994 ieee journal on selected areas in communications,...

994 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 35, NO. 4, APRIL 2017

Mobile Data Trading: Behavioral EconomicsAnalysis and Algorithm Design

Junlin Yu, Student Member, IEEE, Man Hon Cheung, Jianwei Huang, Fellow, IEEE,and H. Vincent Poor, Fellow, IEEE

Abstract— Motivated by the recently launched mobile datatrading markets (e.g., China Mobile Hong Kong’s 2nd exChangeMarket), in this paper, the mobile data trading problem is stud-ied under future data demand uncertainty. A brokerage-basedmarket is introduced, in which sellers and buyers propose theirselling and buying quantities, respectively, to the trading platformthat matches the market supply and demand. To understand theusers’ realistic trading behaviors, a prospect theory (PT) modelfrom behavioral economics is proposed, which includes the widelyadopted expected utility theory (EUT) as a special case. Althoughthe PT modeling leads to a challenging non-convex optimizationproblem, the optimal solution can be characterized by exploitingthe unimodal structure of the objective function. Building uponthis analysis, an algorithm is designed to help estimate the users’risk preference and provide trading recommendations dynami-cally, considering the latest market and usage information. It isshown via simulations that the risk preferences have a significantimpact on a user’s decision and outcome: a risk-averse dominantuser can guarantee a higher minimum profit in the trading, whilea risk-seeking dominant user can achieve a higher maximumprofit. By comparing with the EUT benchmark, it is shown thata PT user with a low reference point is more willing to buymobile data. Moreover, compared with an EUT user, a PT useris more willing to buy mobile data when the probability of largedata demand is low.

Index Terms— Behavioral economics, prospect theory, expectedutility theory, mobile data trading.

I. INTRODUCTION

A. Background and Motivation

W ITH the increasing computation and communicationcapabilities of mobile devices, global mobile data

traffic has been growing tremendously in the past fewyears [2], [3]. One way to alleviate the tension between the

Manuscript received September 22, 2016; revised January 13, 2017;accepted January 26, 2017. Date of publication March 2, 2017; date ofcurrent version May 22, 2017. This work was supported in part by theGeneral Research Funds through the University Grant Committee of the HongKong Special Administrative Region, China, under Project CUHK 14202814,Project CUHK 14206315, and Project CUHK 14219016, in part by the U.S.Army Research Office under Grant W911NF-16-1-0448, and in part by the U.S. National Science Foundation under Grant ECCS-1549881. This paper waspresented at the 13th International Symposium on Modeling and Optimizationin Mobile, Ad Hoc and Wireless Networks, Mumbai, India, May 2015 [1].

J. Yu, M. H. Cheung, and J. Huang are with the Departmentof Information Engineering, The Chinese University of Hong Kong,Hong Kong (e-mail: [email protected]; [email protected];[email protected]).

H. V. Poor is with the Department of Electrical Engineering, PrincetonUniversity, Princeton, NJ 08544 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSAC.2017.2676958

mobile data demand and the network capacity is to utilizethe spectrum more efficiently, for example through spectrumsharing [4]–[6]. Another way is to flatten the demand curvethrough pricing [7]–[11]. More specifically, mobile serviceproviders have been experimenting with several innovativepricing schemes, such as usage-based pricing, shared dataplans, and sponsored data pricing, to extract more revenuefrom the growing data while sustaining a good service qualityto users. However, these schemes do not fully take advantageof the heterogeneous demands across all mobile users, andunused data in the monthly plan will be cleared at the endof the month. Recently, China Mobile Hong Kong (CMHK)launched the first 4G data trading platform in the world,called the 2nd exChange Market (2CM), which allows itsusers to trade their monthly 4G mobile data quota directlywith each other. In this platform, a seller can sell some of hisremaining data quota for the current month on the platformwith a desirable price set by himself. If a buyer wants to buysome data at the listed price, the platform will help completethe transaction and transfer the proper data amount from theseller’s quota to the buyer’s quota for that month.

However, there is a shortcoming of the current one-sided2CM mechanism. More specifically, 2CM is a sellers’ market,where a buyer cannot list his desirable buying price andquantity. This means that a buyer needs to frequently checkthe platform to see whether the current (lowest) selling priceis acceptable, while a seller does not know whether he cansell the data at his proposed price immediately. In other words,both buyers and sellers suffer from the incomplete informationof this one-sided market.

To improve the existing CMHK mechanism, we apply thewidely used Walrasian auction used in stock markets [12],[13]. In such a mechanism, both sellers and buyers can submittheir selling and buying prices and quantities to the platform.The platform clears some transaction whenever the highestbuying price among buyers is no smaller than lowest sellingprice among sellers. We are interested in understanding how auser should participate in such a market under the uncertaintyof his future data usage, given his remaining data quota of thecurrent month and the current prices and quantities of othersellers and buyers. More specifically, we would like to answerthe following questions: (i) Should a user choose to be a selleror a buyer? (ii) How much should he sell or buy?

The key feature of the user’s decision problem is the futuredata demand uncertainty, as there will be a satisfaction lossif the user’s realized demand exceeds his monthly data quota

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YU et al.: MOBILE DATA TRADING: BEHAVIORAL ECONOMICS ANALYSIS AND ALGORITHM DESIGN 995

(after incorporating the results of data trading), and there willbe a waste of money if the user’s realized demand is lessthan his monthly data quota (if the user purchases too muchdata). A typical approach to solving a user’s decision problemwith uncertainty is to maximize the user’s expected utility, i.e.,to apply expected utility theory (EUT) (e.g., [14]). Empiricalevidence [15], [16], however, has shown that the EUT modelcan deviate from real world behavior significantly due to thecomplicated psychological aspect of human decision-making.Alternatively, researchers in behavioral economics have shownthat prospect theory (PT), which establishes a more generaltheoretical model that includes EUT as a special case, pro-vides a psychologically more accurate description of decisionmaking under uncertainty, and explains some human behaviorsthat seem to be illogical under EUT [15].

More specifically, PT shows that a decision maker evaluatesan outcome significantly differently from what is commonlyassumed in EUT in several aspects: (1) Impact of refer-ence point: A PT decision maker’s evaluation is based onthe relative gains or losses comparing to a reference point,instead of the absolute values of the outcomes. (2) Thes-shaped asymmetric value function: A PT decision makertends to be risk-averse when considering gains and risk-seeking when considering losses. Furthermore, the PT decisionmaker is loss averse, in the sense that he strongly prefersavoiding losses to achieving gains. (3) Probability distortion:A PT decision maker tends to overweigh low probabilityevents and underweigh high probability events. As PT hasbeen shown to be more accurate than EUT in predicting humanbehavior [15]–[17], it has been applied to gain better under-standings of financial markets [18] and labor markets [19].However, to the authors’ knowledge, there have been no priorPT-based studies devoted to understanding the users’ decisionsin mobile data trading markets.

B. Contributions

In this paper, we aim to understand a user’s realistic tradingbehavior in a mobile data market, considering his future datademand uncertainty.

In the first part of the paper, we focus on deriving theoptimal trading decision of a user based on his remainingquota and possible demand till the end of the billing cycle,without considering future possible trading.1 Specifically, weformulate the problem as a two-stage optimization problem,in which the user decides whether to be a seller or a buyerin Stage I (at a given trading time), and then determines hisselling quantity (as a seller) or buying quantity (as a buyer) inStage II. Besides considering the optimal decision of a risk-neutral user in the EUT framework, we will also considerthe impact of the user’s risk preferences on the decision. Tobe more specific, a risk-seeking decision maker is aggressiveand wants to achieve a high maximum profit even with therisk of a low minimum profit, while a risk-averse decisionmaker is conservative and wants to guarantee a satisfactorylevel of minimum profit. PT provides a comprehensive ana-lytical framework for understanding the optimal decisions of

1For example, the billing cycle of a monthly data plan is a month.

different types of decision makers. However, the correspondingoptimization is non-convex, and hence is challenging to solve.Nevertheless, by exploiting the unimodal structure in each sub-interval of the feasible set, we can obtain a globally optimalsolution of the non-convex optimization problem. We furtherobtain some practical insight by comparing the analysis underPT and EUT for the case with binary outcomes.

In the second part of the paper, we introduce an algorithmfor autonomous and adaptive data trading based on the theorydeveloped in the first part. In such an algorithm, a usercan trade multiple times during a billing cycle, with eachtrading decisions being made in a “myopic” fashion withoutconsidering the possible future trading opportunities. Since auser’s risk preference will significantly impact the result ofthis algorithm, we design another algorithm to estimate theuser’s risk preference. We implement the algorithms on anAndroid app2 and evaluate our algorithm’s performances underdifferent risk preferences through numerical examples.

Our key contributions are summarized as follows:• Behavioral economics modeling of uncertainty: We use

prospect theory to model the user’s trading behavior underfuture data demand uncertainty. We consider all threekey characteristics of PT and derive key insights thatcharacterize the optimal selling and buying decisions.

• Characterization of the optimal trading solution: Despitethe non-convexity of the user’s decision problem, we areable to obtain a globally optimal solution by exploitingthe convexity and unimodality in different sub-intervalsof the feasible set. We further evaluate how differentbehavioral characteristics (i.e., reference point, probabil-ity distortion, and s-shaped valuation) affect this optimaldecision.

• Engineering insights on risk preferences: Comparing withthe benchmark EUT result, we show that a PT user witha low reference point is more willing to buy mobile dataand less willing to sell mobile data. Moreover, a PTuser is even more willing to buy mobile data when theprobability of high future data demand is small, mainlydue to the probability distortion.

• Evaluation of algorithms: We evaluate the user’s profitunder our proposed algorithm numerically. Based onthis, we show that a risk-averse user can achieve thehighest minimum profit, a risk-seeking user can achievethe highest maximum profit, and a risk-neutral user canachieve the highest average profit.

Next we review the literature in Section II. In Section III,we formulate the user’s utility functions under both EUT andPT. In Section IV, we compute the optimal user decision,and illustrate the insights through a special case of binaryoutcomes. In Section V, we explain the implementation ofour multi-trade algorithm on an Android app, which estimatesthe user’s risk preferences and compute the optimal tradingdecisions accordingly. In Section VI, we numerically evaluate

2Notice that the app is based on the real CMHK market, and hence it isdifferent from our theory in two aspects. First, there is no buyer’s market,and the seller will make a decision corresponding to a slightly lower than theminimum selling price. Second, a user can make several decisions during abilling cycle, based on his current quota and future data demand uncertainty.


the user’s optimal decision based on several model parameters,and compute the overall profit that our algorithm can achievein a billing cycle under different risk preferences. We concludethe paper in Section VII.

II. LITERATURE REVIEW

Previous studies of mobile data trading problems [20], [21]are based on EUT, in which users maximize their weightedaverage of utilities under different outcomes. To fully capturethe realistic human decision behaviors examined in severalwell known psychological studies in the past few decades [15],[16], [22], in this paper we apply the more general PT, whichtakes into account both the expected payoff and risk preferencein human decision making.

Research on using PT to understand user decisions incommunication networks and smart grids is in its infancy.Due to the complexity of modeling and analysis, all previousliterature has considered only one or two of the three keyfeatures of PT. Li and Mandayam in [23] and [24] andYang et al. in [25] compared the equilibrium strategies ofa binary decision game among wireless network end-usersunder EUT and PT, where they considered a linear valuefunction with probability distortion. Xiao et al. in [26] andWang et al. in [27] characterized the unique Nash equilibriumof an energy exchange game among microgrids under PT,where they considered a linear value function with probabilitydistortion. Yu et al. in [28] studied a secondary wireless oper-ator’s spectrum investment problem, where they considered alinear probability distortion and s-shaped value function. Tothe best of our knowledge, this paper is the first work thatstudies a mobile data trading problem under PT. We capture allthree characteristics of PT when modeling and analyzing theproblem, and as a result, we are able to gain a more thoroughunderstanding of the user’s optimal decisions based on hisspecific risk preferences and derive greater insight into thisproblem.

III. SYSTEM MODEL

In this paper, we consider the trading decision of a singleuser3 in a mobile data trading platform. We first introduce themobile data trading market in Section III-A. Then we discussthe user’s profile in Section III-B and his risk preferencesmodel in Section III-C. In Section III-D, we formulate theuser’s two-stage trading decision problem.

A. Mobile Data Trading Market

We consider a two-sided mobile data trading platform asshown in Fig. 1. The seller’s market lists the sellers’ proposedprices and the corresponding amount of data available for saleat each price. If a buyer wants to purchase some data quotaimmediately, he can choose to purchase at the minimum sellingprice πmin

s in the seller’s market. In Fig. 1, we have πmins =

3Note that there are many users in the market, and a single user’s decisionwill not significantly impact the market. So from a single user’s point of view,the market can be viewed as exogenously given and stochastically changing.

Fig. 1. Example of a trading decision with the data trading platform.

$20.4 Similarly, the buyer’s market lists buyers’ proposedprices and the corresponding amount of data demand at eachprice. If a seller wants to sell some data quota immediately, hecan choose to sell at the maximum buying price πmax

b . In Fig. 1,we have πmax

b = $16.Note that in Fig. 1, the maximum buying price

(πmaxb = $16) is lower than the minimum selling price

(πmins = $20). This is because those selling offers with prices

less than $16 have already been cleared by the market, so arethose buying requests with prices higher than $20.

B. User’s Profile

Remaining Data Quota: For the analytical model in SectionsIII and IV, we assume that the user makes the trading decisionwithout considering potential future trading in the same billingcycle. We use Q to denote his remaining data quota at the timeof the decision. For example, if the user subscribes to a dataplan of 5 GB per month and he has consumed 2 GB so far,then Q = 3 GB for the remaining time of the billing cycle.

Demand Uncertainty: The user has an uncertainty regardinghis future data demand from now till the end of the billingcycle. We assume that his future data demand d follows adiscrete distribution over the set of I possible values, {di :i ∈ I = {1, . . . , I }, d1 < . . . < dI }, with the correspondingprobability mass function P(d = di ) = pi with

∑Ii=1 pi = 1.

To avoid the trivial case, we assume that d1 < Q and dI > Q.We further define ı as the index such that dı < Q anddı+1 ≥ Q.

Satisfaction Loss: The user’s data plan has a two-partpricing tariff, by which the user pays a fixed fee for dataconsumption up to a monthly quota (5 GB in the previousexample), and a linear high usage-based cost for any extra dataconsumption. Such a pricing model is widely used by major

4As evidenced in the real CMHK market, we assume that the quantityassociated with the minimum selling price is large enough, such that a singlebuyer who wants to complete the trade immediately can simply consider asingle price πmin

s . Similar to the buying decision, we assume that the quantityassociated with the maximum buying price is large enough such that a singleseller who wants to sell his data immediately can simply consider a singleprice πmax

b . In this paper, we refer to HK dollar when we mention “dollar”or “$”.


Fig. 2. The s-shaped asymmetrical value function v(x) and the probabilitydistortion function w(p) used in PT.

operators like AT&T in the US and CMHK in Hong Kong [7].Specifically, the user needs to pay a price of κ ($/GB)5

if the user’s future data demand d exceeds his remainingdata quota Q. We define the satisfaction loss of the useras the additional payment (which is a non-positive term) forexceeding the monthly quota:

L(y) ={

0, if y ≥ 0,

κy, if y < 0,(1)

where y < 0 means that the quota is exceeded. Without datatrading, y = Q − d .

C. Risk PreferencesTo model the user’s data trading problem under future data

demand uncertainty, we consider the following three featuresof PT: the reference point Rp , s-shaped value function v(x),and probability distortion function w(p) [15], [29].

1) Reference Point: The reference point Rp indicates theuser’s physiological target of the outcome. The user considersan outcome a gain if it is higher than the reference point, anda loss if it is lower than the reference point. A high referencepoint means that the user is more likely to treat an outcome asa loss, and a low reference point means that he is more likelyto treat an outcome as a gain. This will significantly affect theuser’s subjective valuation of the outcome, as we will explainnext.

2) S-Shaped Asymmetrical Value Function: Fig. 2(a) illus-trates the value function v(x), which maps an objective out-come x to the user’s subjective valuation v(x). Notice that allthe outcomes are measured relatively to the reference point Rp ,which is normalized to x = 0 in the figure. Behavioral studiesshow that the function v(x) is s-shaped, which is concavein the gain region (i.e., x > 0, when the outcome is largerthan the reference point) and convex in the loss region (i.e.,x < 0, when the outcome is smaller than the reference point).Moreover, the impact of loss is larger than the gain, i.e.,|v(−x)| > v(x) for any x > 0. A commonly used valuefunction in the PT literature is [15]

v(x) ={

xβ, if x ≥ 0,

−λ(−x)β, if x < 0,(2)

5For example, for a 4G CMHK user, κ = 60.

Fig. 3. Two-stage optimization.

where 0 < β ≤ 1 and λ ≥ 1. Here β is the risk parameter,where a smaller β means that the value function is moreconcave in the gain region, and hence the user is more risk-averse in gains. Meanwhile, a smaller β also means that thevalue function is more convex in the loss region, and hencethe user is more risk-seeking in losses. Under a high referencepoint Rp , the user is more likely to encounter losses, hence asmaller β means that the user is more risk-seeking dominant.Under a low reference point Rp , however, a smaller β meansthat the user is more risk-averse dominant. The valuation ofthe loss region is further characterized by the loss penaltyparameter λ, where a larger λ indicates that the user is moreloss averse.

We note that the value function in EUT is a special caseof PT, with the parameter choices λ = β = 1, and the valuefunction becomes a linear function, i.e. v(x) = x . In this case,the choice of reference point only leads to a constant shiftof the value function without affecting the user’s decision.Without loss of generality, we will choose Rp = 0 for theEUT case.

3) Probability Distortion: Fig. 2(b) illustrates theprobability distortion function w(p), which captures humans’psychological over-weighting of low probability events andunder-weighting of high probability events [15]. A commonlyused probability distortion function is [29]

w(p) = exp(−(− ln p)μ), 0 < μ ≤ 1, (3)

where p is the objective probability of an outcome and w(p)is the corresponding subjective probability. Here μ is theprobability distortion parameter, which reveals how a per-son’s subjective evaluation distorts the objective probability.A smaller μ means a larger distortion.

When μ = 1, we have w(p) = p, which refers to the caseof EUT without probability distortion.

D. Two-Stage Decision Problem

Next we derive the user’s expected utilities associated withbeing a buyer and a seller, respectively, with the remainingdata quota Q and a probability distribution of the future datademand d .

Fig. 3 shows how a user makes a trading decision in twostages. In Stage I, he decides whether to sell or to buy in themarket. In Stage II, he decides the price and quantity as aseller or as a buyer, depending on his choice in Stage I.


1) Stage I’s Problem: In Stage I, a user makes a decisiona ∈ A = {s, b}, where s and b correspond to being a sellerand a buyer, respectively. We use u(a) to denote the user’smaximum utility that can be achieved under the choice ofa (through the optimized decisions in Stage II), as definedin (5) and (6). Then, the user’s Stage I optimization problem is

maxa∈{s,b} u(a). (4)

2) Stage II’s Problem: A buyer in Stage II needs to decidehis buying quantity qb, given the minimum selling price πmin

sas discussed in Section III-A. Thus, the buyer’s problem is tomaximize his expected utility6:

u(b) = maxqb≥0

U(b, qb) =I∑

i=1

w(pi )v(−πmins qb

+ L(Q + qb − di ) − Rp), (5)

where πmins qb is the cost of buying the data at the price πmin

s ,and L(Q + qb − di ) is the satisfaction loss after trading if thefuture data demand is di .

On the other hand, a seller in Stage II needs to decide hisselling quantity qs , given the maximum buying price πmax

b :

u(s) = maxqs≥0

U(s, qs) =I∑

i=1

w(pi )v(πmaxb qs

+ L(Q − qs − di ) − Rp), (6)

where πmaxb qs is the revenue obtained from selling the data

at the price πmaxb , and L(Q − qs − di ) is the satisfaction loss

after trading if the future data demand is di .In the next section, we will solve the user’s two-stage opti-

mal trading problems (4), (5), and (6) by backward induction.

IV. SOLVING THE TWO-STAGE OPTIMIZATION PROBLEM

In this section, we first derive the user’s optimal selling orbuying decision in Stage II. Then, we consider whether theuser chooses to be a seller or a buyer in Stage I by comparinghis maximum achievable utilities under both cases.

Problems (5) and (6) are challenging analytically due to thenon-convexity of the s-shaped value function v(x), especiallyunder an arbitrary reference point. To obtain clear engineeringinsights, we focus on two choices of reference points in thefollowing analysis:

• High reference point Rp = 0: This choice reflectsthe user’s expectation of observing the lowest possibledemand level d1 and hence having no excessive demand.

• Low reference point Rp = κ(Q − dI ) < 0: Thischoice reflects the user’s expectation of observing thehighest possible demand level dI and paying for thecorresponding excessive demand (without trading).

The high reference point refers to the best case scenariowithout trading, while the low reference point refers to theworst case scenario without trading. Best case and worst case

6For all the optimization problems discussed in this paper, we will considerthe three features of PT as discussed in Section III-C, and EUT is a specialcase under proper parameter choices. We will not repeat these points eachtime.

scenarios are widely used concepts in risk management [30],and are frequently used as benchmarks for evaluating invest-ment performance [18]. For a particular given outcome, it ismore likely to be considered as a gain under Rp = κ(Q − dI )than under Rp = 0.

To get around the non-convexity issue of problems(5) and (6), we partition the whole feasible range of thedecision variable into several sub-intervals based on the piece-wise linearity of the satisfaction loss function L(y) in (1), suchthat the objective function in each sub-interval is either convexor unimodal. We then compute the unique optimal solution byconfining the problem to each sub-interval, and finally identifya global optimum by comparing the optimal objective functionvalues of all sub-intervals.

In order to understand the impact of the risk parameterson the optimal trading decisions, we further consider a specialcase with binary possible demand I = 2, in which case we areable to characterize the user’s optimal decision in closed-form.

A. Stage II: Solving Buyer’s Problem (5)

1) General Case of I ≥ 2: The technique for solvingproblem (5) will depend on the choice of reference point.Under the high reference point Rp = 0, we will partitionthe whole feasible range of qb into I − ı + 1 sub-intervalsbased on I possible realizations of di . We will show thatU(b, qb) is convex in each sub-interval, which implies that theoptimal q∗

b for each sub-interval is one of the two boundarypoints. An example of U(b, qb) under Rp = 0 is shown inFig. 4(a). In this example, we assume I = 3, where d1 < Qand Q < d2 < d3, so that ı = 1. As we can see fromFig. 4(a), the feasible range of qb can be divided into threesub-intervals: [0, d2 − Q], [d2 − Q, d3 − Q], and [d3 − Q,∞).The function U(b, qb) is convex in each sub-interval, so thatwe can find a globally optimal qb by comparing the functionvalues at the boundary points of the sub-intervals (i.e., U(b, 0),U(b, d2 − Q), and U(b, d3 − Q)).

Under the low reference point Rp = κ(Q − dI ), we canshow that U(b, qb) is a concave function in each sub-interval.Thus, the optimal q∗

b for each sub-interval is either at oneof the boundary points or at the critical point (where the firstorder derivative equals zero). As long as we obtain the optimalsolution for each sub-interval, we can compute a globallyoptimal solution by comparing the I − ı + 1 sub-intervals’optimal points.

Before introducing the following theorem, we first define

Xb ={

qb : ∂U(b, qb)

∂qb= 0 under Rp = κ(Q − dI )

}

, (7)

which is the set of critical points. We can also prove (see [31])that there are at most I critical points in the whole feasiblerange (i.e., |Xb| ≤ I ).

Theorem 1: The buyer’s optimal buying quantity obtainedby solving problem (5) under the high reference point Rp = 0is

q∗b = arg max

qb∈{Q−di ,i=ı+1,...,I }∪{0}{U(b, qb)}, (8)


Fig. 4. Examples of (a) U(b, qb) in (5) under Rp = 0, and (b) U(s, qs)in (6) under Rp = 0.

and that under the low reference point Rp = κ(Q − dI ) is

q∗b = arg max

qb∈{Q−di ,i=ı+1,...,I }∪Xb∪{0}{U(b, qb)}. (9)

The proof of Theorem 1 is given in [31].Next, we show the impact of the value function, probability

distortion, and reference point in the special case of binaryoutcomes.

2) Special Case of I = 2: To better illustrate the impact ofvarious parameters on the buyer’s optimal decision, we nextconsider the buyer’s optimization problem with I = 2 possibledemands. More specifically, there are two possible realizationsof the future data demand: d1 = dl and d2 = dh , with 0 <dl < Q < dh . The probability of observing the high demanddh is p, and the probability of observing the low demand dl

is 1 − p.We first define the buyer’s threshold price under different

reference points. As we will show in Theorem 2, the optimalbuying amount equals dh − Q when the minimum selling priceπmin

s is below the buyer’s threshold price:

π EU Tb � κp, π PT h

b � κ

[w(p)

w(p) + w(1 − p)

] 1β

,

π PT lb � κw(p)

w(1 − p) + w(p). (10)

Theorem 2: The buyer’s optimal buying amount obtainedby solving problem (5) under EUT is

q∗b =

{dh − Q, if πmin

s < π EU Tb ,

0, if πmins ≥ π EU T

b .(11)

His optimal buying amount obtained by solving problem (5)under PT with high reference point Rp = 0 is

q∗b =

{dh − Q, if πmin

s < π PT hb ,

0, if πmins ≥ π PT h

b ,(12)

and that with low reference point Rp = κ(Q − dh) is

q∗b

=

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

dh − Q,

if πmins < π PT l

b ,

0,

if πmins ≥ π PT l

b and β = 1,κ(Q − dh)

[w(p)(κ − πmin

s )β

w(1 − p)πmins

]1

β − 1 + πmins

,

if πmins ≥ π PT l

b and β < 1.

(13)

Theorem 2 is a special case of Theorem 1, and the proofis given in [31]. The result in (11) follows directly from (12)and (13) by setting β = μ = λ = 1.

In (11) and (12), we observe that the optimal buyingquantity is discontinuous at the buyer’s threshold price. Thisis due to the linearity of the utility function in the EUT caseand the convexity of the utility function in the PT case withRp = 0. Details are given in [31].

From Theorem 2, we have the following observations onthe impact of the reference point when we fix the probabilitydistortion parameter μ = 1 (hence removing the impact ofprobability distortion).

Observation 1: (PT vs EUT under the high reference point)When μ = 1 and Rp = 0, we have π PT h

b < π EU Tb . This means

that under a high reference point, a PT buyer is less willingto purchase mobile data than an EUT buyer.

Observation 2: (PT vs EUT under the low reference point)When μ = 1 and Rp = κ(Q − dh), we have π PT l

b = π EU Tb .

However, the optimal buying quantity q∗b of the PT buyer

in (13) is no smaller than that of the EUT buyer in (11) underthe same price πmin

s . This means that under a low referencepoint, a PT buyer is more willing to purchase mobile datathan an EUT buyer.

Notice That Buying Data Reduces the Risk That the FutureData Demand Exceeds the Quota: As we have mentioned inSection III-C, a smaller β means that the buyer is more risk-seeking in losses and more risk-averse in gains. Under a highexpectation (e.g., Rp = 0), the buyer with a smaller β (in thePT case) is more risk-seeking dominant and will not buy data.Under a low expectation (e.g., Rp = κ(Q − dh) < 0), thebuyer is more risk-averse dominant, and will buy an amountequal to dh − Q, which will completely eliminate the risk thatthe future data demand exceeds the updated quota dh .

B. Stage II: Solving Seller’s Problem (6)

1) General Case of I ≥ 2: To solve problem (6) underboth Rp = 0 and Rp = κ(Q − dI ), we partition the wholeinterval of qs into ı + 1 sub-intervals. We show that U(s, qs)has a special unimodal structure in each sub-interval. Thefirst order derivative of a unimodal function will cross zeroat most once in each sub-interval, and thus the optimal q∗

s foreach sub-interval is either at one of the boundary points orat the critical point. Then, by comparing the ı + 1 optimal


points, we can find a globally optimal solution. An exampleof U(s, qs) under Rp = 0 is shown in Fig. 4(b). In thisexample, we assume I = 3, where d1 < d2 < Q andQ < d3, so that ı = 2. As we can see from Fig. 4(b), thefeasible range of qs can be divided into three sub-intervals:[0, Q − d2], [Q − d2, Q − d1], and [Q − d1,∞). The functionU(s, qs) is unimodal in each sub-interval, so that we canfind a global optimal q∗

s by comparing the boundary functionvalues of the sub-intervals (i.e., U(s, 0), U(s, Q − d2), andU(s, Q − d1)) and the function values of critical points ifthey exist (i.e., U(s, qs), qs ∈ {qs : ∂U (s,qs)

∂qs= 0 under

Rp = 0}).Before introducing the following theorem, we first define

Xsh ={

qs : ∂U(s, qs)

∂qs= 0 under Rp = 0

}

and

Xsl ={

qs : ∂U(s, qs)

∂qs= 0 under Rp = κ(Q − dI )

}

, (14)

which are the sets of critical points. We can also prove (see[31]) that there are at most I critical points in the wholefeasible range under both Rp = 0 and Rp = κ(Q − dI ) (i.e.,|Xsh | ≤ I and |Xsh | ≤ I ).

Theorem 3: The seller’s optimal selling quantity q∗s of

problem (6) under PT with the high reference point Rp = 0 is

q∗s = arg max

qs∈{Q−di ,i=1,...,ı}∪Xsh∪{0}{U(s, qs)}, (15)

and that with the low reference point Rp = κ(Q − dI ) is

q∗s = arg max

qs∈{Q−di ,i=1,...,ı}∪Xsl∪{0}{U(s, qs)}. (16)

The proof of Theorem 3 is given in [31]. Next, we showthe impact of the value function, probability distortion, andreference point for the special case of binary outcomes.

2) Special Case of I = 2: To illuminate the above result,we next consider the seller’s optimization problem with I = 2possible demands.

We first define the seller’s threshold price under differentrisk preferences. As we will show in Theorem 4, the optimalselling amount equals Q − dl when the maximum buyingprice πmax

b is above the seller’s threshold price. The seller’sthreshold prices π EU T

s , π PT hs , and π PT l

s are the unique7

solutions of the following three equations:

π EU Ts = κp, (17)

λ(κ − π PT hs )βw(p)

(π PT hs )βw(1 − p)

(

1 + κ(dh − Q)

(κ − π PT hs )(Q − dl)

)β−1

= 1,

(18)

w(1− p){[(π PTls −κ)Q + κdh − π PT l

s dl]β −[κ(dh − Q)]β}= λw(p)[(κ − π PT l

s )(Q − dl)]β. (19)

Theorem 4: The seller’s optimal selling quantity in problem(6) under EUT is

q∗s =

{Q − dl , if πmax

b > π EU Ts ,

0, if πmaxb ≤ π EU T

s .(20)

7The proof of the uniqueness is in [31].

His optimal selling quantity in problem (6) under PT with thehigh reference point Rp = 0 is

q∗s

=

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

Q − dl,

if πmaxb > π PT h

s ,

0,

if πmaxb ≤ π PT h

s and β = 1,κ

κ − πmaxb

(dh − Q)

(w(1 − p)πmax

bβ

w(p)λ(κ − πmaxb )β

) 1

β − 1 − 1

,

if πmaxb ≤ π PT h

s and β < 1,

(21)

and that with the low reference point Rp = κ(Q − dh) is

q∗s =

{Q − dl, if πmax

b > π PT hs ,

0, if πmaxb ≤ π PT h

s .(22)

Theorem 4 is a special case of Theorem 3, and the proof ofTheorem 4 is given in [31]. The result in (20) follows directlyfrom (21) and (22) by setting β = μ = λ = 1.

In (20) and (22), we observe that the optimal selling quantityq∗

s is discontinuous at the seller’s threshold price. This is dueto the linearity of the utility function in the EUT case andthe unimodality of the utility function in the PT case withRp = κ(Q − dh). Details are given in [31].

From Theorem 4, we have the following observations onthe impact of the reference point when we fix the probabilitydistortion parameter μ = 1.

Observation 3: (PT vs EUT under the high reference point)When μ = 1 and Rp = 0, we have π PT h

s < π EU Ts . This means

that under a high reference point, a PT seller is more willingto sell mobile data than an EUT seller.

Observation 4: (PT vs EUT under the low reference point)When μ = 1 and Rp = κ(Q − dh), we have π PT l

s > π EU Ts .

This means that under a low reference point, a PT seller isless willing to sell mobile data than an EUT seller.Contrary to Buying Data, Selling Data Increases the Risk Thatthe Future Data Demand Exceeds the Quota: Under a highexpectation (e.g., Rp = 0), a seller with a smaller β is morerisk-seeking dominant and will sell a large amount (Q − dl ).Under a low expectation (e.g., Rp = κ(Q − dh) < 0), a sellerwith a smaller β is more risk-averse dominant and will notsell data.

In Stage I, the user decides whether to be a seller or a buyerby comparing the maximum utilities that he can achieve inboth cases.

V. IMPLEMENTATION OF MOBILE DATA TRADING

Building upon our theoretical analysis in Sections III and IV,here we consider several issues related to the practical imple-mentation of these ideas. We first discuss the mobile data trad-ing algorithm that allows a user to trade multiple times duringa billing cycle to adjust his trading decision in Section V-A.


Fig. 5. Screenshots of the app: (a) Homepage, (b) Market information, and(c) Settings.

Fig. 6. Flowchart of the algorithm (Android app).

Then we introduce a practical algorithm to estimate the user’srisk preferences in Section V-B. Since a user’s predictionof his future data demand may not be accurate, the usermay want to make multiple data trading decisions over time.Here, we design a mobile data trading algorithm to facilitatesuch trading in a semi-automatic fashion, which reduces theuser’s need to frequently check the market prices and estimatethe future data demand. The mobile data trading algorithmrelies on Algorithm 1 (to be discussed in Section V-B) toestimate the user’s risk preferences, and can provide tradingsuggestions at any time based on the current market price, theuser’s current usage, and his risk preferences. Our algorithmis implemented as an Android app, the interface of which isshown in Fig. 5. Fig. 5(a) shows the homepage screen of theAndroid app, which involves four areas: calculator, markethistory, usage history, and settings. Fig. 5(b) shows the currentCMHK market information, which includes the selling pricesand quantities. Fig. 5(c) shows various system parameters thatcan be changed by the user, such as the trading notificationfrequency.8

A. Mobile Data Trading Algorithm Design

Fig. 6 illustrates the key function modules of the mobileapp:

• Market Information: The app retrieves the CMHK mobiledata trading market information, in order to determine theminimum selling price πmin

s and the maximum buying

8The user may not want to be disturbed by frequent notifications. He canadjust this by either turning off the notification alarm, or reduce the notificationfrequency to a low level, e.g., once per 24 hours.

price πmaxb .9

• Trading Frequency: We assume that the app will makeT trading decision in a billing cycle.10 In the followingdiscussions, for the ease of exposition we assume thetrading frequency is once a day, i.e., the user makesT = 30 trading decisions during a monthly billingcycle.11

• Usage: The app records the user’s usage everyday.We denote the actual data usage of day j in month m asδm, j , where month m has Tm days.

• Demand Prediction: We use an adaptive model for theuser’s future data demand prediction. Specifically, assum-ing that we are on day j of months m, we aim toestimate the distribution of the future data demand ofthe remaining time (i.e., from day j to day Tm) of monthm by considering the previous I months’ (denoted asmonths m −1, ..., m− I ) data usage during the same timeperiod (i.e., from day j + 1 to day Tm ). The predicteddata usage of the last Tm − j days in month m for i ∈ I is

di :=Tm−i∑

j=j+1

δm−i, j . (23)

We will use them to predict the future data demand ofthe rest of month m with an equal probability. That is,pi = 1/I for i ∈ I .

• Quota: The remaining quota from day j to the endof month m is Q j , which corresponds to Q inSections III and IV. The value of Qj is an input to theutility maximization problem in (5) and (6), which isupdated every day as follows:

Qj :={

Qj−1 + q∗j−1 − δm,j−1, if j ≥ 2,

Q, if j = 1.(24)

Here q∗j−1 is the trading quantity on day j−1 that we will

discuss below, and it can be zero if no trading happens onthat day. Thus, the first line of (24) means that the quotais updated based on the trading quantity q∗

j−1and usage

δm,j−1, while the second line specifies the initializationof the month quota to Q on the first day of the month.

• Risk Parameters: The risk parameters include the valuefunction parameters β and λ in (2), the probabilitydistortion parameter μ in (3), and the reference pointRp in (5) and (6).

• Utility Maximization Problem: The app solvesproblem (4), which involves solving (5) and (6),based on the market information (πmax

b and πmins ), the

9Recall from Section I-B that there is no buyer’s market in the actual CMHKplatform, so πmax

b in problem (6) is not well defined. To address this issue,we note that although different sellers can set different prices in the CMHKmarket, the system will always try to satisfy the buyers’ demands with thelowest selling price. Based on the fact that the selling quantity at the minimumselling price is often very large (e.g., 4740 GB in Fig. 5(b) on June 22, 2016),the seller is not able to sell his data at a price higher than the minimum sellingprice, so we can assume that the maximum buying price is the same as theminimum selling price, i.e., πmax

b = πmins .

10By default, the app will send every trading suggestion as a notification.The user can change the notification frequency as shown in Fig. 5(c).

11The optimal trading decision may be not to sell or buy any data, i.e.,skipping some of the trading opportunities.


Algorithm 1 Estimation of Value Function Parameters λand β

1 Input: Quota (Qj ), risk parameters (μ, Rp),usage(δm−i, j , i = 0, . . . , I, j = 1, . . . , Tm−i ), marketinformation (πmin

s , πmaxb ).

2 for j = 1 to Tm do3 for i = 1 to I do

4 di :=Tm−i∑

j=j+1δm−i, j and pi := 1/I

5 dmin := arg mini∈I di and dmax := arg maxi∈I di

6 Users input the indifference prices (πbind and π s

ind )7 Substitute dmin, dmax, πb

ind , and π sind into (25) and

(26), and solve them for λ and β8 Set λj := λ and βj := β9 Update Qj according to (24)

10 Output: λ :=∑Tm

j=1 λj

Tmand β :=

∑Tmj=1 βj

Tm

user’s current quota Qj , the risk parameters, usage, andfuture data demand prediction in (23). The output of theutility maximization problem on day j is the optimalbuying or selling quantity q∗

j, which in turn will update

the quota as in (24). Note that a positive q∗j denotes

an optimal buying quantity (i.e., output of (5)), while anegative q∗

j denotes an optimal selling quantity (i.e., theoutput of (6) multiplied by (−1)).

The detailed algorithm for computing the data tradingdecisions with the user’s specific risk preferences is shownin [31].

B. Risk Parameter Estimation

Since the trading decisions are user-dependent, we need toestimate each user’s specific risk preferences. In particular,we want to estimate the user’s value function parametersλ and β in (2), which are problem-specific. For example,the parameters for making financial investments and enjoyingentertainment may be quite different even for the same user.

Algorithm 1 presents the pseudo code of our algorithm toestimate the user’s value function parameters λ and β. Thebasic idea is to solve the two indifference equations below[15], [16] for λ and β in the value function in (2).

I∑

i=1

w(pi )v(−πb

ind (dI − Qj ) + L(dI − di ))

=I∑

i=1

w(pi )v(L(Qj − di )

), (25)

andI∑

i=1

w(pi )v(π s

ind (Qj − d1) + L(d1 − di ))

=I∑

i=1

w(pi )v(L(Qj − di )

). (26)

Here, πbind and π s

ind are the user’s indifference prices, whereπb

ind corresponds to the price below which he is willing buydata at dmax − Qj , and π s

ind is the price above which he iswilling to sell data at Qj − dmin, where dmax and dmin aredefined in line 5.

In [31], we establish that every pair of indifference equa-tions (25) and (26) of Algorithm 1 has a unique solution forλ and β.

When estimating the indifference price, the user may nothave an exact value in mind. Hence, to improve the estimationaccuracy of Algorithm 1, we have an estimation period ofTm days (line 2 to 9), and have Tm pairs of indifferenceequations with different demand predictions. Then, we choosethe average values among the solutions of the equations(line 10).

VI. PERFORMANCE EVALUATION

In Section VI-A, we first illustrate the impact of thePT model parameters on the user’s optimal decision fora single trade in the billing cycle. Then we evaluate theperformance of our algorithm by numerically simulating thecase of making multiple decisions in a billing cycle in SectionVI-B.12

The simulations illustrate the following insights for a PTuser’s optimal trading decision (by comparing with an EUTuser): (i) Risk-seeking dominant under a high reference point:Without considering the effect of probability distortion, a PTbuyer is risk-seeking and is less willing to buy mobile dataand more willing to sell mobile data than an EUT buyer.(ii) Probability distortion: For the case of binary demandrealizations, when the probability of high demand is small,a PT buyer is risk-averse and is more willing to buy mobiledata. On the other hand, when the probability of high demandis large, a PT buyer is risk-seeking and is less willing to buymobile data. (iii) Profit: A PT user achieves a lower averageprofit than an EUT user. However, a risk-seeking dominantuser can achieve a higher maximum profit, while a risk-aversedominant user can guarantee a higher minimum profit.

A. Impact of PT Model Parameters

In this subsection, we illustrate the impact of the PT modelparameters (λ, β, and μ) and market parameters (πmin

s andπmax

b ) on the user’s optimal decision with I = 20 possibleoutcomes in Figs. 7, 8, and 9, and then illustrate the impact ofthe demand uncertainty parameter ( p) with binary outcomes(I = 2) in Fig. 10. Due to space limitations, we will onlyconsider the high reference point Rp = 0 for the PT case.

Impact of the Loss Penalty Parameter λ and the RiskParameter β on a Buyer’s Threshold Price π PT h

b in (10): Herewe assume μ = 1 and p1 = p2 = . . . = p20 = 0.05. Fig. 7shows that the buyer threshold price π PT h

b is increasing in βfor a fixed value of λ, and does not change in λ for a fixedvalue of β. Note that a higher threshold price means that thebuyer is more willing to buy mobile data. This is because under

12In this section, all financial quantities are in units of dollars and all dataquantities are in units of GB.


Fig. 7. Buyer’s threshold price π PT hb versus loss penalty parameter λ for

different values of β.

Fig. 8. Seller’s selling quantity q∗s versus maximum buying price πmax

b fordifferent values of λ.

Fig. 9. Seller’s selling quantity q∗s versus maximum buying price πmax

b fordifferent values of β.

the high reference point Rp = 0, the buyer will consider anypossible outcome as a loss. In this case, a smaller β meansthat the user is more risk-seeking in losses, so he does notneed to purchase mobile data to reduce the risk that the futuredata demand exceeds the quota. Meanwhile, notice that λ isused to differentiate the value function in the loss region andgain region in (2). As the user will never encounter a gain inthis case, the threshold price is independent of λ.

Impact of the Loss Penalty Parameter λ on a Seller’sOptimal Selling Quantity q∗

s : Fig. 8 illustrates how the seller’sselling quantity q∗

s changes with the maximum buying priceπmax

b and λ. Here we assume that p1 = p2 = . . . = p20 =0.05, μ = 1, and β = 0.8. Fig. 8 shows that q∗

s increasesin πmax

b . This is because as πmaxb increases, the seller gains

more revenue from the trade, hence he wants to sell more.Fig. 8 also shows that under the same value of πmax

b , q∗s is

non-increasing in λ. This is because, as λ increases, the sellerbecomes more loss averse, and hence he will sell less in orderto avoid a heavy loss when the future data demand is high.

Fig. 10. Buyer’s threshold price π PT hb versus probability distortion para-

meter μ for different values of p.

Fig. 11. User profit with different risk preferences.

Fig. 12. User profit versus the price variation probabilities under uniformlydistributed usage.

Impact of the Risk Parameter β on a Seller’s Optimal SellingQuantity q∗

s : Fig. 9 illustrates how the seller’s selling quantityq∗

s changes with the maximum buying price πmaxb and β. Here

we assume that μ = 1 and λ = 2. Fig. 9 shows that q∗s is

decreasing in β under a small πmaxb , and is increasing in β

under a large πmaxb . This is because under the high reference

point Rp = 0, the seller will encounter either a small gainor a large loss. In this case, a smaller β means that the useris more risk-averse dominant, hence becomes more willingto sell mobile data. However, when πmax

b is large, the sellerwill encounter a large gain from selling data. In this case, asmaller β means that the user is more risk-seeking dominant,and hence becomes less willing to sell mobile data.

Impact of the Probability Distortion Parameter μ on aBuyer’s Threshold Price π PT h

b in (10): To illustrate the impactof the probability distortion parameter, we assume binaryoutcomes with I = 2. Fig. 10 considers three differentprobabilities of high demand: high (p = 0.8), medium(p = 0.5), and low (p = 0.2). Here we assume β = 0.8 and


λ = 2. We can see that π PT hb decreases in μ when p = 0.2, is

independent of μ when p = 0.5, and increases in μ when p =0.8. As a smaller μ means that the buyer will overweigh thelow probability more, he becomes more risk-averse (i.e., π PT h

bdecreases) when p is small. Similarly, since a smaller μ meansthat the buyer will underweigh the high probability more, heis more risk-seeking (i.e., π PT h

b increases) when p is large.

B. Evaluation of the Mobile Data Trading Algorithm

We now evaluate the total profit generated by our algo-rithm’s trading decisions (introduced in Section V) in a billingcycle. For each simulation, we consider a billing cycle ofT = 30 time slots. In the simulation settings, we assumethat across two consecutive time slots, the prices πmax

b andπmin

s increase by one unit (i.e., dollar) with probability pc,decrease by one unit with probability pc, or remain unchangedwith probability 1 − 2 pc. The changes of πmax

b and πmins

are independent. We set the monthly quota Q = 2 GB, andrandomly generate the previous I months’ total demand di

(defined in (23)) with a mean value of 2 GB.13 The algorithmcalculates the trading decision in every time slot based on theuser’s risk preferences under the high reference point Rp = 0.Specifically, we define the profit14 Pm of month m as

Pm =Tm∑

j=1

−q∗j πj − L

⎛

⎝Q +Tm∑

j=1

q∗j −

Tm∑

j=1

dm,j

⎞

⎠ , (27)

which consists of two parts: the net revenue due to selling orbuying data, and the payment due to satisfaction loss. In (27), apositive q∗

jmeans that the user buys data quota in day j , while

a negative q∗j

means that the user sells data quota in day j .By repeatedly running the simulation for 1000 billing cycles

with randomly generated demands and prices, we first eval-uate the impact of risk preferences on the maximum profit,minimum profit, and the average profit. We then comparethe average profit achieved by the algorithm implemented byour mobile app and several other benchmark strategies underdifferent price variations with different price variations. In thefirst benchmark strategy “trade with certainty”, we assumethat the user is not willing to trade when he has uncertainty.This means that he will only trade once near the end of hisbilling cycle, when he knows the exact value of his monthlyusage. In the second benchmark strategy “no data trading”,the user does not trade at all. We compare these three strategiesunder the uniformly distributed usage.

In Fig. 11, we assume pc = 0.1, and plot the profit ofthe user with different risk preferences. The risk parametersof different users are: (a) risk-averse dominant user: β = 1,λ = 2; (b) risk-neutral user (EUT user): β = λ = 1; and(c) risk-seeking dominant user: β = 0.8, λ = 1.15 Since

13In our simulation, we generate both uniformly distributed and normallydistributed (with standard deviation 1/3) demands.

14The profit may be negative, meaning that the total revenue due to sellingdata is lower than the payment due to buying data plus the payment due tosatisfaction loss.

15A larger λ indicates that the user is more loss averse, hence is more risk-averse. Since we have assumed a high reference point Rp = 0, a smaller βmeans the user is more risk-seeking dominant.

an EUT user makes decision only by maximizing expectedprofit, we can see from Fig. 11 that he can achieve thehighest average profit. On the other hand, a PT user makes adecision by taking into account both the expected profit and itsrisk preferences. More specifically, although both risk-seekingdominant and risk-averse dominant PT users achieve a lowerexpected profit comparing to an EUT user, the risk-seekingdominant user can earn a higher maximum possible profit,while the risk-averse dominant user can guarantee a higherminimum possible profit. This is because the risk-seekingdominant user trades more quota, and hence earns more whenthe price change is profitable and loses more when the pricechange is unprofitable.

In Fig. 12, we plot the profit of the risk-neutral user versusthe price variation probability pc under uniformly distributedusage. Fig. 12 shows that the gap between the profits generatedby “our mobile app” and the “trade with certainty” strategiesincreases with pc, e.g., the gap at pc = 0.4 is 500% larger thanthe gap at pc = 0.1. This is because our mobile app suggestsusers buy when the price is low and sell when the price is high,hence taking advantage of the price variation. Comparing withthe “no data trading” strategy, the user significantly benefitsfrom the data trading market (i.e., reduces his net payment by50%).

VII. CONCLUSION

In this paper, we have considered a mobile data tradingmarket that is motivated by the CMHK’s 2CM platform.We have analyzed the optimal trading decision of a singleuser under a large market regime. We have compared andcontrasted the user’s optimal decisions under prospect theoryand expected utility theory, and have highlighted several keyinsights. Comparing with an EUT user, a PT user with a highreference point is less willing to buy mobile data and morewilling to sell mobile data. Moreover, when the probability ofhigh demand is low, a PT user is more willing to buy mobiledata compared with an EUT user. On the other hand, when theprobability of high demand is high, a PT user is less willing tobuy mobile data. In addition, we have designed a mobile datatrading algorithm to recommend multiple trading decisionsbased on the user’s current usage and risk preferences. Ourresults suggest that a risk averse dominant user can achievethe highest minimum profit, a risk-seeking dominant user canachieve the highest maximum profit, while a risk-neutral usercan achieve the highest average profit.

This study has demonstrated that more realistic behavioralmodeling based on PT can provide important insights inunderstanding user behavior in mobile data trading. In thefuture work, we plan to use our app to collect data from thereal market to help us understand users’ actual behavior indata trading, to study the trading decision equilibria amongall the market users and to consider the optimization of theservice provider’s data plan.

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Junlin Yu (S’14) is currently pursuing the Ph.D.degree with the Department of Information Engi-neering, the Chinese University of Hong Kong.His research interests include behavioral economicalstudies in wireless communication networks andoptimization in mobile data trading.

Man Hon Cheung received the B.Eng. and M.Phil.degrees in information engineering from the ChineseUniversity of Hong Kong (CUHK) in 2005 and2007, respectively, and the Ph.D. degree in electricaland computer engineering from the University ofBritish Columbia (UBC) in 2012. He is currently aPost-Doctoral Fellow with the Department of Infor-mation Engineering, CUHK. His research interestsinclude the design and analysis of wireless networkprotocols using optimization theory, game theory,and dynamic programming, with current focus on

mobile data offloading, mobile crowd sensing, and network economics.He serves as a Technical Program Committee member of the IEEE ICC,Globecom, and WCNC. He received the IEEE Student Travel Grant forattending IEEE ICC 2009. He received the Graduate Student InternationalResearch Mobility Award from UBC and the Global Scholarship Programmefor Research Excellence from CUHK.

Jianwei Huang (F’16) received the Ph.D. degreefrom Northwestern University in 2005. He was aPost-Doctoral Research Associate with PrincetonUniversity from 2005 to 2007. He is currently anAssociate Professor and the Director of the Net-work Communications and Economics Laboratory,Department of Information Engineering, the ChineseUniversity of Hong Kong. He has co-authored sixbooks, including the textbook on Wireless NetworkPricing. He was a co-recipient of eight Best PaperAwards, including the IEEE Marconi Prize Paper

Award in Wireless Communications in 2011. He received the CUHK YoungResearcher Award in 2014 and the IEEE ComSoc Asia-Pacific OutstandingYoung Researcher Award in 2009. He has served as the Chair of theIEEE ComSoc Cognitive Network Technical Committee and the MultimediaCommunications Technical Committee. He is a Distinguished Lecturer ofthe IEEE Communications Society and a Thomson Reuters Highly CitedResearcher in Computer Science.

H. Vincent Poor (S’72–M’77–SM’82–F’87)received the Ph.D. degree in EECS from PrincetonUniversity in 1977. From 1977 until 1990, hewas on the faculty of the University of Illinoisat Urbana–Champaign. Since 1990, he has beenon the faculty at Princeton, where he is currentlythe Michael Henry Strater University Professorof Electrical Engineering. From 2006 to 2016,he served as the Dean of Princeton’s School ofEngineering and Applied Science. His researchinterests are in the areas of information theory,

statistical signal processing and stochastic analysis, and their applications inwireless networks and related fields, such as smart grid and social networks.Among his publications in these areas is the book Mechanisms and Gamesfor Dynamic Spectrum Allocation (Cambridge University Press, 2014).

Dr. Poor is a member of the National Academy of Engineering andthe National Academy of Sciences, and a foreign member of the RoyalSociety. He is also a fellow of the American Academy of Arts and Sciences,the National Academy of Inventors, and other national and internationalacademies. He received the Marconi and Armstrong Awards of the IEEECommunications Society in 2007 and 2009, respectively. Recent recognitionof his work includes the 2016 John Fritz Medal, the 2017 IEEE AlexanderGraham Bell Medal, honorary professorships at Peking University andTsinghua University, both conferred in 2016, and a D.Sc. honoris causafrom Syracuse University in 2017.

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