Bargaining behavior and payoff uncertainty: Experimental evidence

Bargaining behavior and payoff uncertainty: Experimental evidence

Journal of Economic Psychology 20 (1999) 407±429 www.elsevier.com/locate/joep Bargaining behavior and payo€ uncertainty: Experimental evidence Bryan...

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Journal of Economic Psychology 20 (1999) 407±429

www.elsevier.com/locate/joep

Bargaining behavior and payo€ uncertainty: Experimental evidence Bryan K. Church

a,*

, Ping Zhang

b,1

a

b

DuPree College of Management, Georgia Tech, Atlanta, GA 30332-0520, USA School of Accountancy, Faculty of Arts, University of Waterloo, ON, Canada N2L 3G1 Received 2 August 1998; accepted 18 March 1999

Abstract This study uses an experimental economics method to examine bargaining behavior in a setting analogous to one in which buyer±seller pairs negotiate over the provision of professional services. We construct a two-player negotiation game that captures an important feature of this setting: uncertainty in the seller's payo€ with the possibility of a negative payo€. Our experimental ®ndings indicate that, under various conditions in multi-period settings, the terms of negotiated agreements are a€ected by the nature of the seller's payo€. The seller is able to achieve more favorable terms when the seller's payo€ is uncertain versus certain. In contrast, in a single-period setting the nature of the seller's payo€ does not a€ect the terms of negotiated agreements. Ó 1999 Elsevier Science B.V. All rights reserved. PsycINFO classi®cation: 3020 JEL classi®cation: C72; C90 Keywords: Bargaining game; Negotiations; Uncertain payo€

*

Corresponding author. Tel.: +1 404 894 3907; fax: +1 404 894 6030; e-mail: [email protected] 1 E-mail: [email protected] 0167-4870/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 4 8 7 0 ( 9 9 ) 0 0 0 1 5 - X

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1. Introduction This study uses an experimental economics method to examine bargaining behavior in a setting analogous to one in which buyer±seller pairs negotiate over the provision of professional services. A seller (e.g., an appraiser, attorney, auditor, underwriter) is hired to provide information or credibility regarding value. The need for the services can be triggered by various events, including the ordinary course of ®nancial reporting, mergers or acquisitions, leveraged buyouts, partnership agreements, initial or seasoned stock o€erings, and bond o€erings. With buyer±seller pairs, negotiations arise because the two players have di€erent preferences. For instance, a manager may hire an auditor to report on ®rm value, where the reported value a€ects each player's payo€. The manager prefers a high value in order to maximize return. The auditor, on the other hand, prefers a low value because of potential legal costs (i.e., the auditor can be held liable if the reported value is high and the actual value is low). 2 Negotiations are permissible because ®rm value is subjective and open to interpretation. Previous studies in economics have investigated bargaining behavior in abstract, two-player games. 3 The simplest type of bargaining game involves two players negotiating the split of a ®xed amount of money, with the stipulation that both parties receive a zero payo€ if an agreement is not reached within a speci®ed amount of time. In general, experimental ®ndings are not consistent with game-theoretic predictions: a non-trivial number of nonagreements occur and negotiated settlements are far less extreme than predicted. We extend prior bargaining research by focusing on behavior in a setting that captures an important feature in the provision of professional services: uncertainty in the seller's payo€ with the possibility of a negative payo€. In most bargaining games, including ultimatum and shrinking pie games, players' payo€s are non-negative and certain once an agreement is reached. By comparison, a seller's (professional's) payo€ is not certain and can even be negative following the provision of services: it typically includes a component that re¯ects the expected cost of professional liability. The seller earns a normal pro®t from performing a job (i.e., a fee minus a marginal cost), but may incur an additional cost in the future. The added cost may arise because

2 3

Moreover, the seller may be held liable to third parties as well as the buyer (Marino & Marino, 1994). For an overview, refer to Davis and Holt (1993, Ch. 5) and Roth (1995).

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the seller errs in reporting value and can take the form of negative publicity, loss of reputation, disciplinary action from a governing body, or litigation. The magnitude of the cost increases as the discrepancy in the seller's report increases. For example, if an appraiser overvalues a tract of land, the appraiser's potential liability (to the purchaser of the land) is positively associated with the magnitude of the overvaluation. While some bargaining studies (e.g., Malouf & Roth, 1981; Roth & Murnighan, 1982) introduce uncertainty in both players' payo€s, the e€ect of uncertainty, per se, on the outcome of the negotiation process has not been examined. This study takes a step in that direction. We investigate whether uncertainty in the seller's payo€ a€ects the number of non-agreements and the terms of agreement. We conduct four experiments, each consisting of four sessions. Within each experiment, we manipulate the form of the seller's payo€: in two sessions the seller's payo€ is uncertain and in two it is certain. Experiment 1 provides a base case. Experiments 2±4 are conducted to test the sensitivity of the results to variations in the experimental parameters. In experiment 2, we increase the likelihood that the seller incurs an additional cost from agreeing to a particular settlement. In experiment 3, we alter the fundamental structure of the bargaining process (i.e., players' knowledge about who makes the next o€er). In experiment 4, we examine behavior in a single, rather than multi-period setting. Across the four experiments our focus is on uncertainty in the seller's payo€. This focus allows us to gain insights beyond those that can be gleaned from other bargaining studies. Such insights are important because a thorough understanding of bargaining behavior is necessary for sellers to better manage jobs and gauge fees to achieve an acceptable risk±return tradeo€. Our results indicate that, under various conditions, uncertainty in the seller's payo€ a€ects the terms of agreement, but not the frequency of nonagreements. In multi-period settings, we ®nd that if negotiations proceed up to a deadline, which includes the vast majority of cases, settlements are more likely to favor the seller when the seller's payo€ includes an uncertain component. In this case, the buyer is willing to make concessions, apparently to compensate for the seller's uncertainty. Under such conditions, the buyer does not exploit his or her bargaining advantage. In single-period settings, we ®nd that the seller's payo€ does not a€ect the terms of negotiated agreements. The remainder of the paper is organized as follows. In Section 2 a framework is developed, which a€ords a basis for the research hypotheses. In Section 3 the experimental method is described. In Section 4 the experimental results are presented, and in Section 5 concluding remarks are provided.

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2. Framework 2.1. Overview of experiments We conduct four experiments in which buyer±seller pairs attempt to agree on the number of points that is acceptable to both parties. Players' payo€s are a€ected by the number of points agreed upon: the buyer prefers a larger number of points, whereas the seller prefers a smaller number. Negotiations take place over a series of rounds and failing an agreement, both parties receive nothing. Each experiment consists of four sessions. Experiment 1 provides a base case. Two sessions are conducted in which the seller's payo€ is uncertain (denoted UNCERT). If an agreement is reached, the seller receives a ®xed fee and may incur an additional cost with a known probability. The additional cost is increasing in the number of points agreed upon. In the other two sessions, the seller's payo€ is certain and includes a ®xed fee minus the expected cost of a particular agreement (denoted EV). In all four sessions, the buyer's payo€ is certain and increasing in the number of points agreed upon. The design of experiments 2±4 is similar, with the following exceptions. In experiment 2, the probability that the seller incurs an additional cost is increased as compared to the base case (40% vs. 20%). In experiment 3, the two players alternate making o€ers over a maximum of three rounds, whereas in the base case each player has a known probability of making an o€er in a particular round. Finally, in experiment 4, negotiations only last one round, versus a maximum of three rounds in the base case. By conducting four experiments, we are able to assess the extent to which the results obtained in the base case can be generalized to other settings. 2.2. Frequency of non-agreements We investigate the e€ect of uncertainty in the seller's payo€ on the frequency of disagreements. A non-trivial number of non-agreements is documented in numerous experimental studies (see e.g., Forsythe, Keenan & Sopher, 1991) and a comparable number of disputes is observed in ®eld settings (Ashenfelter & Currie, 1990). The experimental ®ndings are curious because rejected o€ers are mutually pro®table: that is, both players are worse o€ by failing to agree. As a starting point, we consider simple bargaining games in which players' payo€s are certain, conditioned on the agreement reached. In such games,

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one player proposes a split of a ®xed amount of money and the other player either accepts or rejects the o€er. An o€er may be rejected because it is perceived as unreasonable (see e.g., Guth, 1995). So players must develop expectations about what is reasonable: that is, how much an o€er may favor one player. Camerer and Thaler (1995) suggest that an o€er must conform loosely with social norms in order to be accepted, and experimental evidence indicates that a 50±50 split is the modal o€er (see e.g., Forsythe, Horowitz, Savin & Sefton, 1994; Ho€man, McCabe, Shachat & Smith, 1994). An o€er to divide funds equally is, without question, reasonable and almost never rejected. O€ers that slightly favor the player with the bargaining advantage also are likely to be viewed as reasonable. For example, o€ers that allocate 60±70% of the total amount to the player making the proposal are typically accepted. By comparison, o€ers that allocate 80% or more to the proposer are usually rejected. Guth (1995) suggests that players determine a minimum acceptable amount, below which o€ers are perceived to be unreasonable. Bolton (1997) points out the importance of reasonable o€ers and argues that such o€ers provide an ecient means to coordinate bargaining behavior. For our purposes, reasonable o€ers are bounded by the perceived maximum amount that the o€er favors one player (or the perceived minimum amount that the recipient is willing to accept). Uncertainty in payo€s adds a level of complexity that can a€ect bargainers' expectations about the terms of agreement: that is, the payo€ that each player reasonably expects to receive. Malouf and Roth (1981) introduce uncertainty through the use of binary lotteries. Bargaining partners negotiate the distribution of lottery tickets, which determines the probability of winning a monetary prize. As such, players' payo€s are positive with a known probability and zero otherwise. Malouf and Roth manipulate the maximum number of tickets that can be allocated to each player and ®nd that disagreements are more likely to occur as the dispersion of observed agreements increases. This result likely arises because dispersion in observed agreements is positively associated with the disparity in expectations among players. In our study, the disparity in expectations among buyer±seller pairs is likely to be greater in experimental sessions with UNCERT payo€ than in those with EV payo€. In the latter, both players' payo€s are certain and nonnegative. Under such conditions, a particular agreement may be focal or prominent and provide a common basis for both players to formulate expectations about what is reasonable. As mentioned earlier, when payo€s are certain bargainers often agree on an equal division of funds. In sessions with

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EV payo€, an equal split provides a basis to facilitate coordination (see e.g., Schelling, 1957, 1960). Due to social norms, such a split, without question, is viewed as fair. In sessions with UNCERT payo€, the seller's payo€ is uncertain and can be negative, conditioned on the terms of agreement. Under such conditions, a unique agreement (or set of agreements) may not be focal because risk attitude and concerns about losses become relevant. These factors a€ect bargainers' expectations about what is reasonable: the determination of a fair split is not so obvious. If di€erent players have di€erent preferences, expectations likely di€er, making it more dicult to agree. Accordingly, our ®rst hypothesis, expressed in its alternative form, is as follows. H1a: The frequency of disagreements is greater in sessions with UNCERT payo€ than in those with EV payo€. 2.3. Terms of agreement We also investigate the e€ect of uncertainty in the seller's payo€ on the observed terms of agreement. In general, previous experimental studies ®nd that bargainers frequently agree to a settlement that produces an equal split or slightly favors the player making the ®nal o€er (the proposer). The proposer may be allowed to capture (slightly) more than 50% of the funds available because this player has a bargaining advantage. The proposer, however, is not allowed to fully exploit this advantage. 4 These ®ndings are contrary to the predictions of non-cooperative game theory, which suggest that the proposer o€er the minimum positive amount feasible. But gametheoretic predictions fail to recognize that unreasonable o€ers may be rejected, even though such behavior reduces both players' earnings. Bolton and Zwick (1995) suggest that unreasonable o€ers are rejected to punish the proposer. Game-theoretic predictions also fail to recognize that fairness considerations, which determine whether an o€er is viewed as reasonable, may play a role in determining bargaining behavior. Grossman and Eckel (1996) and Ru‚e (1998) provide experimental evidence which suggests that such considerations are an integral aspect of behavior.

4 Experimental ®ndings suggest that when a player earns the right to be the proposer, less money is o€ered than otherwise (Ho€man et al., 1994).

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Table 1 Sample payo€s from experiment 1 Number of points agreed upon

4 8 12 16 20 24 28 32 36 40 44 48

Seller's payo€ UNCERT payo€ Without added cost ($)

With added cost ($)

1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68 1.68

1.26 0.84 0.42 0.00 á0.42ñ á0.84ñ á1.26ñ á1.68ñ á2.10ñ á2.52ñ á2.94ñ á3.36ñ

EV payo€ ($)

Buyer's payo€ (UNCERT and EV payo€) ($)

1.60 1.51 1.43 1.34 1.26 1.18 1.09 1.01 0.92 0.84 0.76 0.67

0.13 0.25 0.38 0.50 0.63 0.76 0.88 1.01 1.13 1.26 1.39 1.51

Note: In sessions with UNCERT payo€, the seller receives a ®xed fee and may incur an additional cost with a known probability. In sessions with EV payo€, the seller receives a ®xed fee minus the expected cost of agreeing to a particular settlement.

In our experimental sessions with EV payo€, negotiated agreements may be similar to those reported in prior bargaining studies and at odds with game-theoretic predictions. Sample payo€s from experiment 1 are shown in Table 1 for illustrative purposes. In sessions with EV payo€, both players may coordinate their actions around a settlement of 32 points, which produces an equal split, or one that slightly favors the player with the bargaining advantage. In sessions with UNCERT payo€, the terms likely di€er. With UNCERT payo€, the seller may incur an additional cost with a known probability. If the cost is incurred, the seller's payo€ is decreasing in the number of points agreed upon and eventually becomes negative. Otherwise, the seller's payo€ is una€ected by the terms of agreement. Under such conditions, the seller may be risk averse and loss averse. Such behavior may arise because the seller negotiates over agreements that have a positive probability of producing an outcome that is negative and less than that of disagreeing. 5 Accordingly, the range of feasible agreements likely shifts 5 Theoretically, risk aversion can be advantageous if agreements have a positive probability of yielding an outcome worse than disagreement (see e.g., Kalai & Smorodinsky, 1975; Perles & Maschler, 1981).

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downward: on average a smaller number of points is agreed upon. Our second hypothesis, expressed in its alternative form, is as follows. H2a: The terms of agreement are more favorable to the seller (i.e., a smaller number of points is agreed upon) in sessions with UNCERT payo€ than in those with EV payo€. 3. Experimental method 3.1. Subjects One hundred twenty-eight subjects were recruited to take part in the four experiments, with eight per session. Thirty-two subjects participated in each experiment. The subjects were recruited from undergraduate and post-baccalaureate students attending a medium-sized, Canadian university. Students were paid $3.00 for arriving on time and across the four experiments earned from $4.50 to $21.00, with an average of $15.00, for participating approximately 100 min. 3.2. Procedures At the beginning of each session, instructions were distributed and read aloud. 6 After completing the instructions, the experimenters passed out cards numbered 1±8. Subjects receiving an odd-numbered card completed the experiment in an adjacent room. All experimental sessions consisted of 18 periods; however, subjects were not informed beforehand of the number of periods. Each period, subjects in one room took the role of the seller and those in the other room took the role of the buyer. 7 Player roles were assigned randomly each period with the following constraint. All subjects assumed each role approximately the same number of times. This constraint was necessary to ensure that all subjects had the same opportunity to generate earnings throughout the course of each experiment. The assigned player roles (for subjects in each room) were de6

A copy of the experimental instructions is available from the authors upon request. Throughout the four experiments, we used generic terminology. For example, the buyer and seller were referred to as Players A and B, respectively. Further, subjects negotiated over points rather than reported values. The use of generic terminology allows us to avoid confounds that may arise from the knowledge that subjects bring with them to the experiment and is important to maintain internal validity. 7

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termined randomly prior to conducting the experiments and held constant across all sessions. 8 Each period buyer±seller pairs were assigned on a random basis. At the beginning of a period, an experimenter in each room shu‚ed a deck of cards numbered 1±4. The cards were distributed and the number on the card received represented a subject's bargaining number for the period. Subjects in di€erent rooms who received the same numbered card were paired together. This procedure ensured that subjects did not know the identity of their bargaining partner in a particular period. Within a period, buyer±seller pairs attempted to agree on the number of points that is acceptable. As mentioned previously, we varied the form of the seller's payo€ between sessions within each experiment: two sessions with UNCERT payo€ and two with EV payo€. Some parameters also are varied between experiments. Panels A and B of Table 2 provide detail on the speci®c parameters that are held constant and varied, respectively, across the four experiments. In experiment 1, each player has a known probability of proposing in each round. The probability is 0.60 (0.40) for the buyer (seller). 9 The probabilities provide the buyer with a slight advantage, which likely arises because the buyer has the ability to hire and ®re the seller. The negotiation process could last a maximum of three rounds. Experiment 1 provides the case base against which the other three experiments are compared. In experiment 2, we increased the likelihood that the seller incurs the added cost. We also increased the constant used in the determination of both players' payo€s. This change was necessary in order to equalize subjects' expected earnings across the experiments. In experiment 3, we changed the bargaining structure of the game. Each player has a known probability of making a proposal in round one, after which players alternate making proposals. As a consequence, it becomes obvious who will propose in the ®nal round. The same cannot be said of the base case. In experiment 4, we altered the number of rounds allowed for the negotiation process. Each player has a known probability of making a one-shot, take-it or leave-it (ultimatum) proposal. In our setting, the game-theoretic predictions of one versus three rounds are similar; however, the one-shot setting minimizes subjects' abilities to learn about the expectations' or behavior of their bargaining partner. 8 This approach was followed to maximize comparability across experimental sessions (see e.g., Cason & Friedman, 1996). 9 The player role making a proposal in a particular round was determined prior to conducting the experiments and held constant across sessions.

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Table 2 Experimental parameters Panel A: Parameters that do not vary between the experiments Parameter

Speci®cation

Buyer's payo€ Seller's EV payo€ Seller's UNCERT payo€: When added cost is not incurred When added cost is incurred Prob of buyer proposing in round one Prob of seller proposing in round one

Constant (0.30 points) Constant {16 ± (prob of added cost points)} Constant 16 or Constant (16 ± points) 0.60 0.40

Panel B: Parameters that vary between the experiments Parameter

Experiment 1

Experiment 2

Experiment 3

Experiment 4

Constant Prob of added cost Bargaining structure Bargaining rounds

10.5 0.20 Probabilistic 3

16 0.40 Probabilistic 3

10.5 0.20 Alternating 3

10.5 0.20 One shot 1

Note: For parameters that do not vary between experiments, the seller's payo€ is certain in the EV payo€ condition and uncertain in the UNCERT payo€ condition. In the sessions involving UNCERT payo€, the speci®c periods in which the seller incurred an additional cost were determined randomly prior to conducting the experiments and were not varied across sessions. For parameters that vary between experiments, the constant represents the value used in the determination of payo€s. The value is higher in experiment 2 because the probability of incurring the added cost is higher: the constant was varied in order to equalize subjects' expected earnings across experiments. The probabilistic bargaining structure means that each player has a known probability of proposing in each round. The probability of the buyer (seller) proposing in a given round is 0.60 (0.40). The alternating structure means that each player has a known probability of proposing in round one, after which players alternate. The one-shot bargaining structure means that each player has a known probability of proposing, where the proposal is a take-it or leave-it o€er (ultimatum). The bargaining rounds indicate the maximum allowed per period.

Across the four experiments, negotiations proceeded as follows. All subjects were given a range of acceptable points (0±80 points) in which to negotiate. Subjects also were provided with a table that computed the buyer and seller payo€s across all possible points of agreement. We used a payo€ table to simplify the experiment and to control for learning: over time subjects could learn the di€erent payo€s, but the speed of learning might vary between individuals. Within a period, buyer±seller pairs negotiated over points in rounds. Each round, subjects in one room were given 30 seconds to make a proposal as to the number of points that would be acceptable. They were provided with an index card that indicated the period and bargaining pair number (i.e., 1, 2, 3, or 4), and asked to record their

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proposal. 10 The cards were collected and taken to the room where the other subjects were located. After the cards were distributed, subjects in the other room were given 15 seconds to accept or reject the proposal. In experiments 1±3 (4), the negotiation process could last a maximum of three (one) rounds. If an agreement was not reached by the ®nal round, both players in the bargaining pair received nothing. At the conclusion of each session, the experimenters calculated subjects' total earnings and paid them in cash. During this time, subjects completed a post-experiment questionnaire. The questionnaire was designed to collect general information about subjects and how they viewed the experiment. 11 4. Results 4.1. Frequency of non-agreements The number of agreements and non-agreements per session across experiments 1±4 is shown in Panels A±D, respectively, of Table 3. As can be seen, a non-trivial number of non-agreements occurs. Across the four experiments, the frequency of disagreements per session ranges from 6 of 72 (or 8%) to 24 of 72 (or 33%) which is comparable to that reported elsewhere (see e.g., Guth, Schmittberger & Schwarze, 1982; Spiegel, Currie, Sonnenschein & Sen, 1994). In addition, the data indicate that more disagreements occur in experiment 4 (which allows one round of negotiation) as compared to experiments 1±3 (which allow up to three rounds of negotiation). 12 The ®rst hypothesis suggests that disagreements occur more frequently in sessions with UNCERT payo€ than in those with EV payo€. For each

10 Subjects also were provided with a record sheet on which they kept track of their earnings and bargaining results. 11 Subjects' responses to the post-experiment questionnaire suggest that they found the experiment interesting and the monetary incentives motivating. Subjects responded on a seven-point scale as to how interesting they found the experiment, where 1 ˆ not very interesting and 7 ˆ very interesting. Across the four experiments the mean response was 5.98. Subjects also responded on a seven-point scale as to how they would characterize the amount of money earned for taking part in the experiment, where 1 ˆ nominal amount and 7 ˆ considerable amount. Across the four experiments the mean response was 4.37. 12 We compared the proportion of disagreements in experiment 4 with the proportions in experiments 1±3. In each case, the di€erence is statistically signi®cant: z ˆ 2.30, p ˆ 0.0214 (experiment 4 vs. experiment 1), z ˆ 2.58, p ˆ 0.0098 (experiment 4 vs. experiment 2), and z ˆ 1.77, p ˆ 0.0768 (experiment 4 vs. experiment 3). Bargaining settings that allow multiple periods seem to facilitate agreements being reached.

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Table 3 Frequency of agreements and non-agreements Payo€ condition

Session

Agreements per round Round 1

Non-agreements

Round 2

Round 3

Panel A: Experiment 1 EV 1 2 UNCERT 1 2

4 8 5 2

12 16 12 9

43 38 43 42

13 10 12 19

Panel B: Experiment 2 EV 1 2 UNCERT 1 2

4 4 3 2

11 18 9 5

45 44 50 51

12 6 10 14

Panel C: Experiment 3 EV 1 2 UNCERT 1 2

5 2 1 0

16 3 1 2

36 49 55 59

15 18 15 11

Panel D: Experiment 4 EV 1 2 UNCERT 1 2

53 58 48 52

19 14 24 20

Note: In sessions with UNCERT payo€, the seller receives a ®xed fee and may incur an additional cost with a known probability. In sessions with EV payo€, the seller receives a ®xed fee minus the expected cost of agreeing to a particular settlement. Experiment 4 only consisted of one round, so agreements are not partitioned by round.

experiment, we computed z-statistics to test whether the percentage of disagreements di€ers between sessions with UNCERT and EV payo€. In conducting the tests, we used the normal approximation to the binomial distribution (Mendenhall, Schae€er & Wackerly, 1981). 13 We combined observations from pairs of sessions carried out under the same experimental

13 The calculation of the z-statistic requires a value for the population proportion of agreements reached which is unknown. One solution is to use the sample proportion. The statistics reported in the text are calculated using this method. An alternative approach is to use 0.50 for the population proportion. We calculated all statistics following the alternative approach and found that inferences were una€ected.

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condition. In experiments 1, 2, and 4, more disagreements are observed in sessions with UNCERT payo€ than in those with EV payo€; however, in no case is the di€erence signi®cant at any conventional: z ˆ 1.21, p ˆ 0.2262 (experiment 1), z ˆ 1.00, p ˆ 0.3174 (experiment 2), z ˆ ÿ 1.02, p ˆ 0.3078 (experiment 3), and z ˆ 1:47, p ˆ 0.1416 (experiment 4). We repeated the analysis for each experiment using various subsets of data. We excluded observations from the ®rst four, six, eight, and 12 periods because subjects may require an initial phase to familiarize themselves with the experimental procedures, over which time their behavior may be unstable. We looked at various subsets of the data because di€erent subjects may require di€erent periods of time before behavior stabilizes. In no case, however, were inferences a€ected. Hence, uncertainty in the seller's payo€ does not a€ect the frequency of disagreements, which is not consistent with H1a. 4.2. Terms of agreement Next we examine negotiated settlements. An inspection of Table 3 indicates that the vast majority of agreements does not occur until just before the deadline. Across experiments 1±3, the number of agreements reached in the ®nal round per session ranges from 38 of 62 (or 61%) to 59 of 61 (or 97%). Almost all of the agreements reached under the UNCERT payo€ in experiment 3 occurred in round three. Overall, the data are consistent with the observed deadline e€ect documented by Roth, Murnighan and Schoumaker (1988). Negotiations may take place up to the deadline because buyer±seller pairs are trying to gain an understanding of each others' expectations and bargaining strategies. The second hypothesis suggests that a smaller number of points is agreed upon in sessions with UNCERT payo€ than in those with EV payo€. For each experiment, we performed an analysis of variance (ANOVA). In experiments 1±3, the independent variables include payo€ condition (UNCERT vs. EV), the player making the ®nal, accepted o€er (buyer vs. seller), and the round of agreement (round one or two versus round three). 14 In experiment 4, round of agreement is not included as an independent variable because the setting only allows one round. Across the four experiments, payo€ condition is of primary interest. The other variables are included to

14 We collapsed the data across agreements reached in the ®rst two rounds because relatively few agreements occurred prior to the ®nal round.

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Table 4 ANOVA results: The e€ect of PAYOFF, PROPOSER, and ROUND on the number of points agreed upon df Panel A: Experiment 1 Main e€ects PAYOFF PROPOSER ROUND 2-way interactions PAYOFF ´ PROPOSER PAYOFF ´ ROUND PROPOSER ´ ROUND 3-way interaction PAYOFF ´ PROPOSER Residual Panel B: Experiment 2 Main e€ects PAYOFF PROPOSER ROUND 2-way interactions PAYOFF ´ PROPOSER PAYOFF ´ ROUND PROPOSER ´ ROUND 3-way interaction PAYOFF ´ PROPOSER ´ ROUND Residual Panel C: Experiment 3 Main e€ects PAYOFF PROPOSER ROUND 2-way interactions PAYOFF ´ PROPOSER PAYOFF ´ ROUND PROPOSER ´ ROUND 3-way interaction PAYOFF ´ PROPOSER ´ ROUND Residual Panel D: Experiment 4 Main e€ects PAYOFF PROPOSER

Sum of squares

F-statistic

p-value

1 1 1

733.49 4,077.49 210.76

8.02 44.58 2.30

0.005 0.000 0.130

1 1 1

644.27 357.92 1,863.79

7.04 3.93 20.38

0.009 0.049 0.000

1 226

450.80 20,670.84

4.93

0.027

1 1 1

414.34 1,088.26 103.24

19.38 50.91 4.83

0.000 0.000 0.029

1 1 1

79.46 200.59 438.65

3.72 9.38 20.52

0.055 0.002 0.000

1 8

27.38 5,087.38

1.28

0.259

1 1 1

1,230.63 154.95 194.13

27.64 3.48 4.36

0.000 0.063 0.038

1 1 1

50.56 25.97 136.66

1.14 0.58 3.07

0.288 0.446 0.081

1 228

48.34 20,670.84

1.09

0.299

1 1

15.13 585.37

0.22 8.67

0.636 0.004

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Table 4 (Continued)

2-way interactions PAYOFF ´ PROPOSER Residual

df

Sum of squares

1 210

112.51 14,739.70

F-statistic 1.67

p-value 0.198

Note: PAYOFF is the payo€ condition (UNCERT vs. EV), PROPOSER is the player making the ®nal, accepted o€er (buyer versus seller), and ROUND is the round of agreement (round one or two vs. round three).

control for bargaining advantage. In experiments 1±3, the buyer has a slight bargaining advantage in the ®rst two rounds (because the probability of the buyer making an o€er in subsequent rounds is greater than that of the seller). The proposer has the bargaining advantage in the ®nal round. In carrying out the analyses, we combined observations from pairs of sessions conducted under the same experimental condition. The ANOVA results for experiments 1±4 are shown in Panels A±D, respectively, of Table 4. 15 The cell means are reported in Panels A±D of Table 5. As shown in Panels A and B of Table 4, payo€ condition is signi®cant at p < 0.01 in experiments 1 and 2, respectively. But several interactions also are statistically signi®cant, making it dicult to interpret main e€ects. For experiments 1 and 2, additional analyses are conducted to investigate the simple e€ect of payo€ condition on the terms of agreement. The data are partitioned into four groups based on the player making the ®nal o€er and round of agreement and four one-way ANOVAs are performed. 16 For experiment 1, payo€ condition is signi®cant at p ˆ 0.000 when the buyer makes an o€er in the ®nal round. The mean o€er is higher in the EV group than the UNCERT group and the di€erence is in the expected direction (refer to Panel A of Table 5). In no other case, however, is payo€ condition signi®cant at any conventional level, not even when the seller makes an o€er in the ®nal round. Interestingly, while the buyer is willing to accept a smaller number of points when the seller's payo€ is uncertain and

15

All analyses are repeated excluding data from the ®rst four, six, eight, and 12 periods. In no case were inferences a€ected. 16 Although not reported, the ®ndings for the player making the ®nal accepted proposal and the round of agreement are consistent with intuition. In general, across experiments 1±3, an o€er made in round three is more favorable to the player making the proposal than an o€er made in rounds one or two.

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Table 5 Mean number of points agreed upon by experimental cell Player making the ®nal, accepted o€er

Panel A: Experiment 1 Buyer Seller

Panel B: Experiment 2 Buyer Seller

Panel C: Experiment 3 Buyer Seller

Panel D: Experiment 4 Payo€ condition EV UNCERT

Payo€ condition

Round of agreement Round 1 or 2

Round 3

EV payo€ UNCERT payo€ EV payo€ UNCERT payo€

34.10 35.44 35.05 34.17

(n ˆ 20) (n ˆ 16) (n ˆ 20) (n ˆ 12)

43.05 33.11 26.05 26.32

(n ˆ 40) (n ˆ 47) (n ˆ 41) (n ˆ 38)

EV payo€ UNCERT payo€ EV payo€ UNCERT payo€

23.59 22.30 22.30 26.11

(n ˆ 27) (n ˆ 10) (n ˆ 10) (n ˆ 9)

25.94 21.46 19.29 16.47

(n ˆ 51) (n ˆ 54) (n ˆ 38) (n ˆ 47)

EV payo€ UNCERT payo€ EV Payo€ UNCERT Payo€

26.22 20.00 32.41 15.33

(n ˆ 9) (n ˆ 1) (n ˆ 17) (n ˆ 3)

36.88 27.48 29.32 19.83

(n ˆ 48) (n ˆ 60) (n ˆ 37) (n ˆ 54)

Player making ®nal, accepted o€er Buyer Seller 35.33 (n ˆ 67) 30.45 (n ˆ 44) 33.30 (n ˆ 57) 31.40 (n ˆ 43)

Note: In sessions with UNCERT payo€, the seller receives a ®xed fee and may incur an additional cost with a known probability. In sessions with EV payo€, the seller receives a ®xed fee minus the expected cost of agreeing to a particular settlement. Experiment 4 only consisted of one round, so agreements are not partitioned by round.

the deadline is reached, the seller does not necessarily demand such a settlement. For experiment 2, the results of the one-way ANOVAs indicate that payo€ condition is signi®cant at p < 0.01 when agreements are reached in the third round, regardless of the player making the ®nal o€er. In the third round, the mean o€ers are higher in the EV group than the UNCERT group, controlling for the player making the o€er (refer to Panel B of Table 5). The mean di€erences are in the expected direction and consistent with H2a. Uncertainty may a€ect the seller's behavior when the deadline is reached in experiment 2 because the probability of a loss looms larger than in experiment 1 (40% vs. 20%).

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For experiment 3, Panel C of Table 4 indicates that payo€ condition is signi®cant at p ˆ 0.000, whereas the three interactions involving this variable are not signi®cant at any conventional level. Pairwise comparisons indicate that the mean o€ers are higher in the EV group than the UNCERT group, controlling for the player making the ®nal o€er and the round of agreement (refer to Panel C of Table 5). The di€erences are consistent with H2a. When the sequence of o€ers is predetermined (i.e., alternating), the expected e€ect of payo€ condition is observed across the di€erent experimental groups. Lastly, for experiment 4, Panel D of Table 4 indicates that payo€ condition is not signi®cant at any conventional level (p ˆ 0.636). The mean o€ers are not a€ected by the seller's payo€ (refer to Panel D of Table 5). This result is not consistent with H2a and at odds with the ®ndings of experiments 1±3. 4.3. Additional analysis of the terms of agreements As discussed earlier, previous research suggests that bargainers often reach an agreement that produces an equal split or slightly favors the player with the bargaining advantage. In experiments 1, 3, and 4, an agreement of 32 points produces an equal split or an equal expected payo€ for both players (denoted EQUAL). In experiment 2, an agreement of 23 points produces an equal split. We perform t-tests to determine whether group means are signi®cantly di€erent from the EQUAL agreement. For experiments 1±3 (4), we partitioned the data into the eight (four) experimental cells and performed a series of t-tests. For each group, we tested whether the cell mean is signi®cantly di€erent from the EQUAL agreement. The results for experiments 1±4 are shown in Panels A±D, respectively, of Table 6. First we focus on experiments 1±3, each of which involves a multi-period setting. Across the three experiments, the results appear to vary by the round of agreement (refer to Panels A±C of Table 6). When we examine agreements reached in rounds one or two, only three of 11 di€erences are signi®cant at p < 0.10: in most cases, the agreements reached in the ®rst two rounds are not signi®cantly di€erent from the EQUAL agreement. 17 By comparison,

17

In addition, one t-test, which achieves statistical signi®cance, is conducted using only three observations. The test involves experiment 3, when the seller faces an UNCERT payo€ and makes the ®nal o€er in rounds one or two.

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Table 6 A comparison of negotiated agreements and EQUAL agreements Player making the ®nal, accepted o€er

Payo€ condition

Round of agreement Round 1 or 2

Panel A: Experiment 1 Buyer Seller

Panel B: Experiment 2 Buyer Seller

Panel C: Experiment 3 Buyer Seller

Panel D: Experiment 4 Payo€ condition EV UNCERT

EV payo€ UNCERT payo€ EV payo€ UNCERT payo€

2.10 3.24 3.05 2.36

(1.03) (1.32) (3.02) (0.81)

Round 3 10.44 (7.85) 2.04 (1.13) ÿ6.38 (ÿ6.79) ÿ6.64 (ÿ3.03)

EV payo€ UNCERT payo€ EV payo€ UNCERT payo€

0.59 (3.31) ÿ0.70 (ÿ0.41) ÿ0.70 (ÿ1.66) 3.11 (0.89)

2.90 (7.57) ÿ1.78 (ÿ2.07) ÿ3.66 (ÿ7.07) ÿ6.32 (ÿ7.65)

EV payo€ UNCERT payo€ EV payo€ UNCERT payo€

ÿ3.78 (ÿ1.33) 12.00 (N/A) 0.41 (0.59) ÿ16.67 (ÿ5.74)

4.88 (8.82) ÿ4.52 (ÿ4.10) ÿ2.68 (ÿ4.49) ÿ12.17 (ÿ10.81)

Player making ®nal, accepted o€er Buyer Seller ÿ1.55 (ÿ1.60) 3.33 (4.27) 1.30 (0.96) ÿ0.60 (ÿ0.43)

Note: Each entry indicates the di€erences between the mean observed agreement and the EQUAL agreement, where EQUAL agreements produce an equal split or an equal expected payo€ for both players. The value in parentheses is the t-statistic to test whether the observed and EQUAL agreements are signi®cantly di€erent from one another. One asterisk indicates that the di€erence is statistically signi®cant at p < 0.01 and two indicates signi®cance at p < 0.05. In experiment 3, only one agreement was reached in the ®rst two rounds when the buyer made the ®nal o€er and the seller's payo€ was UNCERT. As such, a test was not performed on the data in this cell. Further, in experiment 3 only three agreements were reached in the ®rst two rounds when the seller made the ®nal o€er and the seller's payo€ was UNCERT. The t-test for this cell should be interpreted with caution.

when we examine agreements reached in round three, 11 of 12 are statistically signi®cant at p < 0.05. We ®nd that when the seller makes the proposal in round three, the mean negotiated agreement is typically less than the EQUAL agreement: six of six di€erences are negative and signi®cant at p < 0.01. In other words, the seller is permitted to exploit, to some degree, his or her bargaining advantage in the ®nal round. When the buyer makes the

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®nal o€er, on the other hand, the di€erence is positive sometimes and negative other times. In the EV (UNCERT) payo€ condition, three of three (two of three) di€erences are positive (negative) and signi®cant at p < 0.01 (p < 0.05). Interestingly, when the seller's payo€ is UNCERT, the buyer is willing to accept settlements that are not signi®cantly di€erent or signi®cantly less than the EQUAL agreement. The buyer appears willing to make concessions when the seller's payo€ is UNCERT. 18 Next, we turn to experiment 4, which involves a single round of negotiation. As shown in Panel D of Table 6, only one of four di€erences is statistically signi®cant. When the buyer makes an o€er and the seller has an EV payo€, the negotiated agreement exceeds the EQUAL agreement at p < 0.01. None of the other di€erences are signi®cant at any conventional level. Notably, when the seller makes the o€er in a single-period setting, the seller does not exploit his or her bargaining advantage.

4.4. Concerns of fairness Lastly, we investigate whether concerns of fairness, which determine whether players' perceive that an o€er is reasonable, a€ect the negotiation process. Our data suggest that in multi-period settings, bargainers may attempt to coordinate negotiations initially around an EQUAL agreement. This result may arise because bargainers are concerned about being fair with one another (see e.g., Kahneman, Knetsch & Thaler, 1986; Guth & Tietz, 1990). Alternatively, bargainers may perceive that such behavior is necessary to maximize payo€s. To address this issue, we investigate the primary reason that players o€ered a particular number of points. As part of the post-experiment questionnaire, subjects were asked to indicate the primary reason underlying their o€ers, where they could respond (1) maximizing my payo€, (2) being fair with my bargaining partner, (3) avoiding no agreement, (4) minimizing the payo€ of my bargaining partner, or (5) other. Subjects' responses are summarized in Table 7. The majority of subjects (54%) were concerned about maximizing their payo€s. The second most frequent response was being fair to the other

18 Across the four experiments, the seller's payo€ is negative if the additional cost is incurred and the number of points agreed upon is greater than 16.

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Table 7 Primary reason why subjects make a particular o€er Primary reason

Maximizing my payo€ Being fair with my bargaining partner Avoiding no agreement Minimizing the payo€ of my bargaining partner Other

Number of responses Experiment 1

Experiment 2

Experiment 3

Experiment 4

Total

16 10

20 9

17 7

15 9

68 35

3 1

2 1

7 0

6 0

18 2

1

0

0

0

1

Note: In experiments 1, 3, and 4, a total of three subjects checked more than one reason. These subjects' responses are not included. In experiment 4, one subject did not complete the post-experiment questionnaire. Accordingly, the total number of responses across experiments 1±4 is 31, 32, 31, and 30, respectively.

person (28%) and the third most frequent was avoiding no agreement (15%). The pattern of responses appears to be similar across the four experiments. Hence, the data suggest that while fairness is considered in the negotiation process, payo€ maximization by whatever means is typically the primary objective. Payo€ maximization may require a consideration of fairness or it may not. Walster, Berscheid and Walster (1973, p. 153) note that if subjects believe that they can maximize their payo€s by behaving equitably, they will do so. By comparison, if they believe that they can maximize their payo€s by behaving inequitably, they will behave inequitably.

5. Conclusion This study uses an experimental economics method to examine bargaining behavior in a setting analogous to one in which buyer±seller pairs negotiate over the provision of professional services. We construct a two-player negotiation game that captures an important feature of this setting: uncertainty in the seller's payo€ with the possibility of a negative payo€. We examine whether uncertainty a€ects the outcome of the negotiation process. We ®nd that under various conditions uncertainty a€ects the terms of agreement, but not the frequency of non-agreements. In multi-period set-

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tings, if negotiations proceed up to a deadline, which includes the vast majority of cases, settlements are more favorable to the seller when the seller's payo€ includes an uncertain component. In this case, the buyer is willing to make concessions, apparently to compensate for the seller's uncertainty. We observe that when the deadline is reached and the seller's payo€ is uncertain, the buyer does not attempt to exploit his or her bargaining advantage. In a single-period setting, we ®nd that the seller's payo€ does not a€ect the terms of negotiated agreements. Our data provide some evidence that in the early rounds of negotiations, buyer±seller pairs coordinate their negotiations around a settlement that produces an equal split or an equal expected payo€ for both players. In multi-period settings, the average agreement reached prior to the deadline, in general, does not di€er from one that produces an equal split. By comparison, if negotiations proceed up to the deadline, the terms of agreement often favor the player making the ®nal proposal: bargainers are allowed to partially exploit their bargaining advantage. An exception, however, occurs when the buyer makes the ®nal proposal and the seller has an uncertain payo€. In this case, the buyer makes concessions and o€ers settlements that give the seller a higher expected value. Finally, in a single-period setting, we ®nd that negotiated agreements often do not deviate from that which produces an equal split. This result is at odds with the ®nding that players exploit their bargaining advantage in the ®nal round of a multi-period setting. We speculate that in a single-period setting players behave more conservatively because they do not have the opportunity to learn about the expectations and behavior of their bargaining partners. In conclusion, our ®ndings are far from consistent with game-theoretic predictions. The speci®c di€erences observed between the EV and UNCERT payo€ conditions and between the single and multi-period settings merit further investigation. In the future, researchers are advised to incorporate behavioral aspects in the development of theoretical models.

Acknowledgements Zhang acknowledges the ®nancial support of Wilfrid Laurier University. The authors acknowledge the helpful comments of Lucy Ackert, Glenn Feltham, Arnie Schneider, and Massoud Yahyazadeh and the research assistance of Shawna White.

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