running head: structure in negotiation and the search for

Structure Matters in Negotiation 1

Running Head: STRUCTURE IN NEGOTIATION

Structure Matters in Negotiation Offers

and the Search for Agreement

Michael J. Prietula Goizueta Business School

Emory University Altanta, GA 30322-2710 [email protected]

Laurie R. Weingart

David A. Tepper School of Business Carnegie Mellon University

Pittsburgh, PA 15213 [email protected]

12/1/2006 Acknowledgements. We thank Jeanne Brett, Don Moore, Sally Blount-Lyon, Elizabeth Mannix, Kevin Rockmann and Francesca Gino for comments on versions of this manuscript. This project was partially funded by the Dean’s Research Fund, Tepper School of Business. This paper was presented at the Academy of Management Meetings, Honolulu, Hawaii, August, 2005


Abstract

We present a theoretical framework and associated propositions for interpreting a key

component of negotiation dynamics – offer exchange. We view negotiation as

collaborative search of a complex offer space, whereby negotiators simplify and

coordinate search via information contained in offer exchanges, isolating sub-regions of

the offer space for potential solutions. We suggest that early search is influenced more by

value of offers to the negotiators, but later is influenced more by structure of offers in the

exchange, whereby there appears to be a heuristic for selecting offers that are structurally

similar to prior offers. As both negotiators tend to engage this heuristic, the result is a

joint-focusing on subsets of the offer space and a bias toward structural proximity of

offers and agreements.


Structure Matters in Negotiation Offers

and the Search for Agreement

Negotiation is a remarkable and recurring element of decision making that is largely ill-

defined, underspecified, and emergent. Furthermore, as Howard Raiffa commented on the first

sentence of his famous volume, “There is no shortage of disputes” (Raiffa, 1982, p. 7).

Negotiation opportunities arise when we are dealing with our children, our students, our friends,

our family and so on virtually every day. Negotiation, in one form or another, is ubiquitous.

Defined as a dynamic interaction process in which two or more parties attempt to find

solutions that satisfy their conflicting interests (Lax & Sebenius, 1986; Raiffa, 1982; Walton &

McKersie, 1965), researchers are just beginning to understand the nature of those dynamics. In

route to an agreement, negotiators are known to communicate their preferences and priorities via

direct and indirect information exchange (e.g., Thompson, 1991; Weingart, Hyder, Prietula, &

Weingart, 1996). We suggest that offers uniquely emerge from that communicative milieu as a

critical indicator of the negotiators’ conceptualization of, and search for, a potentially viable

agreement. Consequently, offers provide information that allows negotiators to update and

improve their understanding of the set of viable alternatives and the sequence of offers reveals

how this understanding develops over time.

While much is known about how negotiators use offers in single issue negotiations, such

as concession patterns and rates in bilateral monopoly type tasks (e.g., Siegel & Fouraker, 1960),

less is known about the role of offers in more complex negotiations that involve multiple issues

such that win-win solutions are possible. Toward that end, we develop a descriptive, problem

solving model of how two negotiators (within a dyad) use offers to coordinate search for

mutually acceptable agreements in scorable multi-issue negotiations with integrative potential.


Although stylized, these types of negotiation tasks have been (and are) used in many laboratory-

based studies (e.g., Pruitt & Lewis, 1975; Bazerman, Magliozzi, & Neale, 1985; Thompson,

1990; also see Tripp & Sondak, 1992) and serve as a reasonable starting context for exploring a

theory of negotiation. Note that we are not developing a theory of problem solving (for that is

sufficiently established for our purposes), but a framework describing how to apply a theory of

how problem solvers address a particular problem within the context of presumed psychological

mechanisms. That is, we specify salient characteristics of a negotiation task that influence

individual choice (Newell & Simon, 1972) and suggest how the task characteristics influence

joint problem solving.

We see negotiation as a joint problem solving activity, where two individuals need to

collaborate to discover a solution (as neither individual generally has full information) that is

mutually beneficial (Carroll, Bazerman, & Maury, 1988; Prietula & Weingart, 1994). We

employ the robust “standard model” of information processing psychology as it provides the

theoretical foundation for defining problem solving as search through a problem space (or set) of

possible alternatives (e.g., Klahr & Kotovsky, 1989; Newell & Simon, 1972; Simon, 1978;

Simon & Kaplan, 1989). According to information processing psychology, problems are

characterized by individuals creating problem spaces – dynamic internal (cognitive)

representations of the particular task environment (the problem as presented to the problem

solver) – which include goals to be achieved, a model of the current state of the task, the

allowable actions that are presumed to be possible (as problem solving steps), information

available, and perhaps other elements of the task environment as perceived by the problem solver

(Dunbar, 1998; Newell & Simon ,1972). Problem solving is seen as an active search process for

potential solutions within that internal representation (Hayes, 1989; Newell & Simon, 1972).


Furthermore, when problem spaces get sufficiently large or complex such that a problem solver

is unable to search (consider) all of the alternatives, methods must be engaged to reduce the

search effort, as humans are indeed boundedly rational, but still function to address the task at

hand (Gigerenzer & Selton, 2001; Groner, Groner & Bischof, 1983; Simon 1956, 1982).

Conceptually, our framework is about search. In negotiation, the negotiator’s cognitive

representation of the task environment necessarily includes the issues and their preferences, the

goals and constraints for the negotiation (e.g., “maximize your own negotiated outcome,”

“solutions must included agreements on all issues”), and the other negotiator and his/her actions;

therefore, each problem solver’s representation and search both influences and is influenced by

the dynamics of interaction. Offers afford a trace of the negotiation process, but are not the

whole of the negotiation process as they are used in combination with other negotiation

behaviors (e.g., direct information exchange). Instead, the exchange of offers and counter-offers

is seen as critical communication acts that reflect coordinated action by individuals working

toward their goals (Baker, 1995; Clark, 1996).

Our framework focuses on the underlying search space that is the context of this

communication, called the offer space, which is necessarily jointly-searched by the negotiators.

Yet, even in a simple 3-issue negotiation task for example, the total number of possible solutions

that could be proposed can be quite large – much larger than the number of offers actually made

during a negotiation (see Mumpower, 1991). Given the apparent complexity of the task (as

defined by the number of potential solutions in the offer space), this presents three fundamental

questions: How do negotiators jointly search a large offer space for potential offers? How do

negotiators select the offers they propose? How do these offers converge toward an agreement?


Answers to these questions would improve our understanding of negotiation in at least

two ways. First, answers would provide additional insight into the negotiation process,

complementing extant knowledge regarding integrative and distributive tactical behavior. Aside

from the prior work on heuristic trial and error/systematic concession making, few have

considered the role of the content of the offers in the multi-issue negotiation process more

generally (see Putnam & Holmer, 1992 for a qualitative analysis of issue development).

Research on negotiation process using tasks with integrative potential has largely focused on the

use of integrative and distributive tactical behavior – such as information exchange, offers,

argumentation, threats – in terms of their frequency, sequences, and phases (Weingart &

Olekalns, 2004). That research differentiates between single versus multi-issue offers and

considers how often and when they, and other tactical behavior, occur. Results reflect the ways

negotiators tactically respond to one another during the course of the negotiation (e.g., are offers

reciprocated?) and whether negotiations pass through predictable phases (e.g., when do offers

occur?). For the most part, within this work there is an (often tacit) assumption that negotiators

interpret offers strictly in terms of their preferences; that is, potential offers and counter-offers

are searched and considered primarily in terms of their (collective) value to the negotiator. Our

framework complements this work by examining the structure of offers (as defined by the

particular options of the constituent issues), as well as the value of offers (as defined by the total

value to the negotiator expects to experience associated with the preferences), and how

negotiators alter the structure of offers over time in response to prior offers in their search for

mutually acceptable agreements. The structure and value of offers provide information about the

potential solutions negotiators are currently considering and how information is incorporated into

subsequent offers during search. We argue that negotiators are more likely to search based on


the structure of offers as long as the offers meet minimum value requirements. This structure-

based heuristic provides a way to predict where subsequent offers might occur, as it biases the

generation of offers and, consequently, the regions of offer space that are searched.

Second, answers to these questions would also improve our ability to predict where

agreements might occur in terms of more restricted regions within the set of possible outcomes.

As offers and counter-offers serve to limit the portion of the offer space being searched, this also

constrains how negotiators think about the set of possible solutions. We suggest that final

agreements are more likely to occur within or nearby these more constrained sets. This approach

can supplement and hopefully improve upon current approaches to predicting agreements which

tend to rely on initiating conditions (e.g., social motives of negotiators, relationships between

negotiators) and tactical behavior (e.g., information exchange). Under this framework, it is

possible to make predictions of regional proximity. As we shall see, an analysis of these offer-

counteroffer exchanges provides insight into the problem solving processes involved and clues to

the answers (Ericsson & Simon, 1993, 1998).

We suggest that negotiators engage in two basic types of search when making offers and

counter-offers. First, and often initially, negotiators engage in a speculative, broad form of joint

search in which they attempt to more precisely define, refine, and align their understanding to

establish a “common ground” (Clark & Marshall, 1981; Pickering & Garrod, 2004). Second, this

search leads to a specific discussion and an (perhaps tenuous) agreement on a particular issue.

Once this becomes the focus of attention, this anchors and constrains the set of offers that are

considered, resulting in a distinctly more coordinated search activity. When the two negotiators

agree on even one issue, the size of the search space is substantially reduced, coordinated

examination of smaller regions can effectively ensue, and potential agreements are more likely.


The paper is organized as follows. We first characterize the offer space (i.e., the set of all

possible offers) in terms of our typical negotiation research task (three issues with integrative

potential). Here we introduce three concepts that relate to defining the equivalence of offers:

value equivalence, mutual value equivalence, and structural similarity. We then briefly consider

the primary literature in negotiation that has relied on the examination of offer patterns, for it is

toward an explanation of these types of patterns of behavior that our work is directed, especially

systematic concession making (Siegel & Fouraker, 1960) and the dance of packages (Raiffa,

2002). Next we focus on the dynamics of search, where we discuss the two search patterns,

value exploration and offer refinement. Within this discussion we identify the central role of the

structure of offers in reducing task complexity, explaining search, and identifying where final

agreements might occur.

As our discussion unfolds, we will assert specific theoretical propositions suggested by

the framework. We also use illustrative data from this task to demonstrate how we code and

interpret these concepts. In the concluding section, we build on these concepts and show how

they can serve as heuristics for offer generation as well as the foundation for description and

analysis of negotiation dynamics. We offer a summary of the key terms of our framework in

Tables 1 and 2.

--------------------------------------- Insert Tables 1 & 2 about here --------------------------------------

Characterizing the Offer Space

We characterize the offer (i.e., solution) space for a typical negotiation task of the type

used in many laboratory studies – a three-issue (9 option levels per issue), role-playing task

conducted between two individuals negotiating typing services (first described in Weingart,


Thompson, Bazerman, & Carroll, 1990). This characterization will provide the foundation for

our theory development. Whereas our framework can be applied to more complex negotiations,

we restrict our discussion to this simpler negotiation problem for ease of presentation. For this

problem, there are 729 possible (and discrete) three-issue (i.e., comprehensive) offers, as each of

the three issues has 9 possible choices of options (Table 3 show the specific preference schedules

for each negotiator). It is assumed (and is often imposed as a condition of the experiment) that a

negotiator does not accept final agreements valued as a loss in comparison to their best

alternative to a negotiated agreement (BATNA, see Fisher & Ury, 1981), which can be to

maintain the status quo (worth 0 preference points). When substandard potential final

agreements are removed from the set for both parties, the remaining offers are sometimes called

the bargaining zone or the zone of possible agreement (Raiffa, 1982). This zone represents the

set of plausible solutions for the negotiation as any solution in this set represents a gain over a

failed negotiation or over the value of negotiators’ BATNA. Solutions within this set essentially

reflect the negotiation alternatives when the problem solvers are playing properly (as the

outcomes exceed their bottom lines), but not necessarily playing effectively (as the outcomes

might not be optimal). In this task, there are 521 such possible solutions remaining when

negatively values (total points < 0) are removed from the set.

---------------------- Insert Table 3 here ----------------------

Negotiation offer spaces are often displayed as a two-dimensional, joint-sum plot where

possible offers are mapped into the respective offer values of the two negotiators (Sebenius,

1992). The axes represent the total value of an offer (summed utilities over issue levels) for each

negotiator.1 From these plots, measures of performance, such as joint outcome, Pareto efficiency,

and an integrativeness quotient, have been discussed (e.g., Clyman, 1995; Tripp & Sondak,


1992). Visually, this representation suggests obvious and intuitive concepts of value distance

(between offers, or from the Pareto frontier). This type of joint-sum plot for our example is

shown in Fig. 1.

------------------------- Insert Fig. 1 here

-------------------------

From this plot, it can be seen that there are several possible offers of equivalent value to a

negotiator, given a value on the negotiator’s axis. To more formally define this for our three-

issue (i, j, k) problem, we first define the concept of structural difference and structural

equivalence.

Structural Difference (Equivalence). Assume two offers, O1(i1, j1, k1) and O2(i2, j2, k2),

where i, j, and k refer to the option level of the offer (not the value to the negotiator).

Structural difference refers to option levels that are not commonly held between the

offers (e.g., i1 ≠ i2 or j1 ≠ j2 or k1 ≠ k2) and structural equivalence refers to option levels

that are common to issues in both offers (e.g., i1 = i2 or j1 = j2 or k1 = k2).

The option level refers to the semantic choice of a particular issue, such as “3 days” for Speed, or

“Max 3” errors for Editing. Thus, for two offers to be structurally different, at least one of the

option levels has to be different. Now we can formally define how two offers that are structurally

different, can have the same (total preference) value to a negotiator:

Value Equivalence. Given two offers, O1(i1, j1, k1) and O2(i2, j2, k2), that are structurally

different, these offers are said to have value equivalence if Value[O1(i1, j1, k1)] =

Value[O2(i2, j2, k2)]. The set of equivalently valued offers for a negotiator is called the

value equivalent set.


Value equivalence, in other contexts sometimes called strategic equivalence (Keeney &

Raiffa, 1993), states that two (or more) offers that differ on at least one issue are actually equal in

total (preference) value to the particular negotiator, thus the negotiator should be indifferent to

any offer in this set. Using Fig. 1, we highlight the points (as open circles) representing a value

equivalence set of 2600 for the Buyer and a value equivalence set of 3800 for the Seller. If each

of these values represent acceptable individual outcomes to the negotiators, this plot suggests

that an agreement may be likely as there is actually one point in common (the triangle). To

discover this outcome, the negotiators each need to consider three or four optional offers within

their respective value equivalence sets.

However, in actuality Fig. 1 only depicts 31.6% of the possible solutions for the entire

offer space. This is because the plotted offers reflect the 165 uniquely-valued offers, but not the

521 uniquely-configured offers. A uniquely-configured offer means that two offers differ in their

structure (i.e., the particular configuration of options selected for each issue), but have the same

value. In fact, most of the offer solutions (as points) in Fig. 1 represent multiple offer

configurations yielding the same particular value (to each negotiator); that is, most of the

“points” plotted in the figure actually represent sets of offers. We refer to these sets as mutual

value-equivalence sets, because each of the offers within a set has the same (mutual) value to the

pair of negotiators. This is shown in Fig. 2.

Mutual Value-Equivalence. Given two offers, O1(i1, j1, k1) and O2(i2, j2, k2), that are

structurally different, these offers are said to have mutual value-equivalence if

Value[O1(i1, j1, k1)] = Value [O2(i2, j2, k2)] holds for both negotiators. A given set of

offers where mutual value-equivalence holds is called a mutual value-equivalence set.


From an omniscient observer’s perspective, mutual value-equivalence sets produce a

“third-dimension of density” to the joint-sum plot that indicates the number of differently

configured, but equally-valued solutions for a particular joint-sum point (for Fig. 2 this ranges

from 1 to 5). Consequently, the space yields a more complex landscape of offers than is typically

depicted and further suggests the necessity for (and existence of) negotiator mechanisms to

systematically reduce the complexity of search of that landscape. In fact, for the previously

discussed example in Fig. 1, the total set of different offers for the Seller to consider that

generate a value of 3800 is eight, while the Buyer must consider sixteen at a value of 2600. This

is an important, but rarely identified, feature of the offer space.

------------------------- Insert Fig. 2 here

-------------------------

From an individual negotiator’s perspective, value equivalence affords a flexibility of

indifference to proposed offers that differ in structure. However, negotiators are (generally)

neither privy to nor capable of calculating the entirety of this landscape, as humans are

boundedly rational (Gigerenzer & Selton, 2001; Groner et al., 1983; Simon 1956, 1982).

Therefore, they must reduce the complexity of the search of this space both to address their

individual preferences and to accommodate the joint-goal of reaching an agreement.

Proposition 1: Negotiators will reduce the complexity of the search by considering only a

subset of potential offers.

Two different and fundamental methods of search reduction are actually afforded by this

negotiation offer space: constraints imposed by value and constraints imposed by structure. For

the former, regions of the space that are similar in value are searched (and proposed) as offers.

For the latter, regions of the space that are similar in terms of structure are searched (and


proposed) as offers. Evidence of how search is actually conducted and constrained is suggested

through the exchange of offers.

Exchanging Offers

Offer/counter-offer pairs are the primary units of analysis for our framework. We

adopted this approach based on three theoretical positions. First, the offer/counter-offer sequence

is consistent with the “presentation-acceptance” model of discourse contribution in that people

integrate others’ communications into their own (Clark & Schaefer, 1989). Second, taking turns

in discourse is fundamental to conversations (Sacks, Schegloff & Jefferson, 1974; Schegloff &

Sacks, 1973). Third, language (in the context of problem solving and game playing) reflects not

only the existence of joint action, but embodies the mechanisms to coordinate that action (e.g.,

Clark, 1996; Schelling, 1960). Furthermore, joint action serves to define and refine elements of

the common ground, and the offer/counter-offer pairs reflect key changes in that common ground

state (the structure of a proposed solution).

Negotiators exchange information in their attempts to reach agreement. They provide

information about their preferences and priorities, argue their positions, and exchange offers

(Olekalns, Smith, & Walsh, 1996; Putnam & Wilson, 1989; Weingart, Thompson, Bazerman &

Carroll, 1990; Weingart, Hyder, & Prietula, 1996). Offers are proposals made to the other party

that reflect an acceptable alternative to the source. Offers provide information to the other party

about one’s own desires, and the progression of offers over time provides information about

one’s willingness to concede (Komorita & Brenner, 1968; Kwon & Weingart, 2004). Offers can

include single or multiple issues. While single issue offers reflect desires on a given issue, multi-

issue offers combine preferences on issues such that the issues can be packaged together or

traded off across the parties. Crafting a multi-issue offer is not a simple task – previously


considered single-issue offers (i.e., independent operators) must be jointly associated to form

multi-issue offers (similar to macro- or complex operators), at times requiring the negotiator to

abandon a goal for a single issue as a means of obtaining a higher outcome overall (Hyder,

Prietula, & Weingart, 2000). Multi-issue offers thus can provide information about how a

negotiator values the issues relative to one another. Consequently, much information is

contained in multi-issue offers and in offer sequences, and in negotiation, perhaps the most

important communication is indeed the exchange of offers and counter-offers (Tutzauer, 1992).

Offer patterns have been studied in distributive negotiations where two parties are

attempting to reach agreement on a single issue. In this literature, offers are framed in terms of

the concessions they represent and analyzed in terms of the amount and timing of the

concessions (Allen, Donohue, & Stewart, 1990; Komorita & Brenner, 1968; Smith, Pruitt, &

Carnevale, 1982). More relevant to our framework, in multi-issues negotiations that are

characterized by integrative potential (such that both parties can increase their outcomes

simultaneously), offer patterns have been studied in terms of “systematic concessions” (Kelley &

Schenitzki, 1972; Siegel & Fouraker, 1960) or “heuristic trial and error” (Pruitt, 1981) as well as

in terms of the “dance of packages” and “joint construction of compromise contracts” (Raiffa,

2002). While these have provided insight into the way offers might be constructed and thus

inform our framework, these streams of research have not provided sufficient insight into

detailed processes accounting for joint offer patterns.

Systematic concession making is a model of negotiation process whereby negotiators

open with packaged offers (including all the issues) that provide maximum benefit to themselves

and then examine packages at the next level of reduced value (to themselves) before conceding

more (Siegel & Fouraker, 1960). With each concession, negotiators lower their aspirations,


expanding their set of acceptable agreements. When the two negotiators’ sets intersect, they will

reach agreement. The systematic concessions model “assumes nothing about the bargainers’

ability to identify or distinguish between the various contracts” (Kelley & Schenitzki, 1972:

323); negotiators are modeled as employing own value-based rather than structure-based search.

When using systematic concession making, negotiators do not need any information about the

other party to formulate their package offers and do not incorporate information received from

the other party even if it is available. In contrast, we assume that negotiators do incorporate

information obtained from the other party in crafting their own responses. Research on

negotiation processes has demonstrated the temporal interdependencies of negotiator behavior

(Putnam & Jones, 1982; Weingart, Prietula, Hyder, & Genovese, 1999). If negotiators do

respond to the other party’s behavior, then we would not expect offers to progress as suggested

by the systematic concession making model, but rather incorporate information for the other

party’s prior offer. As we suggest, this includes information about the value and the structure of

offers.

Proposition 2: Subsequent offers will incorporate information regarding the value and

structure of prior offers.

Raiffa (1982, 2002) describes two (extreme) patterns of offers that most closely resemble

our theoretical approach of offers as search. The first pattern is the “dance of packages” whereby

the two parties exchange packaged offers as a consequence of strategic choice and in response to

the other party. Both parties negotiate at the “package level” which may (or may not) result in

either an orderly procession of offers toward the frontier or reasonable results. Raiffa (2002)

characterizes this dance of packages as moving in and out of the feasibility domain and being

somewhat “disorderly” at times when graphed in joint-sum space (p. 275). We relate this pattern


to our concept of value-based exploration, and suggest that there are underlying search heuristics

can explain the apparent disorder in these graphs. Raiffa (2002) describes the second pattern as a

“joint construction of a compromise contract” whereby a negotiation is resolved as the result of a

series or succession of agreements on individual issues or subsets of issues. In this pattern, offers

built on issue sub-agreements are tentative, for “agreements made early on are not treated as

irrevocable, but are reviewed later as the package evolves and gains in complexity” (p. 277). We

relate this pattern to offer-refinement search, and suggest that agreements on issues afford a

structural reduction in the search space and therefore less discontinuity and more (in Raiffa’s

terminology) migration.

Searching the Offer Space

When viewing the sequences of offers and counter-offers that emerge from actual dyadic

negotiations, the resulting paths are often irregular, seemingly random when graphed over the

offer space (e.g., joint sum plots), and sometimes quite complex movements toward an

agreement (Raiffa, 2002; Weingart & Prietula, 1998). We suggest that the apparent complexities

of the offer traces are described by two simple and systematic search patterns conducted by the

negotiators – patterns that are primarily defined in terms of how the offer and counter-offers

relate in terms of structure, rather than value. Though both are certainly influential, we propose

that there are significant tendencies for structure to guide “where” the search space will be

explored and for value to guide “which” offers in that region are acceptable.

The first pattern, value-based exploration, is less coordinated across the two parties, more

individualistic in that it is driven by assessments of value to oneself, and introduces new

potential sets of solutions into the negotiation. Value-based exploration represents a broad search

for an acceptable agreement that is not anchored by the structure of prior offers. Although not


constrained by the structure of prior offers, value-based exploration is constrained by value

aspirations and bottom lines of the individual negotiator. Because negotiators are aware of their

own value, but not their opponents’, value-based exploration offers are less likely to

systematically address the preferences of the other party.

We formally define value-based exploration as consecutive offers that do not share issue

options. The Seller (S) and the Buyer (B) make a series of offers, where each offer is depicted as

(i, j, k) reflecting the ith option of Speed, the jth option level of Edit and the kth option of

Appearance (as defined in Table 3). Let us consider two offers, O1 and O2, one made by the

Seller (or Buyer) and one subsequently made by the Buyer (or Seller).

Value-based Exploration. Any two sequential offers from two negotiators, O1(i1, j1, k1)

and O2(i2, j2, k2) are said to represent a value-based exploration pattern if i1 ≠ i2 and j1 ≠

j2 and k1 ≠ k2, and Value[O 1] ≠ Value [O 2].

Thus, when an offer suggested by one negotiator is followed by another offer from the other

negotiator, and the two offers differ on all issues of the negotiation, we define this as value-based

exploration by the two parties. To illustrate exploration, we employ data from “Group 4” from

Weingart et al. (1990).2 Consider the following initial offer sequence (as coded) from Group 4,

where the values in the parentheses refer to the option levels for the three issues in Table 3: [1]

B(449) → [2] S(667). Here the Buyer initiates the negotiation with an offer indicating

preferences for a 4-day turnaround (Speed, option 4), a maximum of three typographical errors

(Editing, option 4), and will accept a low quality typewritten document (Appearance, option 9).

The Seller counters with an offer that differs (in option levels) on all three issues; therefore, we

categorize this sequence as value-based exploration. We presume that this type of search in the

offer space reflects no commitment to refinement of the common ground.


The other pattern, offer refinement, demands more coordination but defines a smaller

region of the offer space to which joint attention is paid, resulting in a more focused search.

Offer refinement is a distinctly more coordinated activity that begins when the two parties start

to converge to an understanding of what constitutes a possible solution. When engaged in offer

refinement, negotiators construct their offers by building directly off of the preceding offers’

structure made by the other party. In this way negotiators are integrating information from the

other party into their own representation of the problem resulting in convergence on some

common ground that can be exploited. Thus, we formally define offer refinement as a sequence

of offers that contain at least one shared issue option.

Offer refinement. Any two sequential offers from two negotiators, O1(i1, j1, k1) and O2(i2,

j2, k2) are said to represent an offer refinement sequence if they are structurally equivalent

on at least one issue.

From the same example, consider the next sequence of offers: [2] S(667) → [3] B(467).

Here the Buyer (offer 3) incorporates both the options of Editing and Appearance set by the

Seller in the prior offer (offer 2). Conceptually, these negotiators tentatively agree on two of the

required three issues, thus narrowing the possible solutions remaining to be searched to (467),

(567), and (667). Note here that during offer refinement, the offer values may or may not be

equivalent. If the offer values are equivalent, then there is a high likelihood that agreement

would occur as negotiators are reciprocating offers located at the same point in the offer space,

otherwise the search moves toward further refinement.

Proposition 3: Offer refinement sequences that provide offers of mutual value-

equivalence increase the likelihood of agreement.


In that negotiators work in a world of issues and options, and value is derived from

potential outcomes, it should be cognitively easier for negotiators to first consider variations in

structure and then consider the resulting value, than vice versa. It is also collaboratively easier

for negotiators to think in terms of the structure (or content) of offers, as offers and counter-

offers are communicated in terms of their structural characteristics (e.g., tomorrow, max 3 errors,

letter quality), not computing their underlying values across various preference options. For these

reasons, we expect the structure of offers to play a more central role in determining subsequent

offers than the value of those offers.

Proposition 4: The structure of offers will more strongly guide the progression of offers

within the search space than will the value of offers.

When an offer is made, it serves as a signal to the other negotiator as to what may

constitute an agreement. Because negotiators only have direct information about the total value

of an offer to themselves, value-based exploration offers are likely to reflect high value to

oneself, but variable value to the other party as negotiators perhaps blindly search for an

acceptable offer to the other party. In contrast, offer refinement configurations are influenced by

structural components of prior offers (both the other party’s and their own) and evaluated within

that context, and are more likely to reflect more moderate value to oneself and to the other party

as negotiators’ offers reflect more knowledge about the interdependence between own and

others’ outcomes. Put together, this implies that exploration offers (search by value) should

provide more benefit to oneself than refinement offers (search by structure). And while on

average the total benefit to the other party may be the same, the variance will be higher for

explorative than refinement offers. The structure of offers thus constrains the values of the offers

and, consequently, the value of the agreement.


From any two sequential offers representing a refinement sequence, we can generate two

important metrics describing the structural state of the negotiation: the region of the offer space

that remains “viable” given an agreement on any issue, called the refinement set, and the

distance between these (or any) two offers in terms of their structure.

Offer Refinement Sets

When negotiators’ offers contain equivalent issue options, they are effectively narrowing

the search space. By (even tentatively) agreeing on an issue option, negotiators’ attention (and

discussion) is shifted away from the “solved” component of the agreement, and towards the

“unsolved” component(s) of the agreement. Once an issue option is accepted, the possible

agreements that remain, given that agreement, are substantially reduced. We can identify the

reduced region of search by focusing on the range of options that still remain open between

sequential offers. The set of possible offers that remain defines a restricted region of the offer

space that is now the focus of joint attention.

When negotiators’ offers reflect similar issue options they are narrowing the search

space, which will further constrain subsequent offer progression. We refer to these restricted

regions of the offer space as refinement sets – the set of possible offers that remain after one or

more issue options have been (perhaps tentatively) agreed upon. Refinement sets are not

explicitly defined by negotiators and negotiators are probably not even directly aware of them;

however, they do reflect an alignment of the common ground between the two negotiators and

they do influence subsequent behavior. Refinement sets are thus a residually-defined artifact of

the negotiators’ interaction with the task and with each other, revealing the set of solution

possibilities given a joint agreement on less than all of the issues under negotiation.


Refinement Set. Given any two sequential offers from two negotiators, O1(i1, j1, k1) and

O2(i2, j2, k2), that constitute a refinement sequence, the refinement set is defined as the

inclusive set of possible offers denoted by the structural range of options of the issue or

issues specified, but unresolved.

Returning to our example from Group 4, consider again the second and third offers in the

sequence: [2] S(667) → [3] B(467) where the Buyer agrees with two issues (Editing and

Appearance), but prefers option 4 on the first issue, Speed. These two offers, spanning the range

of options 4, 5, and 6 on Speed, define an initial refinement set consisting of three possible

agreements (depicted as open circles in Fig. 3). In response, the Seller offers [4]: S(657), with

one issue in agreement to the Buyer’s prior offer (third issue, Appearance). This sequence

defines a new refinement set comprised of six (inclusive) potential agreements that reside within

the bounds for Speed (options 4, 5, and 6) and the two potential offers of Editing (options 5 and

6). This second refinement set is represented by open squares in Fig. 3.

------------------------- Insert Fig. 3 here

-------------------------

We do not define refinement sets in terms of two sequential offers from the same

negotiator because, by definition, refinement sets reflect key communication between two

negotiators within the offer space. Thus, a refinement set is the set of possible offers that are

encompassed by the structural differences between two sequential offers from opposing parties –

refinement is a process engaged by both negotiators. As a refinement set contains more than one

possible solution, it is informative to determine how many solutions comprise any particular set,

as that size tells us how large of a space the negotiators must subsequently jointly consider. The

size of an refinement set, R, defined by two offers (using a slightly different notation), O1(I1,I2,I3)


and O2(I1,I2,I3), is given as (assuming a three issue negotiation) the simple adjusted product of

the option levels remaining on the issues (Ii), in order to get the interior “volume” of points

within the levels specified:

( )∏=

+−=3

121 1)()(

iii IOIOR

For example, over the course of the negotiation for Group 4, 12 offer exchanges occurred in

refinement sequences (defining 12 refinement sets) before an agreement was reached, and the

average size of a refinement set for this group was 4.5 offers. If one were to merely sum the size

of the refinement sets, Group 4 could be said to have considered 40 potential solutions. However,

this number is misleading, as refinement sets should overlap. Because offer refinement holds

constant some issue options, we would expect redundancy across refinement sets.

Proposition 5: Offer refinement search will creep across the offer space with few

discontinuities and will reflect substantial overlap with previously defined regions.

Interestingly, within Group 4, for example, there was 70% redundancy of offers across

refinement sets. This creep across the offer space is indicative of the small, sequential structural

adjustments that occur across refinement sets. Placed in perspective for our illustrative data set,

the average size of any given refinement set (7.4) represented about 1.4% of the offer space (see

Table 4). Given the high percentage of redundant offers across refinement sets on average

(37.9%), it’s not surprising that two negotiators jointly considered an upper level estimate of

only 3.4% of the offer space over the entire negotiation (see Table 4).

------------------------ Insert Table 4 here ------------------------

Because of negotiators’ cognitive limitations, it is not surprising that refinement sets are

expected to be substantially smaller than typical offer spaces seen in this type of research.


Reduction might occur as a means of simplifying the task and should reflect integration of

knowledge gained through discussion of preferences and priorities and prior offers made. This is

similar to, and consistent with, the concept of “minimization of collaborative effort” from

collaborative models of discourse (Clark & Wilkes-Gibbs, 1986). That is, if we presume that

each negotiator is boundedly rational and seeks methods that will simplify the individual

demands of the task, it is logical to assume that together they will employ methods that will

jointly accommodate their cognitive restrictions.

Proposition 6: Refinement sets will comprise only a small proportion of the offer space.

Structural Distance

The distances between offers in terms of value are readily calculated and graphed in

joint-sum plots (e.g., prior Figs. 1 and 2), but the similarity of structure across offers has not been

explored. The more similar offers are structurally, the more likely the prior offer was

incorporated into the current offer by a negotiator. We can quantify the similarity of offers by

using a metric of structural distance, DS. We differentiate between simple structural distance,

which is the structural distance between two offers, and average structural distance, which is the

distance between a mutual value-equivalence set (i.e., offers of similar value to each of the

parties, but of different structure) and a prior offer. We score simple structural distance between

two offers by counting the number of issue option changes (structural adjustments) it would take

to transform an offer from one negotiator, O1(I1,I2,I3), into the subsequent offer from the other

negotiator, O2(I1,I2,I3) (see Hamming 1980).

∑=

−=3

121 )()(

iiiS IOIOD

Using this metric we can calculate the simple structural distance from the prior offer

made by the other party (an “across” offer structural similarity measure) and the simple structural


distance from the prior offer made by the same party (a “within” offer structural similarity

measure). Separately, each tells us the influence of the prior offers (own and other) on the current

offer. Together, they tell us which prior offer had greater influence and thus whether the

negotiator is largely negotiating from his/her own perspective (higher “within”) or from a joint

perspective (higher “across”). This allows us to quantify the effect of prior offers on current

offers. Thus, an offer with more changes on more issues is deemed “farther” away than another

offer that has fewer changes in the offer options. Similarly, the average structural distance tells

us, on average, how far a set of offers is from a prior offer. It provides the context within which

one can determine the relative magnitude of the simple structural distance of an offer as

compared to a set of similarly valued alternative offers.

Heuristic and Bias in Offer Generation

Given the prior discussion, we can now describe some fundamental observations on offer

generation, movement, and agreement in negotiation. When negotiators have a choice of offers

that are equivalent in value, and thus generally indifferent in terms of value, how will they select

from that set the particular offer to make? We can use the notion of a value equivalence set (the

set of offers that have equivalent value to a negotiator) to illustrate the influence of prior offers

on subsequent offers. For example consider the discussed sequence of offers: [2] S(667) → [3]

B(467). The Buyer’s value equivalence set for the offer B(467) has 15 equivalently valued (but

structurally different) offers. Given the prior offer from the Seller, S(667), the Buyer’s response

had an implicit agreement on two issues (Editing = 6, Appearance = 7). Of the 15 possible

responses that were equivalent in value, the one selected by the Buyer, B(467), was the one in

the set that was most similar in structure to the Seller’s prior offer. It appears that the Buyer’s


offer, although probabilistically unlikely (1/15 = 0.06%), was dependent on the structure of the

Seller’s prior offer.

Simple structural distances were computed from the illustrative data, averaged within

group, and the results are shown in Table 5 along with the average size of the value equivalence

sets. For example, in the negotiation of Group 1, the average offer differed structurally from the

prior offer of the other party by 2.3 options and differed from the prior offer made by the same

party by 1.6 options, suggesting negotiators relied more on their own prior offer than that of the

other party when constructing their next offer. In responding to an offer, the negotiators had an

average value equivalence set size of 12.5 offers from which to choose, so the likelihood of

choosing a structurally similar option was .08. This illustrates what we call the structural

similarity heuristic that will tend to occur as the number of alternative solutions in an offer

equivalence set increases.

Structural Similarity Heuristic. Negotiators will select offers from their value equivalence

sets (i.e., sets of offers whose total preference values are equivalent) those that tend to be

structurally similar to their prior offer.

---------------------- Insert Table 5 here ----------------------

The structural similarity heuristic has consequences during refinement search. As at least

one of the issues are in agreement between the negotiators, the use of this heuristic facilitates the

specification of a common ground of search and, ultimately, to the final agreement. We can

demonstrate the influence of refinement sets on final agreements by examining their structural

distances (Ds). Not surprisingly, the final agreement is very proximal to the penultimate

refinement set. In our illustrative data, the final agreement is one structural adjustment from the


nearest member of the refinement set established immediately prior to the agreed upon offer.

Interestingly, the final agreement is also quite proximal to the initial refinement set, only

differing by two structural adjustments. In fact, an examination of all the illustrative data

demonstrates the proximity the final agreements have to initial and penultimate refinement sets

within the negotiation (see Table 6). As can be seen, the average structural distances between

agreement and refinement sets are, for the most part, low.

----------------------- Insert Table 6 here -----------------------

What this illustrates is not only the influence of structure on negotiation offers, but also

the structural proximity maintained between offers and refinement sets. As noted, we speculate

that it is cognitively easier for negotiators to first consider variations in structure, and then

consider the resulting value, than first consider variations in value, and then craft the requisite

agreement structures that render that value. We also suggest that it is collaboratively easier, as

offers and counter-offers are communicated in terms of their structural characteristics (e.g.,

“tomorrow”, “max 3 errors”, “letter quality”), making the structure more cognitively accessible

to negotiators and the subsequent interpretation into value straight-forward. We suggest that

together these result in a structural proximity bias that facilitates the coordination of the

negotiation search activity.

Structural proximity bias. Offer-refinement sets (as common ground components) tend to

evolve by relatively small changes in proximity (via structural changes in offers) that

serve to maintain the continuity of joint attention and to reduce disturbance to the current

state of the common ground.


The Patterns of Search

Given our framework, four primary patterns of search in negotiation dynamics can be

defined as revealed by changes in offers and refinement sets. The first three search patterns

reflect refinement and the fourth type reflects offer exploration. Taken together, they vary from

highly constrained and local search to completely unconstrained, broad search. Any given

negotiation may evidence any or all of these patterns. First, search can exhibit a pattern of low

(or zero) movement toward the frontier and include high proximal activity (i.e., offers that are

generated from the offer refinement set) within the offer space. This is the case when offers

made between negotiators are generated from current or past offer refinement sets, or current or

past refinement sets are modified via reconstituted offers. Thus, existing (though not necessarily

articulated) alternatives are revisited. For example, consider the negotiation of Group 4. Within

that negotiation, there is a refinement sequence when the Buyer makes an offer, B(467) and the

Seller responds, S(459), defining an refinement set {4, 5-6, 7-9} that is comprised of six

potential solutions. Over the subsequent exchanges, eleven offers are made and five of those,

including the eventual agreement, originate from that set.

Second, search can exhibit a systematic extension into neighboring regions of the offer

space not covered by the existing refinement set, but is proximate to the refinement set. In this

case, the emergence of offers and refinement sets are tightly intertwined such that offers are

influenced by the most recent offers and active refinement sets. This results in a systematic and

constrained pattern of extension into the offer space within a relatively narrow region. Consider

an example from Group 2. The first two offers defined the initial refinement set and the third

offer came from outside (but near) that set and redefined the refinement set closer to the Pareto

frontier. The final offer was resolved via a within-refinement set search of the third refinement


set.

Third, there can be a reorientation of the refinement set. This involves what can be

described as a pivot that reorients a refinement set according to the range of joint value to the

negotiators. There can be one or more solutions common to the reoriented refinement set (few

rather than more), but the set itself undergoes a substantial change in average value to

negotiators. Consider the negotiation of a new group, Group 7, shown in Fig. 4. The initial

refinement set is depicted as open squares as defined by the two offers: B(583), S(588). For this

refinement set, the average value to the Buyer is 850 (with a low standard deviation of

alternatives, as can be induced by the low range the set covers on the x-axis), while the average

value to the Seller is 2950 (with a higher standard deviation of alternatives). The Buyer then

poses a counter offer, B(388), that reorients the refinement set (as shown by open circles), by

agreeing on the Editing issue (option 8) and appearance (option 8), but altering the proposed

options on speed. The effect of this reorientation is to radically reduce the number of alternatives

in the joint search for both negotiators. If the resulting values are acceptable to both parties, this

can be effective in achieving a solution.

------------------------ Insert Fig. 4 here

------------------------ Finally, search can involve a discontinuous shift to a new offer refinement set via

exploration. This is more likely to occur early in negotiation, if at all (see prior Table 4), as

exploration will tend to quickly shift to refinement as negotiators converge on issue options.

Proposition 7: Offer exploration is more likely to occur early in the negotiation, prior to

offer refinement.

However, occasionally a new offer is made later in the negotiation that has no issue

options in common with the active or prior refinement sets, reflecting Raiffa’s dance of


packages. Consider the same example, Group 7, shown in Fig. 4. The Buyer shifts from an offer

refinement process to an explorative process, via an offer that is worth substantially more for the

Buyer, but less (in fact below the reservation value) for the Seller, Offer 4:B(332). The Seller

responds with an explorative offer, Offer 5:S(268) and, from that offer, the next sequences define

the final refinement set that contains the agreement that is determined by refinement search. In

this case, the initial refinement sets were not acceptable as defining regions in the offer space

that could support joint search. However, the discontinuities afforded by exploration did result in

a refinement set that accommodated the joint interest of the parties.

The dominant search pattern during a negotiation should influence the likelihood of

optimal agreements. Negotiations characterized by proximal search within a highly constrained

refinement set are less likely to reach optimal agreements because the search is overly restricted

to a local region. Unless an early offer happens to be proximal to the optimal frontier, these

negotiators are unlikely to discover an optimal agreement because of a prematurely formed

refinement set.

Proposition 8: Negotiations characterized by early or inflexible proximal search are less

likely to reach optimal agreements.

Although some refinement sets are defined early in the negotiation, we would assume

that search patterns that systematically extend the refinement set have a higher probability of

reaching optimal solutions. The reason is simply based on the likelihood of an initial refinement

set containing solutions on, or even close to, the Pareto optimal frontier.

Proposition 9: Search patterns that systematically extend the refinement set have a higher

probability of reaching optimal solutions.

The incremental nature of systematic extension search relies on consistent use of that


strategy to optimize outcomes. Movements away from the optimal frontier will not be reinforced

by the other party because it represents a Pareto-inferior movement, and thus repeated extensions

away from optimality are unlikely.

Reorientations of the exploration space shifts the negotiators into a new region of the

offer space and have the potential of reframing the negotiation. Reorientations might reflect

insight into the integrative potential of the task, as they rely on some commonalities, but

restructure the offer in a way that redefines the active refinement set. At the far extreme,

exploration, as evidenced by discontinuous shifts, represents independent search. It is less likely

to include mutually acceptable offers, as those offers do not integrate aspects of the other party’s

prior offer. However, exploration is a mechanism that may actually improve the process if the

negotiators are “stuck” in a prematurely defined suboptimal refinement set.

Exploration is less likely to include mutually acceptable offers, as those offers do not

integrate aspects of the other party’s prior offer, but may serve to “reorient” search to another

region of the offer space. Thus, while a discontinuous shift might result in an offer on the

optimal frontier, it is less likely to result in one the other party will accept. Instead, we expect

those offers to strongly favor the party making that offer.

Discussion

In thinking about the how this model advances the field of negotiation, we need to

consider how it relates to prior research on negotiation processes. Earlier we mentioned research

on distributive bargaining offer patterns, systematic concession making, and package offer

patterns and considered how our approach extended that work. Whereas previous theories of

offers took a more individual negotiator-centric approach, our framework considers the co-

construction of knowledge and search via offers. Our framework suggests an alternative way to


conceptualize offer exchange and novel approaches to tracking and predicting the effects of

offers on negotiated agreements. Rather than focusing exclusively on the individual without

consideration of context, our framework embodies the social interaction. As a result, we provide

a more comprehensive representation of negotiator cognition and add to our understanding of

negotiation process and the potential for more accurate predictions of offer making and

outcomes. Rather than focus on concession rate and systematic value-based search, our

framework considers proximity of offers and exploration (perhaps value-based) versus

refinement (structure-based) search processes. Rather then focus on point predictions of outcome

optimality, our framework focuses on predictions of patterns (as refinement sets) and properties

of patterns, such as proximity and size, as a consequence of boundedly-rational beings engaging

in a collaborative problem solving process. By recognizing the cognitive limitations of

negotiators and considering how that influences offer-making, we gain a better understanding of

how negotiators actually compose offers and how those offers lead to agreements. We build off

Raiffa’s (1982, 2002) distinction between the dance of packages and the joint construction of a

compromise contract to do so.

We can also relate this framework to the use of negotiation reference points. Reference

points are relevant comparators that can serve as cognitive anchors for subsequent offers and

outcomes (Blount, Thomas-Hunt, & Neale ,1996; Galinksy, Mussweiler, & Medvec, 2002). Both

internal (e.g., reservation prices, aspirations, or opening offers) and external (e.g., market value)

reference points have been examined in the context of two-party price negotiations (Galinsky,

Mussweiler & Medvec, 2002; Kristensen & Garling, 1997, 2000; Van Poucke & Buelens, 2002)

and the relative weighting of these reference points depends on the context of the negotiation

(Blount et al., 1996). Whereas this literature considers the impact of fixed reference points on


initial offers and outcomes, as well as on satisfaction with outcomes, our framework takes a

more dynamic approach by framing all offers as potential cognitive anchors from which

negotiators will formulate their responses. Thus, our framework picks up from where the

reference point literature leaves off by considering how negotiators update their framing of the

negotiation in response to subsequent offers. We also extend current conceptualizations of

cognitive anchors (or reference points) by considering their structural component. Certainly

many types of anchors exist, and together they serve to simplify the task by reducing the search

space and need for cognitive exertion.

Research is needed to both develop and extend our framework. Additional framework

development is needed as it relates to the inclusion of continuous (rather than only discrete)

issues, the introduction of new issues into the bargaining mix, and multi-party settings. Model

extension is also needed to embed our framework into the broader behavioral research on

negotiation. We explore ideas of model development and extensions below. However, it is

important to note that the general form of the structure we have depicted in our examples is not

at all uncommon.

Framework Development

This initial formulation of our framework required several simplifying assumptions. Issue

options were treated as discrete, the bargaining mix (i.e., set of issues) was assumed to be static,

and the negotiation only involved two parties. While these assumptions provide a reasonable

starting place, they represent only a subset of negotiations. Relaxing these assumptions would

allow us to model a broader range of negotiation dynamics, but also requires development to our

framework.

An obvious refinement of the framework is needed to consider the treatment of issues


that are continuous in nature, like price, when capturing offer movement and refinement sets.

Our formulae for defining exploration, refinement, equivalence sets, structural distance, and

refinement sets all presumed issues whose options were discrete, but ordered in terms of

preferences to oneself (see Footnote 1). Additional work is needed to expand the

conceptualization to include negotiations that include issues whose options are continuous, or

afford more complex contingencies in the preference schedules that cause various forms of

discontinuities in the offer space landscape. At the most simplistic level, discrete options could

be generated by identifying ranges of values (e.g., Raiffa, 1982, p. 136). Or structure could only

be examined for the discrete issues and continuous options could be added in when plotting the

offers and identifying the refinement sets. In the case where the issue options are monetized

(e.g., price), the distinction between value and structure search becomes blurred.

Another necessary refinement of the framework relates to the introduction of new issues

into the bargaining mix. We presented the framework only in terms of complete offers – in our

example, 3-issue offers within a negotiation that encompassed only 3 issues. However, offers

might include only a subset of the issues, gradually folding in additional issues until a final

agreement is reached. Raiffa (2002) refers to this process as the joint construction of a

compromise contract (p. 276). Partial offers could be accommodated in our framework by

assuming the missing issue open and including the full range of the missing issue (“it’s all fair

game”). Each offer would be plotted in terms of the value represented by the subset of issues, but

refinement sets would be plotted to include the full range of the missing issue. Our framework

could also be developed to accommodate an offer that includes an issue that was not previously

on the table for either party. The additional issue would redefine the shape and location of the

Pareto optimal frontier. Thus not only would the offer patterns be dynamic, but so would the


offer space.

Our framework focuses on a two-party situation; extension into multi-party settings, in

which there are more than two “sides” to the discussion, present an interesting challenge. Multi-

party negotiations are common and introduce informational complexities to the dynamics of a

negotiation (Bazerman, Mannix, & Thompson, 1988; Brett, 1991). The current approach maps

refinement sets and offer patterns in terms of value to each party. As we add more parties into

the mix, the mapping would be in n-dimensional space. While visualization may be difficult,

calculation of exploration, refinement, equivalence sets, structural distance, and refinement sets

would largely be the same because those measures tap into structural change (offer content)

rather than offer value change to each of the parties. Similar extensions can be made by

increasing the number of issues. In either case, would exploration sequences be extended?

Would refinement and common ground be more resistant to change? Is the 2-offer refinement

definition invariant and a consequence of bounded rationality?

Model Extension

While developing our framework, we delineated propositions regarding the mechanisms

of search. Our propositions addressed how negotiators would search the offer space, how offers

build on other offers, the differential roles of value-based exploration and offer refinement, and

heuristics of search. Once these mechanisms are well understood, additional theory should be

developed and empirical research conducted relating external causal factors that affect search

and its subsequent influence on quality of agreement. External factors of interest could include

social motives (discussed in more detail below), deadlines, knowledge of other parties’ priorities,

negotiation expertise, among others. Future research should also explore how to embed our

information processing model of negotiation into more behavioral and strategic models of


negotiation. Ultimately, our goal would be to understand how the motivational, cognitive, and

strategic aspects of negotiation interrelate.

In that search is goal directed behavior, our framework should be extended to consider

the one of the most widely studied goal-related constructs in negotiation research, social motives

(e.g., whether negotiators are more cooperative or individualistic in their orientation toward a

negotiation) (De Dreu, Weingart, & Kwon, 2000). Social motives are typically defined in terms

of goal maximization – individualists work toward a goal of maximizing their own outcomes

whereas cooperators work toward maximizing their own and others’ outcomes simultaneously.

Research show that cooperators engage more problem-solving strategies than do individualists,

achieve higher joint gain (De Dreu et al., 2000), and tend to be more responsive to other

negotiators in their strategic approach (Weingart, Brett, Olekalns, & Smith, 2006). We might

expect individualists to be more exhaustive than cooperatives in their value equivalence set

search, being reluctant to sacrifice their own value, but less concerned with their opponent’s

outcome. They might also be less likely than cooperatives to incorporate information from their

opponent’s offers into their own, such that their offer is more similar in structure to their own

prior offer than to the other party’s prior offer.

Perhaps one of the most important extensions to the framework will be the understanding

of how offer structure, in conjunction with other tactical behavior, influences quality of

agreement and the discovery of Pareto optimal solutions. Offers are not the only mechanism for

search and discovery; information exchange, a foundational tactical behavior, also serves a

search function (Adair, Weingart, & Brett, in press). Interesting questions arise when

considering both approaches simultaneously. How do information exchange and offer structure

play off one another? Do negotiators use information exchange to “fill in the blanks” between


offers – that is, will simultaneously capturing information exchange help us predict the ways in

which offers are altered and when negotiators might engage in exploration as opposed to

refinement? If a negotiating group relies on one mechanism (offers or direct information

exchange) over the other, will that influence their ability to discover an optimal agreement? Are

there situations where exploration with offers is more effective than information exchange-as-

search (or vice-versa)?

In conclusion, Raiffa (2002) notes that in the real world, negotiators often exchange

packages and advises that the worst thing a negotiator can do is to “go into the details of AAA’s

package and propose amendments to it.” (p. 274). We agree that this approach will be

counterproductive for a negotiator when those details anchor the negotiator in terms of offer

value. However, negotiators must, and we believe do, pay attention to the information embedded

in those offers to help them find agreements that are mutually acceptable, if not Pareto optimal.

This is the role of offers as search. Negotiators also must, and we believe do, accommodate the

demands of the task complexity with their limits as boundedly rational individuals. This is role of

refinement sets. We believe our framework moves us toward understanding how negotiators use

offers to search via exploration and refinement of the potential set of agreements. A more

complete understanding of the progression of offers during a negotiation can move us closer

toward mapping the routes through which agreements are reached and toward predicting the

regions of agreements.


Footnotes

1 Specifically, we assume typical preference requirements for issue options (e.g., any two

option levels are comparable and no intransitivities exist), as well as pair wise preferentially

independence, so that the value function for each negotiator can be expressed in additive form,

allowing the joint-sum to be calculated (see Keeney & Raiffa, 1993).

2 To demonstrate the constructs, we employ dyadic negotiation data (n = 8 dyads) from a

previously published study that used the negotiation task summarized in Table 1 (Weingart et al.,

1990). It is important to note that we did not use the data to test our framework, but rather to

illustrate how we might understand our constructs using real data. The authors randomly chose 8

dyads from the existing data set and recoded the transcripts identifying where offers were made

and the structure (i.e., content) of those offers. Data from all 8 transcripts are used to

demonstrate aggregate measures of offer patterns. Specific examples from selected transcripts

were used to demonstrate different patterns of offers. Thus, the sequences of offers described

below were not randomly chosen, but were chosen because they provided a clear illustration of

the concept being proposed. Excerpts from Group 4 (discussed in the text) are shown in the

Appendix.


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Appendix

Excerpt from Group 4 (from Weingart et al., 1990) Speaker Content Offer #,

source, and issue options

Buyer …and what type of typewriter do you have available to you? Seller Well, I have a Smith Corona and that’s what I normally use on my

papers.

Buyer Again, this is a manuscript. It’s very important for my degree here at Northwestern and ideally I would like it typeset.

Seller It seems to me thought that you’re saying that speed is for you what’s going to be most important, that you need a rapid turnaround. And for me the easiest thing is to type this on a machine that’s available to me now. If I have to do anything more sophisticated I have to go out and rent that and it may take me a few days to just obtain that kind of a better quality machine.

Buyer But you’re a professional, you do this full time, that’s really whether or not you got to rent the machine isn’t really of my concern. I need this thing done. If you look at all three of these factors, if you can do it in four days with three errors per page, and that’s really at the bottom of my list.

1. B (449)

Seller Well, I’m willing to do some combination of the three variables that seem to help both of our situations. If I were to say come down to six days with five errors and a near letter quality printer, that to me seems very reasonable. I don’t know how much better you could do with anybody else on campus given that it is the end of the quarter and there’s going to be a lot of demand.

2. S (667)

Buyer Well, six days is going to be pressing it. If we were to say four days? How about four days with five errors and near letter quality? I mean the near letter quality is definitely, I mean ink jet would be kind of the bottom of that for me.

3. B (467)

Seller How about six days and four errors and the near letter quality? The near letter quality printer, that’s something I can get from some-one I know who can get this to me probably tonight and I can start working on it and I wouldn’t get the whole thing done for a number of days but at least I can get started on it. And certainly with the edit-ing, if you are looking at reduced errors I need time to read through these 50 pages and that’s going to take quite a bit of time to make sure the spelling and everything is correct.

4. S (657)

…13, 3-issue offers exchanged; final agreement: (459)…


Table 1

Static Components of Framework

Key Component Name Component Definition Comprehensive Offer An assertion (package) specifying the preferred options to a negotiator

across all issues. We refer to these simply as Offers. Offer Space (Search Space) Set of all potential Offers definable within the negotiation task. Offer Value Total value of an Offer to a single negotiator as defined by the sum of

the preferences for each option specified across all issues. Offer Structure The option of each issue comprising an Offer. Value Equivalence Offers that differ structurally (in terms of issue options), but have the

same total value to a single negotiator (not considering the value to the other negotiator) are said to have Value Equivalence.

Value Equivalence Set A set of offers in the Offer Space that have Offer Value Equivalence. Mutual Value-Equivalence Offers in the Offer Space that differ structurally (in terms of issue

options), but have the same total value to both negotiators are said to have Mutual Value Equivalence.

Mutual Value Equivalence Set A set of offers in the Offer Space that have Mutual Value Equivalence. Structural Difference/Equivalence Offers differ structurally when the option levels for an issue are

different (not equivalent). Structural Distance The number of incremental changes in option levels that one Offer

differs from another Offer. Structural Similarity The extent to which two Offers differ in their Structural Distance.


Table 2 Dynamic Components of Framework

Key Component Name Component Definition Offer Exchange When an Offer made by one negotiator is followed by an Offer from

the other negotiator. Value-based Exploration A less coordinated search evidenced by an Offer Exchange where the

two Offers are Structurally Different across all issues. Offer-Refinement A more coordinated search evidenced by an Offer Exchange where the

two Offers are in agreement on at least one issue. Refinement Set The subset of the Offer Space that remains potentially acceptable to

both parties after Offer-Refinement. Structural Proximity Bias Refinement sets (as common ground components) tend to evolve by

relatively small changes in proximity (via structural changes in offers).


Table 3

Preference schedules for each negotiator for each option (from Weingart et al., 1990)

SPEED EDITING APPEARANCE

Option Done by Buyer Seller Errors Buyer Seller Printer Buyer Seller

1 1 day 3000 -200 None 1800 -600 Typeset 600 -1000

2 2 days 2500 -100 Max 1 1500 -300 Laser 500 -500

3 3 days 2000 0 Max 2 1200 0 Letter Quality

400 0

4 4 days 1500 100 Max 3 900 300 IBM Selectric

300 500

5 5 days 1000 200 Max 4 600 600 Spinwriter 200 1000

6 6 days 500 300 Max 5 300 900 Ink Jet 100 1500

7 7 days 0 400 Max 6 0 1200 Near Letter Quality

0 2000

8 8 days -500 500 Max 7 -300 1500 Dot Matrix -100 2500

9 9 days -1000 600 Max 8 -600 1800 Smith-Corona

-200 3000


Table 4

Basic properties of refinement sets for the illustrative data

Group

Average Size

Average Size as % of Offer

Spacea

Percent Redundancyb

Percent of Offer Space Searchedc

1 3.2 0.6 68.0 1.5

2 13.0 2.4 30.9 5.5

3 4.0 0.7 0.0 1.5

4 4.5 0.8 67.5 2.4

5 4.6 0.8 15.3 2.1

6 14.8 2.8 25.0 4.6

7 12.0 2.3 57.1 7.4

8 3.3 0.6 40.0 2.4

Average 7.4 1.4 37.9 3.4

a This is the percent of offer space covered by the average size of the refinement set, based on the adjusted 521 possible solutions within the zone of possible agreement for this problem.

b Percent redundancy is over all refinement sets of that negotiation. c Percent of offer space covered over the entire negotiation by number of unique offers

generated over all refinement sets, based on the adjusted 521 possible solutions within the zone of possible agreement for this problem.


Table 5

Mean distances (DS) between offers in offer refinement sequences

Average Ds between offersa Average Size of Offer Group Across Within Value Equivalence Setb

1 2.3 1.6 12.5

2 6.0 6.0 8.0

3 3.0 1.9 21.0

4 2.5 2.3 11.1

5 2.0 6.0 10.0

6 4.5 4.1 9.3

7 5.4 4.9 9.0

8 2.0 1.8 8.3

Ave 3.4 4.2 11.1

a Number of issue options that differ between adjacent offers within offer refinement sequences. “Across” refers to adjacent offers that are exchanges between negotiators; “Within” refers to adjacent offers made by the same negotiator.

bAverage number of unique structural combinations in the offer value equivalence set.


Table 6 Distance of agreement from refinement sets

Group DS from initial refinement set [Average DS from set]

DS from penultimate refinement set

[Average DS from set] 1 0 [1.4] 0 [1.4]*

2 2 [4.8] 1 [3.5] 3 1 [2.5] 0 [1.4] 4 3 [4.0] 0 [1.0] 5 2 [4.0] 2 [2.0] 6 2 [7.8] 4 [7.0] 7 7 [9.5] 2 [2.5] 8 0 [1.0] 0 [1.0]

Average 2.1 [4.3] 1.1 [2.4]

Numbers represent minimal distance of the agreement to that set, numbers in parentheses represent the average distance from each member of that set to the final agreement.


Figure Captions

Figure 1. Typical joint sum plot of discrete 3-issue offer space Figure 2. Joint sum density plot of discrete 3-issue offer space (all solutions) Figure 3. Sample refinement sets for Group 4 Figure 4. Partial offer trace and refinement sets for Group 7


Figure 1

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Pareto optimal frontier

Offer value equilence set for Buyer (2600)

Offer value equilence set for Seller (3800)


Figure 2

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Figure 3

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Initial refinement set (circles)

Final refinement set (triangles)

Agreement

Pareto frontier

Second refinement set (squares)


Figure 4

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Subsequent Offer by Seller, 2:S(588) Counter Offer

by Buyer, 3:B(388)

Initial Offer by Buyer, 1:B(583)

Explorative Offer by Buyer, 4:B(332)

Explorative Offer by Seller, 5:S(268)

Final Refinement set {1-2, 2-6,9}

Agreement

running head: structure in negotiation and the search for

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