Using experiments to compare the predictive power of models of multilateral negotiations

International Journal of Industrial Organization 70 (2020) 102612

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International Journal of Industrial Organization journal homepage: www.elsevier.com/locate/ijio

Using experiments to compare the predictive power of models of multilateral negotiations ✩ Cary A. Deck a,b, Charles J. Thomas b,c,∗ a

Department of Economics, Finance and Legal Studies, The University of Alabama, 200 Alston Hall, Tuscaloosa, AL, 35487, USA Econonomic Science Institute, Chapman Univeristy, One University Dr., Orange, CA 92866, USA c Department of Economics, Clemson University, 228 Sirrine Hall, Clemson, SC 29634, USA b

a r t i c l e

i n f o

Article history: Received 17 May 2019 Revised 26 February 2020 Accepted 3 March 2020 Available online 19 March 2020 JEL Codes: C7 (Game Theory & Bargaining Theory) C9 (Design of Experiments) D4 (Market Structure, Pricing and Design) L1 (Market Structure, Firm Strategy and Market Performance) Keywords: Negotiations & Bargaining Laboratory Experiments Procurement Mergers & Acquisitions Investment

a b s t r a c t We conduct unstructured negotiations in a laboratory experiment designed to empirically assess the predictive power of models of the multilateral negotiations observed in diverse strategic settings. For concreteness we consider two sellers negotiating with a buyer who wants to make only one trade, and we categorize the models by whether introducing a second seller to bilateral negotiations always, never, or sometimes increases the buyer’s payoff. Our experiment features two scenarios within which the three categories of models have observationally distinct predictions: a differentiated scenario with one high-surplus seller and one low-surplus seller, and a homogeneous scenario with identical high-surplus sellers. In both scenarios the buyer tends to trade with a high-surplus seller at terms indistinguishable from those in bilateral negotiations with a high-surplus seller, meaning that introducing a competing seller does not substantially affect the observed terms of trade. Our findings match the predictions from models in the never-matters category, supporting their use when modeling multilateral negotiations. © 2020 Elsevier B.V. All rights reserved.

1. Introduction Multilateral negotiations are an exchange mechanism frequently observed when one party wishes to trade with one of several others offering potentially different amounts of surplus to be split. For example, procurement often involves negotiations with suppliers who differ in their quality or goodness-of-fit, as illustrated by Express Scripts’ decision to include on its formulary AbbieVie’s hepatitis C drug Viekira Pak rather than Gilead’s blockbuster drug Sovaldi.1 The takeover con✩ Deck served as the Rasmuson Chair in Economics at the University of Alaska Anchorage while this project was conducted and recognizes their generous support. Thomas (corresponding author) thanks Chapman University’s Economic Science Institute & Argyros School of Business and Economics for their generosity in inviting him to be an Affiliated Research Scientist. This work was completed in part while Thomas was a Visiting Associate Professor at Clemson University’s John E. Walker Department of Economics, whom he thanks for their hospitality. Patrick Warren, Bart Wilson, Co-Editor Armin Schmutzler, and two anonymous referees provided helpful comments, but any errors are our own. Funding: This work was supported by the University of Alaska Anchorage. ∗ Corresponding author. E-mail addresses: [email protected] (C.A. Deck), [email protected] (C.J. Thomas). 1 “New Hep C Drug Gets Helping Hand — As High-Cost Treatments Vie, Express Scripts Opts to Use AbbVie’s Over Gilead’s.” Wall Street Journal, Dec 22, 2014, B.1.

https://doi.org/10.1016/j.ijindorg.2020.102612 0167-7187/© 2020 Elsevier B.V. All rights reserved.

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test for Pep Boys pitted Carl Icahn against Bridgestone, with both acquirers presumably having different benefits from the transaction.2 General Electric’s decision to relocate its corporate headquarters to Boston concluded a lengthy battle among 40 municipalities, reportedly including ones in Connecticut, Georgia, New York, and Texas.3 Several theoretical models yielding distinct predictions are applicable to multilateral negotiations, and in this paper we provide evidence to discriminate among them based on how well they predict actual negotiated outcomes. Selecting an appropriate model matters for analyzing specific negotiation settings, such as the three mentioned in the prior paragraph. It also matters for analyzing other strategic problems to which the negotiation model merely is an input, such as investment, product design, mergers, hold-up, dual-sourcing, entry, collusion, or R&D. For example, using a different bargaining model might qualitatively change one’s conclusions regarding whether countervailing power in the supply chain reduces prices to final consumers, as in von Ungern-Sternberg (1996); merger decisions and technology choice, as in Inderst and Wey (2003); or the competitive impact of resale price maintenance, as in Rey and Verge (2010). In Section 2 we describe three models that we frame as procurement settings in which two sellers negotiate with a buyer who wants to make only one trade, then we categorize them and related models based on how their predicted outcomes change when moving from bilateral to multilateral negotiations. In our framework these categories differ in whether introducing a weakly inferior seller to a bilateral setting always, never, or sometimes increases the buyer’s negotiated payoff, as a function of how close of a substitute is the new seller for the original one. We assess the models’ empirical relevance by comparing their predicted outcomes to actual outcomes of unstructured negotiations conducted in the laboratory. Using an experiment allows us to control variables that might not be observable with naturally-occurring data: we induce players’ preferences, specify the possible trading partners, and perfectly observe negotiated outcomes. We conduct unstructured negotiations rather than implement structured protocols from the models, because those models’ purpose is to make meaningful predictions about situations lacking such structure. The models impose structure on behavior not to reflect actual protocols by which negotiations are conducted in practice, but to enable derivation of equilibrium strategies that lead to predicted outcomes. Consequently, assessing those theoretical predictions’ practical reliability requires empirical evidence about unstructured negotiations.4 Our approach follows insights from Friedman (1953), who recognizes that the measure of a model’s value is how well it predicts rather than how closely its assumptions match reality. Our approach also follows that taken in the many early experimental studies of bargaining surveyed by Roth (1995), and in more recent research such as Leider and Lovejoy (2016). The experimental design we present in Section 3 describes two scenarios we use for which the three categories of models have observationally distinct combinations of predictions: a differentiated scenario with one high-surplus seller and one lowsurplus seller, and a homogeneous scenario with two identical high-surplus sellers. In the always-matters category of models, the second seller affects the outcome no matter how poor of a substitute it is for the first seller. In the never-matters category, the second seller is irrelevant to the outcome no matter how close of a substitute it is for the first seller. In the sometimes-matters category, the second seller affects the outcome if and only if it is a sufficiently close substitute for the first seller. In Section 4 we show that in both scenarios the buyer tends to trade with a high-surplus seller at terms indistinguishable from those in a baseline scenario with the buyer and a single high-surplus seller negotiating bilaterally, meaning that introducing a weakly inferior seller does not affect the terms of trade. Our findings match the predictions from the never-matters models, supporting their use when modeling multilateral negotiations. While our main goal is informing model selection in applications, our analysis also contributes to understanding how rivalry affects the intensity of competition. This issue has long been of interest in industrial organization, as shown by the industry studies in Weiss (1989) and the historical empirical and theoretical references in Schmalensee (1989) and Shapiro (1989). In Section 5 we relate our findings to those from theoretical and empirical research on procurement that finds wrinkles in the conventional wisdom that increasing the number of sellers benefits buyers by increasing the intensity of competition.

2. Modeling background In this section we describe three complete-information models of multilateral negotiations in strategic environments that allow trade with different partners to yield different surpluses; we also discuss how these and other models can be categorized by their predicted outcomes. Although the models fit varied situations in which one party wants to trade with one of several others, for concreteness we frame the models as a buyer negotiating with two sellers. The different surpluses available from trade with different sellers reflect differences in the sellers’ opportunity costs or the buyer’s value for each seller’s product. We denote the surplus (or “pie”) available from trading with seller i by i , and we assume 1 ≥ 2 > 0.

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“Icahn Wins Pep Boys Bidding Contest.” Wall Street Journal, Dec 31, 2015, B.3. “GE Decamps to Boston — City Beats Back Fierce Competition as the Company Moves its Base from Connecticut.” Wall Street Journal, Jan 14, 2016, B.1. 4 Implementing structured protocols is a distinct experimental approach aimed at testing a model’s internal validity rather than its relationship to naturally-occurring phenomena. 3

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2.1. A baseline model of bilateral negotiations We begin by describing the bilateral negotiation model from Rubinstein (1982) that forms the basis for the multilateral negotiation models considered later, following the presentation in Muthoo (1999). A buyer and seller 1 negotiate to split the surplus 1 > 0, and they have instantaneous rates of time preference rB > 0 and r1 > 0. The game’s structure and parameters are common knowledge among both players. Trade is conducted as follows, where time is measured in discrete periods t ∈ {0, 1, 2, . . .} that are of length  > 0. In an even-numbered period t ∈ {0, 2, 4, . . .} seller 1 makes a proposal (st , 1 − st ) ∈ [0, 1 ]2 to the buyer that specifies the amount st of the surplus 1 that seller 1 demands for itself, with the remainder 1 − st that it offers to the buyer. If the buyer accepts, then the negotiations conclude. Otherwise, in odd-numbered period t + 1 the buyer makes a proposal (bt+1 , 1 − bt+1 ) ∈ [0, 1 ]2 to seller 1 that specifies the amount bt+1 of the surplus 1 that the buyer demands for itself, with the remainder 1 − bt+1 that it offers to seller 1. If seller 1 accepts, then the negotiations conclude. Otherwise, play continues to the next period. A transaction in an even-numbered period t yields the buyer and seller 1 respective payoffs (1 − st )e−rB t  and −r st e 1 t  , while a transaction in an odd-numbered period t yields the buyer and seller 1 respective payoffs bt e−rB t  and (1 − bt )e−r1 t  . If no transaction occurs in any period, then each party’s payoff is 0. For notational convenience define δk ≡ e−rk  , where δ k ∈ (0, 1) is player k’s discount factor, for k ∈ {B, 1}. This infinite-horizon game has a unique subgame-perfect Nash equilibrium (SPNE) in which the players’ payoffs depend on whose turn it is to make offers. Deriving the equilibrium exploits the game’s stationary structure: each even-numbered period is the initial period of an infinite-horizon subgame that begins with seller 1 making an offer to the buyer, and every such subgame is identical. Similarly, each odd-numbered period is the initial period of an infinite-horizon subgame that begins with the buyer making an offer to seller 1, and every such subgame is identical. The players’ SPNE payoffs in the “seller-offer” and “buyer-offer” subgames are



πBso = δB  π = bo B

1 − δ1 1 − δ1 δB

1 − δ1 1 − δ1 δB





1

 1

1 − δB 1 − δ1 δB

and

π1so =

and

π = δ1



bo 1

 1

1 − δB 1 − δ1 δB

 1 .

The SPNE features each player offering just enough to induce its rival to accept, namely the rival’s net present value of waiting until the next period. For example, seller 1 s payoff π1bo when the buyer makes offers equals δ1 π1so, the net present value to seller 1 of rejecting the buyer’s offer and moving to a “seller-offer” subgame next period. Muthoo (1999, Ch. 3.2) suggests the appropriate case to consider is when the time between offers () converges to zero, because a party making a counteroffer has incentives to do so quickly to reduce its cost of delay. The limiting values of the payoffs as  → 0 also do not depend on who makes the initial proposal, so there is no first-mover advantage in the limit. As  → 0 the buyer’s and seller 1 s payoffs approach

πB∗ =

 r 1

r1 + rB



1 and π1∗ =

 r B

r1 + rB



1 .

Notice that the players split the surplus equally if they have identical discount rates. Otherwise the more patient player receives more than half of the surplus 1 . 2.2. Three models of multilateral negotiations The following three models extend Rubinstein’s bilateral negotiation model to allow for more bargaining parties. While each model has an infinite horizon and uses alternating offers, the models differ in the specifics of their bargaining protocols. As a reminder, our presentation adds seller 2 who has discount rate r2 , and trade with whom creates surplus 2 ∈ (0, 1 ], which lets us assess the impact of adding a weakly inferior seller to an initially bilateral negotiation. In each model the buyer trades with seller 1 in equilibrium, so seller 2 s payoff is 0. Osborne and Rubinstein (1990, Ch. 9.3) consider a buyer with the same value for each seller’s product, while seller 1 s cost is weakly lower than seller 2 s.5 Players have the same discount rate, and play begins with the buyer making offers to both sellers. Seller 1 responds first, seller 2 responds second, and the buyer must trade with the first seller to accept its offer. If neither seller accepts, then next period the sellers make simultaneous offers to the buyer. The buyer chooses which offer to accept, and play continues if the buyer rejects both offers. Assuming offers are unrestricted, as  → 0 the buyer’s and seller 1 s payoffs approach

πB∗ = 1 and π1∗ = 0. 5 The authors actually model a seller facing two buyers with different values for the product of a seller with the same cost for serving either buyer. Our formulation reverses the players’ labels, but is otherwise identical to the original.

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Introducing seller 2 benefits the buyer, regardless of how small is 2 ∈ (0, 1 ]: the buyer obtains the entire surplus 1 , and seller 1 s payoff drops to 0. The equilibrium payoffs just given emerge after eliminating the curious assumption Osborne and Rubinstein make that the buyer must demand the same payoff from both sellers. That restriction on offers dramatically affects the negotiated outcome: in the original model the buyer’s payoff is lower because it is not allowed to make very low offers to each seller. While assumptions need not match protocols used in practice for a model to be useful, one must be wary if such assumptions harm the party on whom they are imposed. This point is made strongly in Binmore (1985): (p. 270): Of course, if a particular bargaining model imposes constraints on a player’s behavior that he would prefer to violate and no mechanism exists in the situation one is trying to model that would prevent such violations, then little insight can be expected from the model. (p. 283): The only firm principle would seem to be that one cannot expect players to submit to constraints that limit their payoffs unless there is some mechanism that forces the constraints on them. Given the preceding points, we view the modified version of the Osborne and Rubinstein model, without the restriction that the buyer make identical price offers to both sellers, as reflecting a distinct model of multilateral negotiations. After all, in multilateral negotiations it is not apparent that the buyer’s offers would be restricted in that manner. Ray (2007) provides an overview of research on coalition formation that can be applied to our setting. Players have the same discount rate, and play begins with the buyer making an offer to one seller. If the seller accepts, then the negotiations conclude. If not, then next period that seller makes an offer to the buyer. Except in the first period, the current offeror is the player who rejected the prior period’s offer, so one seller might never make nor receive an offer. As  → 0 the buyer’s and seller 1 s payoffs approach

πB∗ =

1 2

and

π1∗ =

1 2

.

Introducing seller 2 does not affect the buyer’s payoff, regardless of how close 2 is to 1 : the buyer and seller 1 continue to split equally the surplus 1 .6 Thomas (2018) models one buyer who wants to trade with one of several sellers. Players can have different discount rates, and play begins with the sellers making simultaneous offers to the buyer. If the buyer accepts an offer, then the negotiations conclude. If not, then next period the buyer makes simultaneous offers to the sellers, who respond simultaneously. The buyer chooses whether to trade with a seller that accepted its offer, but it can retract accepted offers. When the buyer and seller 1 have the same discount rate, as  → 0 their payoffs approach



πB∗ = max

1 2



, 2



and

π1∗ = min

1 2



, 1 − 2 .

Introducing seller 2 benefits the buyer if and only if the surplus 2 from trading with seller 2 exceeds the buyer’s payoff 1 1 2 from bilateral negotiations with seller 1: the buyer’s payoff increases from 2 to 2 in that case, but otherwise remains at

1 2

.

2.3. Categorizing models of multilateral negotiations We fit the preceding models into three categories distinguished by how adding a weakly inferior seller to a bilateral setting affects the buyer’s negotiated payoff. The new seller can range from being a very poor substitute for the original seller (2 near 0) to being a perfect substitute (2 = 1 ). The modeling categories differ in whether the new seller always matters (AM), never matters (NM), or sometimes matters (SM) to the buyer’s negotiated payoff, as reflected in the buyer’s   equilibrium payoffs as  → 0: 1 in the always-matters category, 21 in the never-matters category, and max[ 21 , 2 ] in the sometimes-matters category. Models like the modified version of Osborne and Rubinstein (1990, Ch. 9.3) fit in the always-matters category; the buyer extracts the entire surplus from seller 1, regardless of how small is the surplus available to be split with seller 2. This extreme bargaining power is familiar from the ultimatum game first analyzed by Guth et al. (1982), and from bilateral bargaining models in which one party makes all of the offers.7 Models like Ray (2007) fit in the never-matters category; the buyer’s negotiation with seller 1 proceeds as if seller 2 is not present. Other models with similar results include Osborne and Rubinstein (1990, Ch. 9.4.1) and Houba and Bennett (1997). Finally, models like Thomas (2018) fit in the sometimes-matters category; the buyer has no advantage when seller 2 is a distant competitor to seller 1 (unlike in the AM category), but it can leverage a closely competing seller 2 s presence (unlike in the NM category). Similar results emerge in the unmodified version of the Osborne and Rubinstein (1990, Ch. 9.3) 6 This model’s outcome coincides with traditional notions of fairness, but our objective is not to assess players’ motives; we wish to determine which model best predicts outcomes. 7 Osborne and Rubinstein (1990, Ch. 3.10.3) briefly discuss bilateral negotiations with one-sided offers.

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Table 1 Buyer’s predicted payoff, by modeling category and negotiation scenario.

Always Matters Never Matters Sometimes Matters

Baseline

Homogeneous

Differentiated

$5 $5 $5

$10 $5 $10

$10 $5 $5

model and in models of bilateral negotiations with exogenously-specified outside options, such as Binmore et al. (1989), Shaked (1994), and Muthoo (1999, Ch. 5.6). Our experiment discriminates among the three categories’ predictions by having subjects negotiate in two multilateral scenarios, with surpluses specified so the three categories of models have distinct combinations of predictions. Simply speaking, we compare predicted and actual outcomes when rival sellers are either very similar or very different. Of course, the experimental results might be inconsistent with all three categories of models. 3. Experimental design We conducted 10 laboratory sessions at the University of Alaska Anchorage, each consisting of nine human subjects drawn from a standing economic participant pool. Three randomly selected subjects in each session were permanently assigned to be buyers, with the other six permanently assigned to be sellers. None of our 90 unique subjects had previously participated in any related studies. All monetary amounts were denoted in US dollars, and subjects were paid their cumulative earnings. The average subject earned $9.29 plus a $5 participation payment for the one-hour experiment.8 Subjects read instructions informing them they would engage in a sequence of two or three distinct interactions involving buyers and sellers trying to agree on a price at which to trade.9 This buyer/seller framing is commonly used in market experiments to facilitate subjects’ understanding, by using the familiar notion of price as a means to allocate surplus.10 Subjects had no information about the nature of the actual or possible interactions they would encounter, in terms of available surpluses and the number of buyers or sellers. Within a session each subject participated in each of the following three scenarios at most once. In the baseline scenario a buyer negotiates with a high-surplus seller whose cost is $0 to produce a good the buyer values at $10. In the homogeneous scenario a buyer negotiates to trade with one of two high-surplus sellers. In the differentiated scenario a buyer negotiates to trade with one of a high-surplus seller and a low-surplus seller whose cost is $0 to produce a good the buyer values at $2.11 Each session was temporally divided into three phases, and within a phase subjects were matched into groups to participate in one of the three scenarios.12 We matched subjects so none interacted more than once, a “perfect-strangers protocol” that replicates the models’ one-shot strategic nature by preventing reputation-building or reciprocity. We recognize that having subjects participate in each scenario only once prevents them from learning through experience, but that is a compromise we make to maintain the perfect-strangers protocol. Combining several replications of each scenario with the perfect-strangers protocol would have required prohibitively large numbers of subjects in the lab at the same time. Table 1 reports the buyer’s predicted payoff for each modeling category and negotiation scenario, assuming identical discount rates and that the time between offers () converges to zero.13 We specified the scenarios’ costs and values to let us distinguish among the modeling categories by exploiting their distinct combinations of predictions in the homogeneous and differentiated scenarios. Although each category predicts the buyer’s payoff is $5 in the baseline scenario, we had subjects negotiate bilaterally to calibrate observed behavior. Table 2 depicts one sequence of subject-matchings; in it, Subject 1 is a buyer who interacts with Subjects 4 and 5 in the homogeneous scenario in phase 1, with Subjects 7 and 8 in the differentiated scenario in phase 2, and with Subject 9 in the baseline scenario in phase 3. Other matchings are denoted similarly. To control for learning effects or other behav-

8 Participants were recruited for one hour due to the untimed negotiations, but most sessions finished in approximately 30 minutes including directions and payment. 9 Appendix A contains a copy of the instructions. 10 Market frames have been studied in ultimatum games, where they appear to (weakly) promote self-interested behavior. Hoffman, et al. (1994) report that market framing led to more self-interested behavior than did abstract framing, while Cox and Deck (2005) found no effect of market framing on outcomes. These findings suggest market framing should not lead subjects toward altruistic behavior. 11 Three subjects in the seller role necessarily are inactive when the buyers engage in bilateral negotiations with other sellers. To balance expected payments, the sellers who are inactive in the baseline scenario are put in the favorable position of being the high-surplus seller in the differentiated scenario. 12 In the experiment we referred to the phases as periods. Here we use “phase” to avoid confusion with our use of “period” to denote a point at which a party can make an offer in the bargaining models presented in Section 2. 13 For readers wary of the latter assumption, obtaining sufficient patience to distinguish among Section 2’s modeling predictions can be done even with very impatient subjects and a period-length nowhere near 0: supposing subjects’ discount rate is 100% per year (which is extremely high and reflects 1 ; applying great impatience) and a period is 1 hour (which is extremely long, given that the experiments all concluded in less than an hour),  = 24×365 the associated discount factor of 0.999886 to the non-limiting payoffs from the models described in Section 2 yields the separation we need among their predictions.

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Table 2 Sample subject matching. Sellers Buyers

Subject 4

Subject 5

Subject 6

Subject 7

Subject 8

Subject 9

Subject 1 Subject 2 Subject 3

H–1 H–2 –

H–1 H–3 L–2

– H–1 H–2

L–2 H–1 H–3

H–2 – H–1

H–3 L–2 H–1

Table entries S – P indicate the surplus of the seller (H or L) when interacting with a buyer and the phase (1, 2, or 3) in which they interacted.

Fig. 1. Histogram of buyers’ observed payoffs in baseline scenario.

ioral spillovers, across sessions we used all six possible temporal orderings of the three scenarios (baseline, homogeneous, differentiated; differentiated, baseline, homogeneous; etc.). A matched buyer and seller could communicate with each other both formally and informally. Formal communication consisted of a numeric price offer from the buyer or seller, acceptance of which constituted an agreement and ended the phase for that group of matched subjects. No structure was imposed on the making of price offers. For example, one party could replace its old offer with a new offer, without waiting for a counteroffer by the other party; an offer could be withdrawn at any point before it was accepted; and a new offer did not have to improve upon a previous offer. Informal communication consisted of unstructured, non-binding, real-time text-messaging whose content was unrestricted, except that messages could not contain personally identifying information or offensive language. We anticipated subjects would use this informal channel to discuss possible price offers and offers from rivals. Matched sellers could not communicate with each other, and a seller could not observe price offers or text messages exchanged between its matched buyer and the other seller. A seller who did not trade was informed only that the buyer traded with the other seller. Unmatched subjects could not communicate with each other. Likewise, no subject received information about trading outcomes for other groups of subjects. At the start of each phase, matched subjects learned the number of sellers and the surplus from trade with each seller. There was no time limit on negotiations, nor any mechanism by which a party could terminate the process without trading. 4. Experimental results We present two sets of results. Our primary results assess the predictive power of the three categories of models, using all negotiated outcomes: 30 baseline, 30 homogeneous, and 30 differentiated. Our secondary results analyze how the characteristics of individual negotiations relate to outcomes, based on the chats and formal offers in all 90 negotiations.14 4.1. Assessing the models’ predictive power Beginning with behavior in the baseline scenario, we report our main results in three findings that statistically assess the models’ predictive power. We complement the formal analysis with visual representations of the negotiated payoffs. Fig. 1 is a histogram of buyers’ negotiated payoffs in the baseline scenario;15 the modal payoff is the predicted value of $5. Finding 1. Buyers’ negotiated payoffs in the baseline scenario of bilateral negotiations are statistically indistinguishable from the predicted value of $5. 14

Appendix B briefly provides some sample negotiations. Prices could be negotiated in cents and subjects were paid to the penny. The distributions in Figures 1-3 round each realized payoff to the nearest dollar. Fifty-three percent of payoffs in the baseline scenario were exactly $5. 15

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Fig. 2. Histogram of buyers’ observed payoffs in homogeneous and differentiated scenarios. Table 3 Statistical analysis of buyers’ payoffs in homogeneous and differentiated scenarios.

Average Buyer Payoff Standard Deviation of Buyer Payoff Number of Observations z-test of Ho : Average Buyer Payoff = $5 z-test of Ho : Average Buyer Payoff = $9 Relative chance payoff is $5 rather than $9

Homogeneous Scenario

Differentiated Scenario

$5.03 1.63 30 p-value = 0.9098 p-value < 0.0001 4.62 × 1038

$5.71 1.58 22 p-value = 0.0362 p-value < 0.0001 7.10 × 1019

We test buyer payoff against a value of $9 rather than $10 because prices are forced to be non-negative; because buyer payoff is found to be less than $9 on average, it is also less than $10. The reported p-values are based on the two-sided z-test and the relative chance is the likelihood ratio calculated using the density of the standard normal distributions evaluated at the z-statistics. The z-test is used as an approximation because the distribution of payoffs is not normal. The results reported for the differentiated scenario exclude observations in which the buyer purchased from the lowsurplus seller, but if all data are used the average buyer payoff is $4.44, the p-values are 0.2235 and < 0.0 0 01 for testing the mean is $5 and $9, respectively, and the likelihood ratio is 5.08 × 1020 .

Evidence: In the 30 outcomes in the baseline scenario, the average buyer’s payoff is $4.77 (σˆ = 1.48), which is not statistically different from $5 (z-statistic = −0.8527, p-value = 0.3938).16  The similarity between the buyers’ observed and predicted payoffs in bilateral negotiations implies there is no need to use observed outcomes to normalize behavior in the other scenarios.17 This result also supports our use of the modeling assumptions that subjects have identical discount rates and that the time between offers () converges to zero. Turning to our primary goal of discriminating among the AM, NM, and SM categories, Fig. 2 shows histograms of buyers’ negotiated payoffs in the homogeneous and differentiated scenarios. We focus on buyers rather than sellers because every buyer can trade in both scenarios, while every seller cannot. In both scenarios the modal payoff is the one predicted by the NM category. Fig. 3 is a scatterplot of ordered pairs of each buyer’s payoffs in the homogeneous and differentiated scenarios. Each marker’s size indicates the relative frequency of a particular payoff-pair, while the large open squares denote the predicted payoff-pairs for each modeling category. The experimental data visually match best the NM category, with the modal outcome pair equal to the prediction from the NM category. Finding 2. Buyers’ negotiated payoffs in the homogeneous and differentiated scenarios are generally consistent with the nevermatters category of models, but they are inconsistent with the always-matters and sometimes-matters categories. We conclude that the NM category has greater predictive power than do the AM or SM categories. Evidence: In the 30 outcomes in the homogeneous scenario, the average buyer’s payoff is $5.03 (σˆ = 1.63). Table 3 reports the results of a hypothesis test comparing observed buyers’ payoffs in the homogeneous scenario to a value of $5 as predicted by NM. Because prices must be non-negative, it is not appropriate to conduct a similar test that the mean buyer’s payoff is $10 as predicted by AM and SM. Therefore, we use a conservative test that the mean is $9. If there is evidence that the mean is less than $9, then the mean also is less than $10. The average buyer’s payoff in the homogeneous scenario

16

We use z-tests to approximate p-values because the bounds on prices imply the errors are not normally distributed. For example, if the buyers’ payoffs were $8 in the baseline scenario, then observing buyers’ payoffs are $8 in the homogeneous and differentiated scenarios could be considered evidence in favor of the never-matters category. 17

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Fig. 3. Each buyer’s observed payoffs in homogeneous and differentiated scenarios. Size of marker indicates relative frequency of buyers with the given pair of negotiated payoffs. Black markers indicate buyers who purchased from the high-surplus seller in the differentiated scenario, while gray markers indicate buyers who purchased from the low-surplus seller.

is highly statistically different from $9 (p-value < 0.0 0 01), but it is not statistically different from $5 (p-value = 0.9098).18 Further, the likelihood ratio indicates the observed data are 4.62 × 1038 times more likely to have been generated by a distribution with a mean of $5 than with a mean of $9. This pattern is consistent with the NM category, but it is inconsistent with the AM or SM categories. In the 30 outcomes in the differentiated scenario, the average buyer’s payoff is $4.44, but this includes eight instances in which the buyer purchased from the low-surplus seller.19 These eight observations are shown in Fig. 3 with light gray markers. In the 22 outcomes in which the buyer traded with the high-surplus seller, the average buyer’s payoff is $5.71 (σˆ = 1.58). Table 3 reports the results of hypothesis tests comparing observed buyers’ payoffs in the differentiated scenario to both a value of $9 and a value of $5. The average buyer’s payoff is highly statistically different from $9 (p-value < 0.0 0 01), but it is also statistically different from $5 (p-value = 0.0362). However, the observed data are 7.10 × 1019 times more likely to have been generated by a distribution with a mean of $5 than with a mean of $9. This pattern is somewhat consistent with the NM and SM categories, but it is inconsistent with the AM category. From the preceding results, we conclude that the never-matters category has greater predictive power than do the always-matters or sometimes-matters categories.  Our preceding analyses consider separately each scenario’s average buyer’s payoff, but the three categories of models also predict how a buyer’s payoff differs across scenarios. By leveraging our experimental design’s within-subject nature, we assess the difference in each buyer’s payoff across scenarios. For example, if a buyer’s payoff is $5.75 in the differentiated scenario and $6.00 in the homogeneous scenario, then the payoff difference is $0.25. This technique accounts for variation in buyer-specific attributes such as negotiating ability or a preference for altruism or “fair-mindedness.” Moreover, simply comparing average payoffs across scenarios is inappropriate because observations in different scenarios are not independent. Finding 3. A particular buyer’s negotiated payoff does not differ across scenarios, which implies its payoff is unaffected by a second seller’s presence or type. This result is consistent with the never-matters category of models, but it is inconsistent with the 18 The power of both tests is close to 1 given the small sample-standard deviation under the assumption that the alternative hypothesis is that the mean buyer’s payoff equals X when the null hypothesis is a mean payoff of 14-X. The same is true for the differentiated scenario. 19 Four of the eight buyers who purchased from the low-surplus seller in the differentiated scenario first participated in the homogeneous scenario, suggesting it is unlikely buyers who purchased from the low-surplus seller mistakenly believed they could make two purchases in the differentiated scenario. Further, of the 90 subjects who participated in this study, only five (6%) indicated any level of confusion in a post-experiment questionnaire. Of these, two were in the role of a buyer. After the experiment, one buyer who traded with a low-surplus seller indicated having done so because the electronic chat with that seller was enjoyable. Inspecting the negotiations suggests some trades with the low-surplus seller were driven by the high-surplus seller responding slowly or offering a very high price.

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Table 4 Within-buyer payoff differences across scenarios: observed and predicted. Homogeneous Payoff – Baseline Payoff

Differentiated Payoff – Baseline Payoff

Observed Payoff Difference Average Standard Deviation Number of Observations z-test of H0 : Payoff = $0 z-test of H0 : Payoff = $5 Relative chance Payoff is $0 rather than $5

-$0.264 1.77 30 p-value = 0.4156 p-value < 0.0001 1.96 × 1046

$0.728 2.39 22 p-value = 0.1538 p-value < 0.0001 6.08 × 1014

Predicted Payoff Difference Always Matters Never Matters Sometimes Matters

$5 $0 $5

$5 $0 $0

Homogeneous Payoff – Differentiated Payoff -$0.477 2.42 22 p-value = 0.3543 p-value < 0.0001 2.23 × 1024 $0 $0 $5

The reported p-values are for a z-test of the null hypothesis that the average within-buyer difference between scenarios is $0 based on a two-sided alternative. Comparisons involving the differentiated scenario only include buyers who purchased from the high-surplus seller. If all observations are used, then the results are qualitatively unchanged. The p-values for testing the mean within-subject difference equals $0 between differentiated and baseline and between homogeneous and differentiated are 0.5041 and 0.2429, respectively. The p-values are both < 0.0 0 01 for testing the mean within-subject difference is $5. The likelihood ratios of 3.39 × 1024 and 5.35 × 1015 still strongly favor an average change of $0 over an average change of $5. Table 5 Characteristics of the negotiation process. Summary Statistics for Negotiation Characteristics

Baseline

Homogeneous

Differentiated

Average Duration (in seconds) Average Number of Chat Messages Average Number of Formal Offers Buyer Makes First Formal Offer Formal Offers Alternate between Buyer and Seller Percent of Negotiations Lasting Under 30 S Percent of Negotiations with Only One Offer

129.0 4.7 4.8 53% 40% 13% 17%

90.7 4.8 5.2 30% 57% 30% 3%

89.9 4.4 4.1 43% 57% 27% 17%

−0.002 −0.041 −0.136 −0.332∗ 0.012

0.335∗ 0.431∗ ∗ 0.510∗ ∗ ∗ 0.077 −0.381∗ ∗

0.066 0.074 −0.100 0.090 0.074

Correlation of Negotiation Characteristics and Buyer’s Payoff Duration (in seconds) Number of Chat Messages Number of Formal Offers Buyer Makes Initial Formal Offer Formal Offers Alternate between Buyer and Seller ∗ ∗∗

,

, and

∗∗∗

denote significant correlations at the 10%, 5%, and 1% significance level, respectively.

always-matters and sometimes-matters categories. We conclude that the NM category has greater predictive power than do the AM or SM categories. Evidence: For each pair of scenarios, Table 4 reports buyers’ observed and predicted payoff differences, plus statistical comparisons of them. The unit of observation is the difference in a buyer’s payoffs in the paired scenarios. The average payoff change for a buyer going from the baseline to the homogeneous scenario is -$0.264, from the baseline to the differentiated scenario is $0.728, and from the differentiated to the homogeneous scenario is -$0.477. The payoff changes are not statistically different from $0 (p-values = 0.4156, 0.1538, 0.3543), but each is highly statistically different from $5 (each p-value < 0.0 0 01). We find no statistical evidence that a buyer’s payoff changes due to a second seller’s presence or type. This result is predicted by the NM category of models, but not by the AM or SM categories.  4.2. Exploratory analysis of the negotiations We now report an exploratory analysis of the negotiation process. The top panel of Table 5 provides summary statistics by scenario. Interestingly, negotiations took longer in the baseline scenario than in either the homogeneous or differentiated scenarios, which had similar durations. Despite taking longer, baseline negotiations did not involve substantially more chat messages or formal offers than the other scenarios (although the baseline scenario had more per bargaining pair than the two multilateral scenarios). In the baseline scenario, buyers made 53% of the first formal offers. Combining data from the homogeneous and differentiated scenarios, buyers made 37% of the first formal offers. While this difference might suggest buyers’ reluctance to act first when facing multiple sellers, in all three scenarios the percentage of times the buyer makes the first formal offer is similar to what would occur if the first mover were selected at random. While the never-matters model category reasonably describes outcomes, subjects clearly do not behave in a manner consistent with any of the models’ rigid structures. The models in Section 2 all predict trade occurs at the first offer made, while only 12% of our negotiations end with a single offer; only 23% of negotiations end in thirty seconds or less. There is

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some evidence that parties alternate offers, with 51% of all negotiations following that pattern.20 For the homogeneous and differentiated scenarios, the buyer held simultaneous offers from both sellers at some point in every negotiation. For the homogeneous scenario both sellers simultaneously held offers from the buyer at some point in 60% of negotiations, but this was true in only 27% of negotiations in the differentiated scenario. Finally, we consider how aspects of the negotiations correlate with the buyer’s payoff, as shown in the lower panel of Table 5. In the baseline scenario, the only measure significantly correlated with the buyer’s payoff is who makes the first formal offer – when the buyer makes the first offer the final price is higher. For the homogeneous scenario, it appears more intense negotiations – in terms of duration, number of chat messages, or number of formal offers – are correlated with better outcomes for the buyer. However, negotiations following the alternating-offer pattern lead to higher prices. In the differentiated scenario none of the considered factors is correlated significantly with the buyer’s payoff. While not shown in Table 5, none of the measures listed in its lower panel correlate significantly with the buyer trading with the high-surplus seller.21 Of course, one should be cautious in interpreting these relationships, because the factors were not experimentally manipulated and multiple hypotheses are being tested. 5. Relationship to research on competition in procurement In addition to providing insights for selecting an appropriate model to use in applied analysis, our results tie in to theoretical and empirical research on procurement suggesting a buyer might prefer facing fewer sellers rather than more. Such findings contrast sharply with the conventional wisdom that buyers benefit from more intense competition among sellers. Lang and Rosenthal (1991), Levin and Smith (1994), and Elberfeld and Wolfstetter (1999) model procurement settings in which sellers incur costs to participate, say to develop prototypes or to assess their cost of fulfilling the contract. Sellers simultaneously choose whether to enter the procurement contest, then each seller who entered submits a price offer. Equilibria exhibit randomized entry decisions with a surprising feature: increasing the number of sellers who potentially could enter decreases each seller’s likelihood of entry to the point that less entry occurs on average, leading to higher expected prices. Li and Zheng (2009) estimate models of endogenous entry into auctions for highway mowing contracts in Texas. They find that expected procurement costs can rise as the number of potential entrants increases, consistent with the preceding theoretical models’ predictions. Building on ideas developed in Goldberg (1977) and Bajari and Tadelis (2001), Bajari et al. (2009) empirically analyze procurement for projects that vary in their complexity or degree of contractual incompleteness. Using construction data, they find support for theoretical predictions that a buyer prefers negotiating with one seller rather than holding a multiseller auction if projects are complex or are likely to need post-contractual adaptation. With complex projects, auctions hinder communication between the buyer and each seller that might be important in suitably specifying details about the contract to be awarded. Complex projects also are likely to require adaptation once work commences, but auctions are more difficult to design when the contract must specify more than the price at which a seller is willing to provide its services; for example, the contract might need to describe how renegotiations will be handled if design changes are needed, perhaps as a function of the changes’ size or scope. Bulow and Klemperer (2002) model a procurement setting in which sellers’ costs include “common-value” components that reflect common and unknown shocks to all sellers’ costs. Such a setting introduces concerns about the winner’s curse: a seller must recognize that winning the procurement auction suggests that seller’s estimate of the common cost component is lower than the actual cost, in which case winning the auction might entail losing money. Equilibrium pricing accounts for this issue, which the authors show can be exacerbated as the number of sellers increases, to an extent that the expected price increases. Hong and Shum (2002) find evidence supporting this prediction in their empirical analysis of construction procurement auctions held by the New Jersey Department of Transportation. The preceding findings that increasing the number of sellers may lower the buyer’s payoff can be explained by strategic motives, but the source is less clear for our related finding that increasing the number of sellers from the baseline to the homogeneous scenario does not change the buyer’s payoff. Although this pattern aligns with game-theoretic predictions from the never-matters category of models that effectively prevent the buyer from negotiating simultaneously with multiple sellers, our buyers do conduct parallel negotiations. For some reason the subjects are unable or unwilling to leverage an identical seller’s presence in multilateral negotiations. Comparing our experimental design and results to past experiments suggests the negotiating environment might affect outcomes. Binmore et al. (1989), Binmore et al. (1991), and Kahn and Murnighan (1993) analyze structured bilateral negotiations in which the buyer has an exogenously-specified outside option. They find that small outside options do not increase the buyer’s payoff, but that large outside options do; these results align with the SM models. Dogan et al. (2013) analyze structured negotiations with identical sellers, so the buyer’s outside option to trading with one seller is determined by ne20 This includes the 16% of negotiations that are also consistent with offers only being made by one side of the market, as in the case where only one offer is made. 21 There is at least a nominal difference in payoffs in the homogeneous scenario between buyers who trade in the differentiated scenario with the low-surplus seller rather than the high-surplus seller. This is evident from a comparison of the difference in means between the two treatments that are reported in Table 3 (which includes all buyers in the mean for the homogeneous scenario) and the mean difference reported in the right column of Table 4 (which includes only buyers who trade with the high-surplus seller in the differentiated scenario).

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gotiating with the other. They find that buyers do better in multilateral than in bilateral negotiations, but that buyers do not fully extract the surplus in multilateral negotiations; these results lie between the SM and NM models. By contrast, our experiment analyzes unstructured negotiations with the buyer’s outside option also determined by negotiating with another person; our results align with the NM models. Our findings might be due to welfare or fairness concerns: perhaps buyers or sellers bear implicit costs from highly unequal outcomes. If so, a buyer’s ability to exploit a large outside option might be hampered if creating it requires negotiating with another person, compared to settings with an exogenous outside option that has no implications for a third party’s payoff. Additionally, rigid negotiating protocols might blunt concerns about unequal outcomes, say because parties cannot communicate or might feel they are simply “following the rules” of the game. Our experiment and the prior ones vary in their design and outcomes in a manner consistent with such arguments. 6. Conclusion We report the results of unstructured negotiations conducted in a laboratory experiment that lets us run a horse-race to assess the predictive power of three categories of structural models of the multilateral negotiations observed in strategic settings such as procurement, takeover contests, and large-scale investment. For concreteness we consider two sellers negotiating with a buyer who wants to make only one trade. Trade with each seller can yield either a high or a low surplus, and we specify the surplus amounts in different negotiating scenarios so the three modeling categories have distinct combinations of predictions. At an intuitive level, we analyze negotiated outcomes when the two sellers are either very similar or very different, in terms of the surplus available from trading with each. This approach lets us assess whether introducing a weakly inferior seller always, never, or sometimes increases the buyer’s negotiated payoff from its level in bilateral negotiations. We find that introducing a competing seller does not affect the observed terms of trade, relative to a baseline scenario in which a buyer negotiates with a single high-surplus seller. This finding and the observed buyers’ payoffs are consistent with what we call the never-matters category of models, such as those associated with Ray (2007) and others.22 Our results are inconsistent with models in which the second seller always matters or sometimes matters. Consequently, this experiment supports modeling multilateral negotiations using models that predict extra sellers never matter. In addition to informing model selection in applications, our results contribute to understanding how procurement outcomes vary with the number of sellers. Similar to counterintuitive findings in other procurement settings, we observe that adding a seller to bilateral negotiations does not increase the buyer’s payoff. Unlike those prior findings, ours seem to be driven by behavioral considerations rather than strategic ones, at least when viewed through the lens of existing gametheoretic models. Author contribution statement Both authors contributed equally to this project. Appendix A: Experiment Materials Instructions (read by subjects) You are participating in a study on economic decision making. You will be paid based on your decisions, so it is important that you understand these directions completely. Please do not talk to or disrupt other participants during the study. If you have a question at any point, please raise your hand and someone will assist you. What am I doing in this study? There are 9 people in your session. Each person is permanently assigned the role of either a Buyer or a Seller. Your role appears in the middle of your screen and will not change during the study. The study will last three periods. In each period each person will be assigned to one of multiple markets consisting of 1, 2, or 3 people. 2-person markets have one Buyer and one Seller. 3-person markets have two people in one role and one person in the other role. The matching of Buyers and Sellers into markets is done so that no one is ever in a market with anyone twice. That is, once you interact with someone, you will never interact with them again. Each 2-person and 3-person market is a trading opportunity between people in different roles. Sellers’ costs for their product are always $0.00, but a Buyer’s value for a product can differ from market to market and can differ between two sellers in the same market. Similarly, different Buyers can have different values for a particular Seller’s product from market to market, or within a market. In each market, a Buyer’s value for each Seller’s product is shown on everyone’s screen, so it is common information. If you are assigned to a 1-person market, then in that period you have no trading opportunities. There can be at most one trade in a market. 22 This pattern is similar to the coalitional bargaining result of Bolton, et al. (2003), who find that the coalition with the highest per capita surplus typically splits that surplus evenly.

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Once a Buyer trades with a Seller, the market ends and no other trades can occur. Once all markets in a period end, the study proceeds to the next period: Buyers and Sellers will be assigned to new markets, and Buyers’ values for Sellers’ products will be specified. The price at which you trade affects your earnings from participating in this study. If a Buyer and a Seller make a trade, then Seller’s Profit = Price Buyer’s Profit = Value of Seller’s Product – Price If a person does not make a trade, then that person’s Profit = 0. Your payment for the experiment is the sum of your earnings in the markets in which you participate. All values, costs, prices, and profits are in dollar amounts. How is the price determined? There is a negotiation area for each Buyer and Seller in a market, in which you can chat with other players with a different role than yours, make price offers to them, and accept price offers from them. CHATTING: A Seller in a market can use the Chat feature to send a text message to a Buyer in their market, and vice versa. Messages cannot be sent between two people in the same role, nor can anyone view any message for which they were not the sender or the intended recipient. For example, a Seller cannot chat with another Seller, and a Seller cannot see a message a Buyer sent to another Seller. Chat messages should not contain offensive language or personally identifying information. Anyone sending such messages will be dismissed from the experiment without payment. MAKING A PRICE OFFER: You can propose a price by typing it into the box beside the Offer button in the appropriate negotiation area. Your offer must be between the Seller’s cost of $0.00 and the Buyer’s value for that Seller’s product. The computer rejects offers outside this range or with more than 2 decimal places. If you make an offer that is accepted, then trade takes place at the offered price. If you make an offer, the profit you will earn if it is accepted is displayed next to it. You can make a new offer at any time by typing it into the box beside the Offer button. Your new offer is not restricted by the amount of any earlier offer(s) you made. If you wish to withdraw an offer you already made, you can do so by pressing the Withdraw button. Note that if your current offer is accepted before you change it or withdraw it, then you are committed to trading at your current offer. Also, you do not have to withdraw your current offer before making a new offer; simply enter a new offer in the Offer box. ACCEPTING A PRICE OFFER: If someone makes you a price offer, an Accept button appears next to it along with your profit from accepting the offer. Pressing Accept means that you agree to trade at the price the other person offered. Doing so causes the trade to occur, ends the market, and lets everyone’s profit for the period be calculated. Your screen will show you the number of Buyers and Sellers in your market (including yourself). If there is someone else in the same role as you, you cannot see the offers made between that person and the person in the other role, so “???” will be shown on your screen instead of that information. Once you are done reading these directions, please press Finished with Directions. Summary Announcements (read aloud by experimenter)

1. You will never be in a market with someone more than once. 2. Once one trade occurs in your market, there can be no other trades in your market. 3. All chat messages and offers are only observed by the person sending them and the one person on the other side of the market to whom they are sent. 4. Your payment will be the sum of your earnings from the up to three markets in which you will participate.

Appendix B: Subject Negotiations Below, we provide some sample interactions. In what follows, B→S denotes a message from the buyer to the seller, while S→B denotes the reverse. Actions in brackets indicate binding actions. Messages in quotation marks are verbatim transcripts. The first two examples are from the baseline scenario. The first finishes in 25 s, with no discussion. The second lasts over 7 min, with extensive but occasionally non-serious discussion. Both result in a similar price ($5.00 for the former and $5.50 for the latter).

Negotiation between Buyer and Seller 1

Time

S→B: S→B: S→B: B→S:

2:45:10 2:45:25 2:45:28 2:45:35

[Ask = $6.00] [Withdraw Ask = $6.00] [Ask = $5.00] [Accept @ $5.00]

PM PM PM PM

C.A. Deck and C.J. Thomas / International Journal of Industrial Organization 70 (2020) 102612

Negotiation between Buyer and Seller 1

Time

B→S: [Bid = $1.00] B→S: “hello Seller” S→B: “hello buyer” S→B: “can you go higher then 1?” B→S: “how is your day going” S→B: “lets haggle” B→S: “1.5?” S→B: “good so far i guess” B→S: [Bid = $1.50] S→B: “how about yours?’ S→B [Ask = $10.00] B→S: “I’m doin good” B→S: [Bid = $2.00] S→B [Ask = $8.00] B→S: [Bid = $3.00] S→B: “well thats fantastic” S→B [Ask = $7.00] B→S: [Bid = $3.50] S→B [Ask = $10.00] B→S: [Bid = $4.00] S→B [Ask = $10.00] S→B [Ask = $6.00] B→S: [Bid = $4.50] S→B: “look, im not budging, it tok me years to make these priceless diamond carrots” S→B: “took∗ ” B→S: “hahaha” B→S: “5?” S→B: “6” B→S: [Bid = $5.00] S→B: “finally offer” S→B: “final∗ ” B→S: “5 is my final offer” S→B: “and thats with me giving you a deal. becasue we were in Vietnam together” S→B [Ask = $5.50] B→S: ” that’s exactly why I’m ready to buy it at $5” S→B: “with this money i was goin to buy new medicine for Patches my pet sloth” S→B: “5.5” B→S: “say hi to your pet” B→S: [Accept @ $5.50]

1:17:14 1:17:23 1:17:34 1:17:44 1:17:49 1:17:51 1:18:00 1:18:03 1:18:15 1:18:48 1:18:56 1:19:00 1:19:10 1:19:17 1:19:21 1:19:29 1:19:35 1:19:46 1:20:13 1:20:23 1:20:57 1:21:29 1:21:37 1:22:06 1:22:15 1:22:18 1:22:26 1:22:30 1:22:32 1:22:35 1:22:39 1:23:07 1:23:12 1:23:35 1:23:49 1:24:23 1:24:31 1:24:55 1:24:59

13

PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM

The next two examples are from the homogeneous scenario. In the first, the buyer essentially conducts an auction, twice using the phrase “going once, going twice", although successfully stalling the closing with a prolonged “aaaannd.” This buyer ultimately gets the price down to $1.00 after 7 min. While other subjects invoked notions of fairness to support an equal division of the surplus, this buyer argued that playing the sellers off each other was fair because “I gotta give the other guy a chance.” The second example finished in six seconds, with no discussion, at a price of $5.00.

Negotiation between Buyer and Seller 1

Time

B→S: [Bid = $1.00]

1:25:50 1:25:51 1:25:56 1:25:59 1:26:00 1:26:09 1:26:10 1:26:15 1:26:26 1:26:36 1:26:44 1:27:01 1:27:15 1:27:19 1:27:34 1:27:46 1:27:51 1:27:57 1:27:59 1:28:09 1:28:14 1:28:19

S→B: [Ask = $9.00] B→S: “Hah” S→B: “Funny funny. How about 7?” S→B: [Ask = $7.00]

B→S: “The other guy is offering me 6” S→B: [Ask = $5.75] S→B: “How about that?” B→S: “I believe in fairness. I gotta give the other guy a chance” S→B: “Dont be that person....”

B→S: “The other guys is now lower” S→B: “5.75 is a good deal for our product” B→S: “I have 4.5”

Negotiation between Buyer and Seller 2 PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM

B→S: [Bid = $1.00] S→B: [Ask = $2.00] S→B: [Withdraw Ask = $2.00] S→B: [Ask = $8.00] B→S: “The other guy is offering me 7” S→B: [Ask = $6.00]

B→S: “And the other person is offering less than 6 now”

B→S: “Going once…” B→S: “Going twice....” S→B[Ask = $4.50]

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S→B [Ask = $4.49] S→B: “Now 4.49”

S→B: I guess eventually one of us will take the one dollar B→S: Probably B→S: [Accept @ $1.00]

1:28:25 1:28:35 1:28:36 1:29:03 1:29:07 1:29:15 1:29:16 1:29:23 1:29:26 1:29:30 1:29:38 1:29:42 1:29:46 1:29:50 1:29:52 1:29:57 1:30:01 1:30:14 1:30:23 1:30:30 1:30:33

Negotiation between Buyer and Seller 1

Time

Negotiation between Buyer and Seller 2

B→S: [Bid = $5.00] S→B: [Ask = $5.00]

2:47:31 PM 2:47:32 PM 2:47:36 PM

S→B: [Ask = $5.00] B→S: [Accept @ $5.00]

S→B: “I have 4.3” B→S: “This is gonna go on for days…”

S→B: [Ask = $3.00] S→B: 3? B→S: “Nah, just seconds on the clock”

PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM PM

B→S: B→S: B→S: B→S: S→B: B→S: B→S:

“4.49 is on the table” “going once” “going twice” “aaaannd” [Ask = $4.30] “ok, hold on” “why not say hi?”

S→B: “sorry, hi.” B→S: “:P” B→S: Hello! S→B: “im kinda confused on how this works”

B→S: “I have 3 from the other person now” S→B: “Im nervous that youre lying”

The final two examples are from the differentiated scenario. In the first, the buyer ignores the low-surplus seller and interacts solely with the high-surplus seller, trading at a price of $5.00 in less than one minute. In the second, the lowsurplus seller pleads with the buyer to trade at a price that equally splits the surplus available to them, but after explaining the situation to the low-surplus seller, the buyer trades at a price of $5.00 with the high-surplus seller. Negotiation between Buyer and Seller 1

Time

B→S: [Bid = $2.00] S→B: “how about 5”

10:23:07 10:23:14 10:23:16 10:23:33 10:23:42 10:23:48 10:23:51

S→B: B→S: S→B: B→S:

[Ask = $7.00] “Fine I will take 5.” [Ask = $7.00] [Accept @ $5.00]

Negotiation between Buyer and Seller 1

Time 10:38:56 10:39:06 10:39:15 10:39:35

S→B: “Good morning. I’m willing to sell at a price of $5 which should make both of us happy. I’ll wait to hear from you before making a formal offer”

Negotiation between Buyer and Seller 2 AM AM AM AM AM AM AM

Negotiation between Buyer and Seller 2 AM AM AM AM

S→B: [Ask = $1.00] S→B: “Let’s make this an even trade” S→B: “1 for you, 1 for me” B→S: “I value your product very little though, I could get more value from the other product overall”

10:39:38 AM

10:39:53 AM 10:40:20 AM B→S: [Bid = $5.00] S→B: [Accept @ $5.00]

S→B: [Ask = $2.00]

S→B: “it’s an easy dollar to make” S→B: “I will end up with nothing without your mercy.”

10:40:50 AM 10:41:01 AM

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