality attributes, 4�i11 �i25.

The seller of product i = 1 knows the realized val-ues of the uncertain quality attributes, but the buyeronly knows their common knowledge distribution H .The buyer knows the realized values of the randomcoefficients �, but the seller only knows their com-mon knowledge distribution G. Both H and G havefull support on bounded convex sets with nonemptyinteriors. The realizations of the additive terms �i arealso the private information of the buyer. Letting Frepresent the common knowledge distribution of thei.i.d. �i and f the corresponding density function, weassume that f is log-concave with support on the realline. We assume that the attribute preferences � andattribute qualities � are independent of each other andof the �i’s but allow for possible dependence withinthe components of � and within the components of �.

Let vi denote the buyer’s expectation of Vi givenall available information, so that these estimates andthe idiosyncratic shocks �i determine the probabilitywith which a product is purchased. We assume thatthe buyer purchases at most one product, so the prob-ability that product i is purchased is then

Pi4v5= Pr6vi + �i > max8v−i + �−i970 (1)

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Chakraborty and Harbaugh: Persuasive Puffery388 Marketing Science 33(3), pp. 382–400, © 2014 INFORMS

The seller of product 1 sends a costless, unverifiablemessage to the buyer m ∈ 8m11 0 0 0 1mK9, where K ≥ 2.A communication strategy for the seller specifieswhich message is sent as a function of the state �.The buyer estimates the expected values of � giventhe prior distribution, the seller’s strategy, and theseller’s message m. Representing these prior estimatesby a = E6�7, let the buyer’s updated estimates givenmessage mk be ak = E6� � mk7 for k = 11 0 0 0 1K. Sincethe buyer’s utility for product i is linear in �i, theseexpected values are the only feature of the distribu-tion of � that matter to buyers. Assuming that everymessage is used in equilibrium,17 a (perfect Bayesian)equilibrium of this cheap talk game is fully speci-fied by the seller’s communication strategy mapping� to 8m1 0 0 0 1mK9. The expected purchase probability forproduct i given the buyer’s updated estimate ak isthen

P̄i4ak5=

∫

�Pi4�a

k5 dG4�5 (2)

for k = 11 0 0 0 1K, where we have integrated over therandom coefficients � since they are the private infor-mation of the buyer. The additive terms �i are alreadyincorporated into the definition of Pi. We assume thatprices are fixed, so the seller’s profits are proportionalto P̄14a

k5. We endogenize the price in §5.2.A communication strategy is a cheap talk equilib-

rium if the seller has no incentive to deviate by send-ing a message that is inconsistent with the strategy.If the seller can generate a higher purchase proba-bility from any one message, the seller will alwayssend that message; thus, the seller must be indifferentbetween every message used in equilibrium.18 Hence,the equilibrium condition is

P̄14ak5= P̄14a

k′

5 (3)

for all k, k′ = 11 0 0 0 1K.We will show that there always exists a cheap

talk equilibrium in this game that affects the buyer’sestimates of the attribute qualities. Therefore, ourmain concern is when such communication raisesthe expected purchase probability above the no-communication case, i.e., when P̄14a

k5 > P̄14a5. As seenfrom the logit example in Figure 1, the key to per-suasiveness is the shape of P14v5. The following prop-erties hold for all i.i.d. �i with log-concave densityfunctions and support on the real line. This classincludes the Gumbel distribution on which the logit

17 This assumption in cheap talk games, which precludes the needto specify out of equilibrium beliefs, is without loss of generalitysince any unexpected statement can be interpreted as equivalent toone of the messages.18 If the seller faces some reputational or other costs to lying, thiscan give a strict incentive to tell the truth. Our focus is on howpuffery can be credible and persuasive even without such factors.

model is based, the normal distribution on whichthe probit model is based, and most other standarddistributions. Proofs of these properties and of subse-quent propositions are in the appendix.

Shape Properties of Pi. The purchase probability Pi

is, for j 6= i, (i) convex 4concave5 in vi if Pi is sufficientlysmall 4large5, (ii) convex 4concave5 in vj if Pj is sufficientlylarge 4small5, and (iii) always quasiconcave in 4vi1vj5.

In a standard linear random-effects model, we willshow that revealing information on �i via pufferyincreases variation in vi, so these shape propertiesdetermine the effect of such information on the prob-ability of making a sale. Property (i) implies that, con-sistent with Figure 1, P1 is first convex and then atsome point concave in v1.19 We will use this resultto show that the insight from the introductory exam-ple that puffery helps when the purchase probabilityis small extends generally. Property (ii) implies thatP1 is instead concave–convex in v2. We will use thisproperty to find a corresponding result that negativepuffery of an attribute of a competitor’s product helpswhen the probability of purchasing the competitor’sproduct is large. Properties (i) and (ii) do not implythat P1 is necessarily convex in 4v11v25 over somerange, and instead, property (iii) rules this out. Aswe will see, property (iii) implies that to ensure thatpuffery affecting buyer estimates of the values of boththe seller’s product and a competitor’s product helpsrather than hurts the seller, it must convey to buyerswhich attribute is the comparative advantage of theproduct.20

4.1. Attribute PufferyWe first consider attribute puffery that, as in theintroductory example, only affects buyer estimates ofattributes of the seller’s product 4�111 �125. For com-munication to be informative, it must change thebuyer’s estimates of attribute quality, and differentmessages must change the estimates in differentways so as to create a trade-off between sendingone message or another. Given a message mk, thebuyer’s attribute estimates for the seller’s product areak1 = 4ak111 a

k125 = 4E6�11 � mk71E6�12 � mk75, whereas the

attribute estimates for the other firm’s product remain

19 As with the logit, Pi is always S-shaped for the probit. For n= 1,Pi is S-shaped for all log-concave �i , but if n> 1, then Pi might havemore than one inflection point. Nevertheless, convexity (concavity)still holds for vi low (high) enough.20 The convexity and concavity results are also relevant for otherforms of communication, such as product samples, third-partyreviews, and quality certificates. We focus on ranges of Pi whereconvexity or concavity holds, so Jensen’s inequality applies directly.Kamenica and Gentzkow (2011) examine the optimal partial dis-closure policy that a sender would like to precommit to when thesender’s payoff includes both convex and concave regions.

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at a2 = 4a211 a225= 4E6�2171E6�2275. Thus the equilib-rium condition (3) is P̄14a

k11 a25= P̄14a

k′

1 1 a25, or∫

�P14�1a

k11 +�2a

k121�1a21 +�2a225 dG4�5

=

∫

�P14�1a

k′

11 +�2ak′

121�1a21 +�2a225 dG4�5 (4)

for all k, k′.If � and � are symmetrically distributed, as was

true in the introductory example, the seller clearlyhas no incentive to lie about which attribute is bet-ter. If instead buyers tend to care more about oneof the attributes, buyers can “discount” puffery forthat attribute so that the relative incentive to pushthe attribute is weakened to the point that lying is nolonger worthwhile. For instance, suppose the supportof the distribution of �1 is above that of �2. This givesthe seller an incentive to push attribute 1 rather thanattribute 2; however, if buyers are correctly suspi-cious of such a claim and heavily discount it, then theseller is better off pushing attribute 2. By continuity,there must be some intermediate degree of discount-ing that eliminates the seller’s incentive to alwayspush attribute 1 without creating an incentive insteadto always push attribute 2. In particular, by Theo-rem 1 of Chakraborty and Harbaugh (2010), becausethe seller’s (expert’s) preferences do not depend onthe state � and are continuous in the buyer’s (decisionmaker’s) estimates a, the appropriate degree of dis-counting can always ensure that the seller’s incentiveto lie is eliminated and an informative equilibriumexists.

An informative equilibrium is influential if itchanges buyer behavior. In equilibrium, attributepuffery pushes up the buyer’s estimate for oneattribute a1i and pushes down the buyer’s estimatefor another attribute a1j , but since the buyer’s pref-erences � vary, the trade-off for each different typeof buyer is not exact. Some buyers end up with ahigher v1 and some buyers with a lower v1, whichcreates a mean preserving spread in v1. If P1 is convexin v1, then Jensen’s inequality implies that this raisesthe purchase probability for any given �. Therefore,integrating over all the �, the expected purchase prob-ability P̄1 rises. Conversely, if P1 is concave in v1, thenP̄1 falls.

The following proposition formalizes this argu-ment. Because a rational buyer is always better off onaverage from more information, we focus on the gainto the seller in this and subsequent results.21

21 In particular, puffery of the form we examine partitions the infor-mation space so that the buyer is more informed in the sense ofBlackwell (1953) and hence always benefits in expectation for afixed price. The buyer can still lose for some realizations; e.g., ifthe realized values of both attributes are below the mean, then abuyer who purchases the good based on puffery of one attributewill regret the purchase.

Proposition 1. Attribute puffery by seller i alwaysstrictly raises (lowers) the expected purchase probability P̄i

if the purchase probability Pi4v5 without communication issufficiently small (large) for all v.

As an example, consider a random coefficients logitmodel for the case where the attribute qualities �1jfor the seller’s good are i.i.d. uniform on 60117, so theprior without communication is a1 = 4E6�1171E6�1275=

41/211/25. Letting message m1 correspond to theranking �11 ≥ �12 and message m2 correspond to theopposite ranking, the updated estimates are a1

1 =

4E6max8�111 �12971E6min8�111 �12975 = 42/311/35 anda2

1 = 4E6min8�111 �12971E6max8�111 �12975 = 41/312/35.As shown in Figure 2, panel (a), these are therespective conditional means for the triangles aboveand below the �11 = �12 line. By the law of iteratedexpectations, the unconditional mean a1 lies on aline joining these conditional means as shown inthe figure. We assume that the attribute qualities �2jare uniform i.i.d. on 61/10111/107, so that the otherproduct is known to be of higher quality on average,a2 = 4E6�2171E6�2275 = 43/513/550 The (fixed) prices arep1 = p2 = 10.

In this example, the seller has no reason to “lie” bypuffing up the wrong attribute because pushing eitherattribute will have the same effect on the purchaseprobability. This is seen from the seller’s indiffer-ence or isoprobability curves representing the com-binations of buyer estimates of �11 and �12 that givethe same expected purchase probability P̄i4ai5. Giventhat the same curve passes through a1

1 = 4a1111 a

1125 and

a21 = 4a2

111 a2125, the seller has no reason to misreport the

ranking and claim �1 ≥ �2 when, in fact, �1 < �2, orvice versa.

Because the other product is better on average, thepurchase probability without communication is low,so P1 is convex in v1 = �1a11 + �2a12, and hence P̄1 isconvex in a1 = 4a111 a125. Therefore, as seen from theshape of the isoprobability curves, P̄1 is convex alongthe line connecting a1

1 and a21, implying that the prob-

ability is higher at either endpoint than in the interior,including the prior a1. In this example, the expectedpurchase probability rises from the prior of P̄14a15 =

509% to P̄14ak15= 1009%.22

In any cheap talk game, there is also a “babblingequilibrium” that is completely uninformative in thatthe receiver believes that the messages are uncorre-lated with the sender’s information and so the senderhas no incentive to make the messages correlate. Suchan equilibrium leads to buyer purchase probabilities

22 This convexity approach to proving persuasiveness differs fromthe quasiconvexity approach in Theorem 2 of Chakraborty andHarbaugh (2010). Quasiconvexity is not always preserved by inte-gration, so showing quasiconvexity in Pi4vi5 is not sufficient toshow quasiconvexity in P̄i4ai5.

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Figure 2 Attribute Puffery, Negative Puffery, and Comparative Advantage Puffery

1 –1–1

1�11 – �12�21�11

�12 �22 �21 – �22

(a) Highlight own strength (b) Highlight competitor’s weakness (c) Highlight comparative advantage

0.109

a11

a12 a2

2

a21

d2

d

d1

a1

a2

0.001

0.001

0.500

0.250 0.126

0.126

0.250

0.084

0.750

0 0.10.1

1.1

1.1 11

that are the same as the priors, so our above discus-sion on the gains from puffery can also be interpretedas the gains from an informative cheap talk equilib-rium relative to the babbling equilibrium.23

We have focused discussion on the simplest caseof a two-message equilibrium, but other equilibriacan also exist. Our results on the persuasiveness ofpuffery extend to all influential cheap talk equilibria.For a low probability of making a sale, there alwaysexist more informative equilibria, which involve addi-tional messages that further subdivide, possibly withmixing, the two regions in Figure 2, panel (a).24

Claims that both attributes are better on average thanthe prior can be credible given that the seller faces theopportunity cost of not focusing on just one attribute.In equilibrium, such a message can only be moder-ately favorable about both attributes, because other-wise, the seller would never send a more focusedmessage. Hence, the classic Miller Lite slogan “tastesgreat, less filling” can convey that the beer is betterthan expected on both dimensions, but not particu-larly impressive on either.

4.2. Negative PufferyWe now consider negative puffery, where the seller ofone product highlights a weak attribute of a competi-tor’s product. For instance, a salesperson at one cardealership criticizes a car sold by another dealership,

23 All seller types benefit equally when the probability of a sale islow, and the buyer always benefits from more information givena fixed price, so a Pareto dominance argument can be made forcommunication relative to babbling.24 The existence of multimessage equilibria in our environment isimplied by Theorem 3 of Chakraborty and Harbaugh (2010). For thesymmetric case, there is always an equilibrium with three messagesin which two of the messages indicate the strength of one attributeand the middle message indicates that both attributes are similarand better than the prior, as Crutzen et al. (2013) show in a differentbut related model.

or a negative advertisement by a firm focuses on aweakness of a competing firm’s product.

For our definition of negative puffery, we assumethat communication by the seller of product 1 affectsbuyer estimates of the attributes of product 2, andalso, to distinguish it from other forms of puffery,we assume that it has no effect on buyer estimatesof product 1. Therefore, the equilibrium condition isP̄14a11 a

k25= P̄14a11 a

k′

2 5, or∫

�P14�1a11 +�2a121�1a

k21 +�2a

k225 dG4�5

=

∫

�P14�1a11 +�2a121�1a

k′

21 +�2ak′

225 dG4�5 (5)

for all k, k′, where 4a111 a125 is unaffected by the mes-sages. Following previous arguments, even if thereare asymmetries in the distributions of � or �, The-orem 1 of Chakraborty and Harbaugh (2010) impliesthat there is an influential cheap talk equilibrium sat-isfying this condition.

Negative puffery pulls some buyers away from thecompeting firm, but it also pushes toward them buy-ers who care more about the noncriticized attribute.It might seem that the net result is positive whenthe competitor has a large number of likely buyers topull away, and this is indeed the case. Property (ii)shows that P1 is concave–convex in v2, so any com-munication that increases the variation in v2 in orderto pull in some buyers and push away other buyershelps the seller of good 1 when v2 is large. This canbe seen directly for the logit where 4¡2/¡v2

j 5Pi4v5 =

PiPj42Pj − 15, so Pi is concave in vj for vj sufficientlylow such that Pj ≤ 1/2 and convex in vj for vj suffi-ciently high such that Pj ≥ 1/2.

The following proposition uses this result on theshape of Pi in vj and Jensen’s inequality to show thatthe seller is better or worse off from negative pufferydepending on the competitor’s prior probability ofmaking a sale.

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Proposition 2. Negative puffery by seller i about anattribute of product j always strictly raises (lowers) theexpected purchase probability P̄i if the purchase probabilityPj4v5 of product j without communication is sufficientlylarge (small) for all v.

Figure 2, panel (b) shows isoprobability curves forthe expected purchase probability of product 1 whenthe seller of product 1 provides information on thecompeting product 2. As described earlier, each �2j

is uniform i.i.d. on 600111017 so that the expectedvalues without communication are a2 = 43/513/55.Letting message 1 indicate �21 ≥ �22 and message 2indicate �21 < �22, the expected values with nega-tive puffery are a1

1 = 4E6�21 � m171E6�22 � m15 = 41/10 +

2/311/10 + 1/35= 423/30113/305 and a22 = 4E6�21 �m271

E6�22 �m25= 413/30123/305. Because the other productis better on average, the purchase probability for thatgood is high, so P1 is convex in v2 = �1a21 +�2a22, andhence P̄1 is convex in a2 = 4a211 a225. Therefore, analo-gous to the attribute puffery case, P̄1 is convex alongthe line connecting a1

2 and a22. The firm’s expected

purchase probability is increasing toward the lowerleft; thus, as seen in the figure, negative puffery helpsthe firm.

Because some of the buyers who are pushed awayfrom the competitor end up buying neither prod-uct, it might seem that negative puffery is less effec-tive at gaining customers than directly pushing anattribute of one’s own product, as described in theprevious section. In this example, negative pufferyraises the expected purchase probability from 509% to804% rather than 1009%, so indeed, it is less effective.

4.3. Comparative Advantage PufferyNow suppose that the seller makes comparative state-ments that reveal attribute information about its prod-uct and a competing product so that there are fourvariables on which the seller provides information.We focus on a two-message equilibrium that increasesproduct differentiation by simultaneously indicatingthat one product is relatively better on one attributeand the other product is relatively better on anotherattribute. Such communication can thus be seen asfocusing on the horizontal component of productinformation.

We define comparative advantage puffery as havingtwo features that distinguish it from other forms ofpuffery. First, it affects both attributes of each product(and none others more generally), so the equilibriumcondition is P̄14a

111 a

125= P̄14a

211 a

225, or

∫

�P14�1a

111 +�2a

1121�1a

121 +�2a

1225 dG4�5

=

∫

�P14�1a

211 +�2a

2121�1a

221 +�2a

2225 dG4�50 (6)

Second, each product’s expected quality averagedover the uncertain �’s is the same for each message,

E6�1a1i1 +�2a

1i27= E6�1a

2i1 +�2a

2i27 (7)

for i = 112. This captures the idea of comparativeadvantage puffery as affecting only the distribution ofattributes but not overall quality. The constraints (7)can be seen as reducing the four dimensions of infor-mation to just two dimensions, so that our previousexistence results still apply. More formally, becausethe number of dimensions exceeds the number ofequality constraints, by Proposition 5 of Chakrabortyand Harbaugh (2010, in their online appendix), we areassured of an influential equilibrium.

From shape property (iii), we know that P1 is(strictly) quasiconcave in 4v11v25 and, by linearityof vi, therefore, quasiconcave in 4a11 a25 for given �.This implies that P1 cannot be strictly convex in4a11 a25. However, the lack of convexity of P1 in thefour-dimensional 4a11 a25 space does not preclude con-vexity in lower subdimensions. Constraint (7) restrictsvariation to a two-dimensional subspace, and theequilibrium condition further restricts the space to asingle dimension. For P1 small enough, we find thatP1 is strictly convex along this one-dimensional lineof variation.25

To see this result, consider Figure 2, panel (c),which shows the same situation as in panels (a)and (b) except that the seller of product 1 makesstatements that buyers interpret as about the com-parative advantage of product 1. As shown in thefigure, message 1 indicates that product 1 is rel-atively better at attribute 1 compared with prod-uct 2, �11 − �12 ≥ �21 − �22. And message 2 indicatesthat product 1 is relatively better at attribute 2 com-pared with product 2, �12 − �11 > �22 − �21 (or, equiva-lently, that product 2 is relatively better at attribute 1).The expected values for the differences are d = 4a11 −

a121 a21 −a225= 40105 without communication and dk =

4ak11 −ak121 ak21 −ak225 for messages k = 112. The expected

purchase probability of product 1 increases towardthe upper left and lower right as the estimates moveaway from the prior 40105, and the two isoprobabil-ity curves through the updated estimates representthe same expected purchase probability. Even thoughP̄1 is not convex in 4a11 a25 nor in the differences4a11 − a121 a21 − a225, it is convex along the line join-ing d1 and d2, which includes the prior d = 40105, sothe expected purchase probability of product 1 rises.In this example, it more than doubles from 509% with-out communication to 1206% with comparative advan-tage puffery.

25 This argument provides a weaker sufficient condition for per-suasiveness than that required in Theorem 2 of Chakraborty andHarbaugh (2010).

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The following proposition uses the approach in Fig-ure 2, panel (c) to show how puffery that providesinformation on the comparative advantage of a prod-uct increases the expected purchase probability.

Proposition 3. Puffery of an attribute that is the com-parative advantage of product i relative to that of product jalways strictly raises (lowers) the expected purchase prob-ability P̄i if the purchase probability Pi4v5 without commu-nication is sufficiently small (large) for all v.

This result can help inform the policy debate overwhen comparative advertising should be encour-aged. The FTC has explicitly encouraged comparativeadvertising about “objectively measurable attributesor price” (Federal Trade Commission 1979). Ourresults imply that comparative advertising aboutsubjective attributes can highlight the comparativeadvantage of a product and thereby direct consumersto products that have relative strengths in areas thatthey value.

Before comparing in more detail these three differ-ent forms of puffery that focus on product attributes,suppose that the seller of a single good makes state-ments that push the overall quality of its product ordenigrate the overall quality of a competitor’s prod-uct. Because the firm’s incentive is to always push itsown product, it might seem that there is no possibilityto credibly reveal information through such puffery.In fact, in equilibrium, communication is possible,but it involves a trade-off in which a positive state-ment about the seller’s own product is also treated asgood news about the competitor’s product, whereasa negative statement about the competitor’s productis treated as bad news for both products.26

Although credible, such communication can lowerthe purchase probability for the firm making thecomparison. From Theorem 2 of Chakraborty andHarbaugh (2010), the seller is worse off from cheaptalk if P̄14a5 is quasiconcave in 4a11 a25, whereas fromshape property (iii), P14v5 is quasiconcave in 4v11v25for all values where vi is linear in ai. This impliesthat, as uncertainty about the buyer’s preferences �becomes smaller and P14v5 converges to P̄14a5, pufferythat affects the estimated overall quality of both theseller’s good and the competitor’s good makes theseller worse off. An implication of this result is thatour restriction above in which comparative advantagepuffery leaves overall expected quality unchanged isnecessary to ensure that such puffery benefits theseller.

26 This is consistent with the finding that negative advertising hurtsbuyer impressions of the firm doing the advertising (e.g., Jain andPosovac 2004). Puffery of this form is analyzed more formally inan earlier version of this paper.

Figure 3 Most Persuasive Form of Puffery

P2P0

P1

Babbling

Attributepuffery

Comparativeadvantage puffery

–

– –

4.4. Puffery Forms ComparedWhen are the different forms of puffery most per-suasive? Propositions 1–3 show that puffery is betterthan no communication (or the babbling equilibrium)when the purchase probability is low, but these ana-lytic results do not rank the gains from the differentforms of puffery. From the numerical results for theexample in Figure 2, comparative advantage pufferywas most persuasive, but this result was only forparticular parameter values. We now consider thisproblem further. In our cheap talk environment, thesame messages can be interpreted in different ways bythe buyer, so formally, the question is when differentequilibria (and hence different equilibrium interpreta-tions of the messages) are most persuasive.27

The probability simplex in Figure 3 shows the mostpersuasive equilibrium based on prior expected pur-chase probabilities for the seller and competitor, P̄1and P̄2, and the probability of no sale, P̄0. The calcu-lations use the same example in Figure 2 except thatwe allow �i1 and �i2 to have more general support on6bi11 + bi7 for i = 112. The bi shift parameters allowthe quality ranges for each product to vary and, giventhat prices and preferences are fixed, fully determinethe prior expected probabilities. To allow for directcomparisons of the different forms of puffery, we con-tinue our focus on two-message equilibria that aresymmetric in that they divide the relevant state spacesequally through the prior.

Comparative advantage puffery does best in thebottom right region where P̄2 is high and P̄1 is low.Since P1 is convex in v1 when P1 is low and itis convex in v2 when P2 is high, revealing infor-mation that increases variation in both v1 and v2helps the seller, which is the feature of comparativeadvantage puffery. This is the case in the example

27 In practice, the literal content of the message, e.g., whether itrefers to a competitor explicitly, is likely to help buyers infer theintended meaning. Note that, in any given equilibrium, all sellertypes receive the same payoff, so if one type of seller prefers oneequilibrium, all seller types prefer it.

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of Figure 2 where we assume that the competitor isbetter, �1j ö U601171 �2j ö U600111017, implying priorexpected probabilities of P̄1 = 509%, P̄2 = 5906%, andP̄0 = 3405%. As indicated, the expected purchase prob-ability P̄1 rises to 1009% with attribute puffery, to 804%with negative puffery, and up to 1206% with compar-ative advantage puffery.

Attribute puffery does best in the bottom leftregion where P̄0 is high, so both P̄1 and P̄2 arelow, in which case P1 is convex in v1 and con-cave in v2. With attribute puffery, the seller bene-fits from increased variation in v1, but unlike com-parative advantage puffery, it avoids a loss fromincreased variation in v2. Changing the example fromFigure 2 so that the seller and competitor are symmet-ric, �1j ö U601171 �2j ö U60117, implies prior probabil-ities of P̄1 = P̄2 = 2800% and P̄0 = 4400%. In this case,P̄1 rises to 3009% with attribute puffery, falls to 2700%with negative puffery, and rises to 3000% with com-parative advantage puffery.28

Finally, no communication (babbling) does bestwhen P̄1 is high and the seller does not want to riskscaring away likely buyers. Changing the examplefrom Figure 2 so that the seller is better than the com-petitor, �1j ö U6001110171 �2j ö U60117, the prior prob-abilities are P̄1 = 5906%, P̄2 = 509%, and P̄0 = 3405%.In this case, P̄1 falls to 5700% with attribute puffery, to5407% with negative puffery, and to 5507% with com-parative advantage puffery.

We find that negative puffery is never the best strat-egy. Negative puffery affects v2, so it is most effectivewhen P̄2 is high, but high P̄2 implies low P̄1, whichmeans the seller is not realizing the gains from reveal-ing information about its own product. Hence, in theone case where negative puffery is desirable, com-parative advantage puffery that increases variation inboth v1 and v2 does even better.

For concreteness, we have focused on shifts in thedistributions of attribute quality, but the same effectscan be found by varying other parameters. If the com-petitor has lower costs and can set a lower price,then it will have a higher expected purchase prob-ability, which makes comparative advantage pufferymore attractive. If there are other common knowledgeattributes that make the competitor more popular, thecompetitor will have a higher probability of mak-ing a sale, so again comparative advantage puffery ismore attractive. The degree of product differentiationcan also affect the persuasiveness of different pufferyforms. If the seller and competitor are relatively simi-lar in all aspects, then both cannot have high purchaseprobabilities, so attribute puffery may be more attrac-tive. This effect is strengthened if there are many com-peting products that are all ex ante similar, in which

28 By symmetry, P̄2 also rises to 3000% with comparative advantagepuffery, so both firms benefit.

case the purchase probabilities for the seller and forany given competitor will both be low, thereby favor-ing attribute puffery that focuses on the seller’s ownproduct.

Because the model follows the random coefficientsdiscrete choice framework used throughout market-ing and economics, standard numeric methods can beused to check the effects of puffery in any given sit-uation. The model can also be readily extended in anumber of directions, some of which we pursue in thefollowing section.

5. Extensions and Applications5.1. Buyer Privacy and PanderingWe have assumed that the seller (expert) does notknow the buyer’s (decision maker’s) exact attributepreferences �. Therefore, the trade-off from pushingone attribute at the expense of another is not exactfor each buyer—some buyers end up with a higherv1 and some buyers with a lower v1, which increasesvariation in v1 and allows puffery to be persuasive.If the � coefficients are known, then the seller has anincentive to pretend that whatever attribute the buyercares more about is the product’s strength. Anticipat-ing such pandering, the buyer discounts such claimsso that the seller receives a correspondingly smallergain from pushing that attribute. In equilibrium, thetrade-off must be exact so that v1 is the same for eachmessage, because otherwise, the seller would alwayschoose whatever message induced the higher v1; how-ever, even though the buyer gains some informationon the attributes, the buyer’s decision is completelyunaffected.

The following proposition formalizes this argumentfor our linear random coefficients model and extendsit to negative puffery and comparative advantagepuffery.

Proposition 4. Attribute puffery, negative puffery,and comparative advantage puffery influence buyer behav-ior if and only if the buyer’s preferences � are the buyer’sprivate information.

Because influential communication that benefitsboth the buyer and the seller is only possible if abuyer can conceal her relative preferences for differentattributes from the seller, this result offers insight intowhy buyers (and other decision makers) might valueprivacy about their product attribute preferences.29 Itis particularly relevant for online advertising due tothe increasing ability to customize and target adver-tisements based on consumer preferences. If a seller

29 A buyer may also want to conceal the overall strength of herpreferences because the seller prefers not to communicate attributeinformation to a buyer who is already likely to purchase theproduct.

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learns which buyers care more about which productattributes and can micro-target buyers accordinglywith different advertisements that emphasize differ-ent strengths of the product, then the credibility ofadvertisements is undermined to the detriment ofboth buyer and seller.30

We have analyzed the linear random coefficientsmodel that is widely used in marketing and eco-nomics. If buyer valuations are nonlinear in theattributes, then puffery can still affect the purchaseprobability even if buyer attribute preferences arecommon knowledge. If v1 is strictly convex (con-cave) in 4a11 a25 over the relevant range, then sinceP1 is monotonic in v1, P1 is strictly quasiconvex (qua-siconcave) in 4a11 a25; thus puffery affecting 4a11 a25always helps (hurts) the seller.31 For instance, if thetwo attributes are not substitutes as implied by thelinear model but are perfect complements, then P1is an increasing function of the concave functionmin8a11 a29. In this case, the seller prefers that thebuyer has average estimates of each attribute, so com-municating which attribute is better hurts the seller.In addition, if the two attributes are not bundled butare really two separate choices, e.g., different productsof the same firm, the buyer will choose the one withthe maximum expected value, so P1 is an increasingfunction of the convex function max8a11 a29. In thiscase, the seller always gains from communication thateffectively recommends which product is better, asseen in an example in §5.3 below.

As seen from this case of multiple goods soldby the same seller, the argument that targeting byan individual advertiser undermines communicationdoes not apply to an advertising platform such asGoogle Ads, which benefits from generating con-sumer interest in multiple different products. Theplatform’s choice to display an ad for a particularproduct can be seen as an implicit recommendationthat, based on the platform’s information on both theproduct and the consumer’s preferences, the prod-uct is likely to be a good match.32 This recommen-dation then increases the probability that the buyerclicks on an ad. Goldfarb and Tucker (2011) find thatonline advertisements are more effective when theycan be targeted using consumer information, which is

30 If the buyer does not know whether the seller knows her prefer-ences, then the adjustment for pandering will be incomplete, so theseller can still benefit, and if information is verifiable, then target-ing can still be persuasive even if buyers anticipate seller panderingas shown by Hoffman et al. (2013).31 This follows from direct application of Theorem 2 of Chakrabortyand Harbaugh (2010). See that paper for examples of quasiconcaveand quasiconvex expert preferences.32 The different sellers of advertised products are likely to alsohave private information that affects their bidding for ad positions(Athey and Ellison 2011, Chen and He 2011).

consistent with the platform using its information toeffectively recommend products.

5.2. Endogenous PricesWe have shown that pure cheap talk can influencebuyer behavior even when the seller’s price is fixed.The assumption of fixed prices fits many cases ofdirect salesperson communication to a buyer, it allowsthe results to be compared with experimental researchin marketing that uses fixed prices, and it also allowsthe model to be applied to other persuasion envi-ronments without explicit prices, such as managerialcommunication within a firm or political communica-tion. However, the assumption is less appropriate forother situations such as large advertising campaignswhere the firm might adjust prices based on the cam-paign’s effect on demand.

Incorporation of price changes is straightforwardfor the monopoly case. We assume that the seller firstcommunicates via puffery and then adjusts the pricebased on the equilibrium distribution of buyer valu-ations induced by the message. For the simplest caseof symmetric distributions of attribute qualities andpreferences, in a two-message equilibrium the distri-bution of demand is exactly the same from either mes-sage so the prices will be the same as well. With moremessages, or asymmetries, the prices will differ. How-ever, the model is essentially the same with the differ-ence that the seller’s payoffs need to incorporate thegains from adjusting the price.33

Proposition 5. If the seller first communicates viapuffery and then sets the price p1, attribute puffery,negative puffery, and comparative advantage puffery allincrease seller profits if the purchase probability P14v5 issufficiently small for all v.

The additional gain to the seller from adjusting theprice implies that, contrary to the fixed price case,the seller might still benefit from puffery when thepurchase probability is high. As is known from ver-ifiable information games, information that changesthe demand curve so as to lower quantity demandedat the current price can still increase profits if thesmaller group of buyers is willing to pay a sufficientlyhigher price (Lewis and Sappington 1994, Johnsonand Myatt 2006).

If we consider strategic price responses by multi-ple firms, the same approach can be applied in whichcheap talk is preplay communication before the pric-ing game. As long as there is a unique equilibrium ofthe pricing game, which changes continuously with

33 We assume that buyers do not interpret unexpected deviationsfrom the equilibrium price as information about product attributes.If unit costs increase with attribute quality, then there is the com-plication that higher prices can be a signal of quality as in the pricesignaling literature, e.g., Milgrom and Roberts (1986).

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the buyer attribute estimates, then the firm that iscommunicating will still have a payoff function thatis continuous in the estimates, so the same results onthe credibility of cheap talk can be applied. The maindifference is that price changes by the other firm canaffect the gains or losses from puffery. If the distribu-tions of attributes and coefficients are symmetric, thenpuffery provides information that effectively impliesgreater product differentiation, so we would expectpuffery to lead to higher prices that increase the gainsto the firm but decrease the gains to consumers. How-ever, in asymmetric environments, this may not be thecase. For instance, if comparative advantage pufferyleads the larger firm to lower its price, any gains tothe smaller firm from such puffery might be counter-acted by having to lower its price in response.34 Hencethe effect of puffery on price setting by multiple firmsis an open question.

In addition to adjusting their prices, other strategicresponses are likely to require further analysis. First,other firms might also engage in puffery. If firms onlyhave information about their own products, the sametools we use in this paper can be applied. If theyshare the same information, the game becomes oneof multisender cheap talk and a different approachis required.35 Second, the ability to communicateattribute information should change the incentives offirms to invest in product attributes and, particularly,might induce them to focus their investments on dif-ferent strengths. Johnson and Myatt (2006) considersuch product design issues when product informa-tion can be revealed to buyers, whereas Kalra andLi (2008) show how firms can signal quality throughspecialization. Finally, we also expect that the equilib-rium number of firms in the market will adjust alongwith changes in firm profitability.

5.3. Puffery vs. DisclosureWe have analyzed persuasion via puffery about “softinformation,” whereas most of the literature on sellercommunication has emphasized persuasion via dis-closure of verifiable “hard information.” When thereis no way to verify information, puffery is the onlymethod by which communication can occur. It mightseem that the seller is always better off when thereis hard evidence available on a product’s quality, butthis is not the case. With hard information, standard“unraveling” arguments imply that a seller will be

34 Anderson and Renault (2009) find that such a pattern can arise intheir model of comparative advertising with verifiable information,but the smaller firm still benefits overall.35 Such cheap talk has been analyzed with state-dependent pref-erences (Battaglini 2002) but not in our environment of state-independent preferences. A complication in some contexts such asonline reviews is that buyers might be unsure which sender is thesource of a message (Mayzlin 2006).

compelled in equilibrium to reveal all information,even if it is quite unfavorable (e.g., Milgrom 1981).36

Therefore, even if a seller benefits on average fromrevealing information, some seller types will winwhile others lose. In contrast, when puffery bene-fits the seller, it benefits all types of sellers regard-less of whether their private information is favorable,so some sellers who would be hurt by disclosureof hard information are helped by puffery aboutsoft information. For instance, in the example ofFigure 2, panel (a), types below the isoprobabilitycurve through a1 = 41/211/25, which includes all types4�111 �125 < 41/211/25, are hurt by full disclosure whileevery type benefits from puffery. Note that buyersbenefit on average from puffery but sometimes loseand always benefit more from full disclosure.

Perhaps more surprising, the coarse partition of theseller’s information revealed by puffery is sometimespreferable on average for the firm both to have noinformation disclosure and to have full informationdisclosure. As an example, consider a version of themodel where a single firm sells two products; e.g., arestaurant has two dishes of which the customer canchoose only one. The utility from dish j of the firm(i = 1) is �j�1j − p1j + �1j , where �j = 10 and p1j = 5.Assuming that �11 = �12 so that the error terms areperfectly correlated and that they follow the Gumbeldistribution, the model is a nested logit, and the pur-chase probability is P̄14a111 a125 = e10 max8a111 a129−5/41 +

e10 max8a111 a129−55. Notice that we are assuming fixedcoefficients so P̄1 ≡ P1. Since the max function is con-vex, this is no longer a linear model, and there isan incentive from this convexity to disclose informa-tion even without random coefficients. In particular,because increasing functions of convex functions arequasiconvex, P̄1 is quasiconvex in 4a111 a125 even in theregion where P̄1 is concave in v1, so cheap talk alwaysbenefits the seller.

Assuming �11 and �12 are i.i.d. uniform on 60117 asbefore, without any communication, a11 = a12 = 1/2,so the customer randomly picks a dish, and the pur-chase probability is P̄141/211/25 = e0/41 + e05 = 1/2.If the restaurant pushes its best dish, which it cando credibly by the same arguments as before, thenmax8a111a129 = 2/3, and the purchase probability isP̄142/311/35 = P̄141/312/35 = e5/3/41 + e5/35 = 00841 forall �. With full disclosure of the qualities of each dish,the ex ante expected probability of making a sale is∫ 1

0

∫ 10 e10 max8�111 �129−5/41+e10 max8�111 �129−55 d�11d�12 = 00719,

so the seller is worse off in expectation from full dis-closure (when it is possible) than from partial disclo-sure via puffery. Because puffery of the better dish

36 Milgrom (1981) considers one-dimensional quality. Koessler andRenault (2012) analyze conditions under which firms fully revealproduct match information.

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has already raised the purchase probability up intothe region where P1 is concave in a11 and a12, furtherdisclosure of information would hurt, on average.

This example and the quasiconvexity result provethe following proposition.

Proposition 6. Suppose, contrary to the linear model,that P̄1 is strictly quasiconvex in 4a111 a125 for all P̄1. Thenpartial disclosure via puffery is always persuasive evenwhen P̄1 is concave in v1 and can be more persuasive thanfull disclosure.

This result is related to the literature on opti-mal disclosure policies. Kamenica and Gentzkow(2011) show that partial disclosure can sometimesoutperform full disclosure on average when thesender can precommit to the disclosure policy beforeobtaining any information. In our multidimensionalenvironment, partial disclosure can also do betterthan full disclosure. Moreover, communication viacheap talk does not require precommitment to par-tial disclosure—to the contrary, it is always credibleto reveal some information but not generally credibleto reveal all information.

5.4. Additional AttributesWe have focused on the case where the seller only hasprivate information on two attributes of its productand possibly the corresponding attributes of a com-petitor’s product. The model still applies when thereare more product attributes about which the sellerhas private information. In the symmetric case wherethe distributions of the coefficients on each attributeare identical, similar results as from Chakraborty andHarbaugh (2007) can be applied to show that a com-plete ranking of the different attribute values is cred-ible. For instance, a buyer might infer the rankingfrom the relative amount of emphasis that the sellergives to multiple different attributes. As the numberof attributes increases, such a rank revealing equilib-rium reveals more and more information and in thelimit is equivalent to full disclosure.

If the distributions are too asymmetric to apply theabove result, the case of more than two attributes canbe analyzed in essentially the same way as the two-attribute case. It is still possible to puff up one of theattributes at the expense of any of the other attributes,and in addition, one can consider any combinationof attributes as itself an attribute known to the seller.So it becomes possible to highlight one attribute orone group of attributes as better than the averageof the other attributes. Analysis of negative pufferyand comparative advantage puffery can be similarlyextended.

5.5. Message Space ConstraintsWe find that for unverifiable information, it is oftenonly credible and persuasive to push one attribute.Separate from this credibility constraint, there might

also be constraints on the message space. For instance,there might be a “bandwidth” constraint that lim-its the seller’s ability to provide information—theremight be sufficient time to discuss only one attributewith a customer or sufficient space to highlight onlyone attribute in an advertisement. In a verifiable mes-sage game, such constraints can have a large effect onequilibrium communication (Mayzlin and Shin 2011,Hoffman et al. 2013).

In a simple two-message equilibrium, the band-width constraint can be seen as forcing the seller tofocus on only one attribute, but the constraint is notbinding because in equilibrium the seller does thatanyway. In practice, the constraint might facilitatecommunication by highlighting the trade-off that theseller faces between pushing one attribute or another.A bandwidth constraint might also facilitate commu-nication when there is a multimessage equilibrium inwhich different messages push one attribute over theother to greater or lesser degrees. The amount of timeor space that is devoted to one attribute over anothermight naturally be interpreted by buyers as indicatingthe relative strengths of the attributes.

Given the role that message constraints might playin highlighting the comparative nature of equilibriumcommunication, it might be desirable to restrict themessage space in order to to explicitly emphasizecomparative messages. For instance, a problem withproduct rating websites is fake reviews that promotea firm’s product or denigrate a competitor’s product(Mayzlin et al. 2014). Although these websites some-times allow users to rate the product on differentattributes, e.g., hotel cleanliness and hotel comfort,the format does not encourage comparative cheaptalk. If instead of rating a product from 1 to 5 oneach attribute, suppose the user were forced to rankthe relative strengths and weaknesses of the prod-uct, e.g., allocate only one “5,” one “4,” one “3,”etc. to the different attributes. Because communica-tion would then be comparative, even “fake” reviewsby the seller could credibly emphasize the product’srelative strengths.

5.6. Extreme ExaggerationsPuffery sometimes takes the form of extreme exagger-ations, such as Panasonic’s claim that the 3DO wasthe “most advanced home gaming system in the uni-verse.” A standard explanation for extreme claims isthat they gain attention for their shock or amusementvalue (e.g., Hoffman 2006). Another explanation isthat they are “metamessages” that make the pufferynature of the statement more apparent to buyers andto the courts (Parmentier 1994). Our approach showsthat in addition to gaining attention, extreme claimsby a firm can also provide implicit comparative infor-mation on attributes of a product—Anacin’s claim

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of “fast, fast, fast relief” does not mention whetherthe relief is long-lasting. Similarly, such claims mayprovide implicit comparative information on differ-ent products that a firm sells—the Dunkin’ Donutsslogan “best coffee in America” does not mentiondoughnuts.

Extreme messages appear to be more common inadvertising than in direct salesperson communication.Presumably, a salesperson already has the buyer’sattention, so the need to grab attention with extremeclaims is less. And a salesperson engaged in verbalcommunication has less concern for legal scrutiny, sothe need to establish a puffery defense is also weaker.Our model does not analyze these factors but adds tothe existing explanations in showing that, at least insome cases, extreme claims can also provide compar-ative information.

6. ConclusionPrevious research has assumed that puffery cannot becredible and has argued that puffery either is harmfulbecause it misleads credulous buyers or is harmlessbecause it is ignored by skeptical buyers. We sup-pose that buyers are neither completely credulous norcompletely skeptical but that they interpret puffery asproviding implicit comparative information on prod-uct attributes. Puffery can then be credible and canalso be persuasive in that it makes buyers more likelyto purchase the product. Consistent with this per-spective on how buyers interpret puffery, studies findthat many buyers do not just raise their opinion ofproduct attributes that are featured in an advertise-ment but also lower their opinion of attributes thatare not featured. Further research is needed to deter-mine whether such adjustments are sufficiently largeand frequent that puffery informs more buyers thanit misleads.

Following the definition of puffery as being aboutsubjective soft information, we model puffery as acheap talk game. The implications are very differ-ent from seller communication based on persuasiongames with objective hard information. As shownearly on in the literature on persuasion games, if sell-ers are not allowed to lie about objective information,then in equilibrium they should voluntarily revealinformation to consumers. Therefore, restrictions onthe ability to exaggerate play a central role in reduc-ing information asymmetries about hard information.In our model with subjective information where state-ments cannot be verified or falsified, we show thatallowing sellers some freedom to make unverifiableclaims can still help reduce information asymmetries.Hence, the distinction between cheap talk and per-suasion games is consistent with the legal emphasison allowing puffery for subjective information butrestricting it for objective information.

Much of the policy debate over seller puffery hasfocused on how exactly to draw the line betweensubjective statements that sellers can make withoutproof and objective statements that require proof.When there is confusion over whether a statementis subjective or objective, even sophisticated buyersmight believe puffery without adjusting for sellerincentives.37 Further research on how consumersreact to puffery, and how heterogeneity in consumerresponses affects equilibrium communication, is nec-essary for a more complete understanding of the roleof puffery in seller communication. Because we fol-low a standard discrete choice model that is widelyused in the empirical analysis of consumer choice,our theoretical predictions can be readily tested usingexperimental and field data.

AcknowledgmentsThe authors thank the referees, the editor Preyas Desai,Shanker Krishnan, Dina Mayzlin, André de Palma, JeremySandford, Jiwoong Shin, K. Sudhir, James Taylor, MatthijsWildenbeest, and seminar and conference participants atthe University of Missouri Economics Department, the YaleSchool of Management Marketing Department, the IndianSchool of Business, the 2011 International Industrial Orga-nization Conference at Boston University, the Fourth Con-ference on the Economics of Advertising and Marketing atthe Higher School of Economics in Moscow, and the 2012INFORMS Marketing Science Conference.

Appendix

Proof of Shape Properties. Generalizing from the logit,the probability that product i = 11 0 0 0 1n will be purchased is

Pi4v5 = Pr6vi + �i > max8v−i + �−i97

=

∫ �

−�

f 4x5∏

k 6=i

F 4vi − vk + x5dx0 (8)

Then, for i 6= j ,

¡Pi

¡vj

= −

∫ �

−�

f 4vi − vj + x5f 4x5∏

k 6=i1 j

F 4vi − vk + x5dx

≡ −h4vi − vj1 8vi − vk9k 6=i1 j5 < 0 (9)

so that Pi is decreasing in vj . Prékopa (1973) shows that if afunction g4y1x5 is log-concave in 4y1x5, then

∫

g4y1x5dx islog-concave in y. Applying this result to the above function,since f is log-concave and hence so is F , and since prod-ucts of log-concave functions are log-concave, the productf 4vi−vj +x5

∏

k 6=i1 j f 4x5F 4vi−vk+x5 is log-concave in 4vj1x5.Hence, h is log-concave in vj and so unimodal in vj . If themode is infinite, then Pi is either a strictly decreasing glob-ally concave or a strictly decreasing globally convex func-tion of vj—in either case a contradiction with the fact that

37 Given the difficulty of verifying information, the opposite pat-tern may also arise—buyers may be so skeptical of seller claimsas to treat even “objective” information as puffery and adjustaccordingly.

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Pi is a probability and so bounded in 60117. We concludethat h has a finite mode v̄j in vj (that possibly depends onv−j ) so that Pi is strictly concave in vj for vj < v̄j and strictlyconvex in vj for vj > v̄j . This proves part (ii). By use of thisresult on the shape of Pi in vj , we can now use this to deter-mine the shape of Pi in vi (or, equivalently, Pj in vj ). SincePj = 1 −

∑

j 6=i Pi, we conclude that Pj is an increasing func-tion of vj , which is strictly convex in vj for vj sufficientlysmall and strictly convex in vj for vj sufficiently large. Thisproves part (i).

For part (iii), note that each term f 4x5∏

k 6=i F 4vi − vk + x5in (8) is log-concave in 4v1x5. Therefore, by the same resultof Prékopa (1973) used above, the probability Pi4v5 is log-concave in v and hence quasiconcave. �

Proof of Proposition 1. Suppose that for all possiblev1 the purchase probability is sufficiently low that P14v5 isconvex in v1 as established in shape property (i). In equilib-rium, from (4), the expected purchase probability P̄14a

k11 a25

is the same for any message mk. Consequently, the payofffrom attribute puffery is

P̄14ak11 a25

=

∫

�P14�1a

k11 +�2a

k121�1a21 +�2a225 dG4�5

=

K∑

k=1

Pr6mk7∫

�P14�1a

k11 +�2a

k121�1a21 +�2a225 dG4�5

=

∫

�

K∑

k=1

Pr6mk7P14�1ak11 +�2a

k121�1a21 +�2a225 dG4�5

>∫

�P1

( K∑

k=1

Pr6mk74�1ak11 +�2a

k1251�1a21 +�2a22

)

dG4�5

=

∫

�P14�1a11 +�2a121�1a21 +�2a225 dG4�5= P̄14a11 a251 (10)

where P̄14a5 is the expected purchase probability withoutcommunication. For the inequality, we use the strict con-vexity of P1, Jensen’s inequality, and the full dimensionalityassumption for the random coefficients �. Even though theexpected purchase probability is equal across messages, asrequired in equilibrium, the full dimensionality assumptionguarantees that the arguments �ak1 are not identical (exceptfor a zero measure of �) whenever the estimates ak1 are dif-ferent across messages. The opposite inequality obtains, ifall possible v lie in the region where the purchase probabil-ity is sufficiently high, that P1 is strictly concave. �

Proof of Proposition 2. From shape property (ii), P1 isa decreasing function of v2 that is strictly concave for v2

sufficiently low and strictly convex otherwise. The resultthen follows from arguments analogous to the proof ofProposition 1. �

Proof of Proposition 3. Recall that we restrict theequilibrium to satisfy E6�1a

1i1 + �2a

1i27 = E6�1a

2i1 + �2a

2i27 or

E6�174a1i1 − a2

i15 = E6�274a2i2 − a1

i25 = z 4> 0, w.l.o.g.). SincePr6m17a1

ij +Pr6m27a2ij = aij by the law of iterated expectations,

we may write

v1i 4�5 ≡ �1a

1i1 +�2a

1i2 − pi

= �ai +�14a1i1 − ai15+�24a

1i2 − ai25− pi

= �ai +

[

�1

E6�17−

�2

E6�25

]

41 − Pr6m175z− pi1 (11)

and similarly,

v2i 4�5≡ �ai −

[

�1

E6�17−

�2

E6�27

]

41 − Pr6m275z− pi0 (12)

For any given � and real number t, and each i = 112,define vi4t1�5= �ai + 4�1/4E6�175−�2/4E6�2555t − pi. Noticethat at t = −41 − Pr6m275z, vi4t1�5 = v2

i 4�51 while at t =

41 − Pr6m175z, vi4t1�5 = v1i 4�5. Consider now the purchase

probability of product 1 given � as a function of t:

P14t1�5 =

∫

f 4x5F 4v14t1�5+ x5F 4v14t1�5− v24t1�5+ x5dx

=

∫

f 4x5F

(

�ai −

[

�1

E6�17−

�2

E6�27

]

t − p1 + x

)

· F 4�4a1 − a25− 4p1 − p25+ x5dx0 (13)

So

¡P14t1�5

¡t= −

[

�1

E6�17−

�2

E6�27

]

h

(

�a1 −

[

�1

E6�17−

�2

E6�27

]

t

− p11�4a1 − a25− 4p1 − p25

)

1 (14)

where the function h has been defined and its propertiesdescribed in the shape properties proof. By use of theseproperties, we conclude that P1 is strictly convex in t for asufficiently low purchase probability in which case, usingarguments identical to those in the proof of Proposition 1,we conclude that the equilibrium purchase probability isgreater than that with no communication. Similar argu-ments complete the proof for when P1 is strictly concavein t. �

Proof of Proposition 4. Propositions 1–3 have alreadyshown sufficiency. For necessity, suppose instead the �’s arecommon knowledge. For attribute puffery, the equilibriumcondition (4) simplifies to

P14�1ak11 +�2a

k121�1a21 +�2a225

= P14�1ak′

11 +�2ak′

121�1a21 +�2a2251 (15)

implying �1ak11 + �2a

k12 = �1a

k′

11 + �2ak′

12 for all k, k′. Thisrestriction, combined with the law of iterated expectationsidentity,

∑

k Pr6mk74�1ak11 +�2a

k125= �1a11 +�2a12, implies that

�1ak11 + �2a

k12 = �1a11 + �2a12 for all k. Thus, the purchase

probability with any cheap talk message is the same as theprior probability:

P14�1ak11 +�2a

k121�1a21 +�2a225

= P14�1a11 +�2a121�1a21 +�2a2250 (16)

For negative puffery, (5) simplifies to

P14�1a11 +�2a121�1ak21 +�2a

k225

= P14�1a11 +�2a121�1ak′

21 +�2ak′

2251 (17)

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Chakraborty and Harbaugh: Persuasive PufferyMarketing Science 33(3), pp. 382–400, © 2014 INFORMS 399

which combined with the identity∑

k Pr6mk74�1ak11 +

�2ak125= �1a11 +�2a12 again implies that P1 must be the same

as the prior for all messages. For comparative advantagepuffery, the equilibrium condition (6) simplifies to

P14�1a111 +�2a

1121�1a

121 +�2a

1225

= P14�1a211 +�2a

2121�1a

221 +�2a

22250 (18)

The restrictions (7) simplify to

�1a1i1 +�2a

1i2 = �1a

2i1 +�2a

2i21 (19)

which combined with the identities

Pr6m174�1a1i1 +�2a

1i25+ Pr6m274�1a

2i1 +�2a

2i25

= �1ai1 +�2ai2 (20)

imply that �1a1i1 +�2a

1i2 = �1ai1 +�2ai2. Then

P14�1ak11 +�2a

k121�1a

k21 +�2a

k225

= P14�1a11 +�2a121�1a21 +�2a225 (21)

for k = 112, so again P1 is the same as the prior for allmessages. �

Proof of Proposition 5. Let P̄14p11 a5 be the expectedpurchase probability given price p1 and estimates a. Letp∗

14a5 be the maximand of

ç14p11 a5= P̄14p11 a54p1 − c151 (22)

where c1 is constant unit costs, and let ç∗14a5 = P̄14p

∗14a51 a5

4p∗14a5 − c15 be maximized profits. We wish to show that

ç∗14a5 is strictly convex in a over subsets of the four-

dimensional � space as restricted by puffery.Let � ∈ 40115 and a1a′ be any two distinct estimates sat-

isfying the attribute puffery restriction in which a2 is fixed.As shown in Proposition 1, for P14v5, sufficiently small P̄1 isconvex in a under this restriction. Then

�ç∗

14a5+41−�5ç∗

14a′5

=�P̄14p∗

14a51a54p∗

14a5−c15+41−�5P̄14p∗

14a′51a′54p∗

14a′5−c15

≥�P̄14p∗

14�a+41−�5a′51a54p∗

14�a+41−�5a′5−c15

+41−�5P̄14p∗

14�a+41−�5a′51a′54p∗

14�a+41−�5a′5−c15

>P̄16p∗

14�a+41−�5a′51�a+41−�5a′74p∗

14�a+41−�5a′5−c15

=ç∗

14�a+41−�5a′51 (23)

where the first inequality follows from the definition of p∗1

(note that this inequality is strict if p∗1 is unique) and the

second inequality follows from the strict convexity of P̄1.Identical arguments apply for the negative puffery

restriction that a1 is fixed and for the comparative advan-tage puffery restriction that variation in 4a11 a25 is restrictedby (7). �

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