Bargaining Experiments Research Articles

Learning to bargain

This paper studies how children learn to bargain. We performed simple anonymous bargaining experiments with real payoffs with 256 children from age 8 to 18. Average offers by even the youngest children were close to the amount that maximized their expected monetary payoff. Furthermore offers and responses were similar to what others have reported for adults. The variance of proposals was higher among younger children. Children showed clear evidence of reinforcement learning, responding to a rejection by increasing subsequent proposals. This pattern was strongest for the youngest children, who tended to respond to rejections with larger than payoff-maximizing increases in proposals. We found mixed support for social learning: while proposals increased after other children made larger proposals, they did not increase after proposals by others were rejected.

Dividing Justly in Bargaining Problems with Claims

Theoretical research on claims problems has concentrated on normative properties and axiomatizations of solution concepts. We complement these analyses by empirical evidence on the predictability of three classical solution concepts in a bankruptcy problem. We examine both people’s impartial normative evaluations as well as their actual negotiation behavior in a bargaining with claims environment. We measure people’s judgments on the normative attractiveness of solution concepts with the help of a survey and also observe actual agreements in a bargaining experiment with real money at stake. We find that the proportional solution is the normatively most attractive rule, whereas actual negotiation agreements are closest to the ‘constrained equal-award’ solution.

Ultimatum Bargaining Experiments: The State of the Art

In the basic ultimatum bargaining game two players, P1 and P2, must divide a pie ( ). P1 proposes a division in which he gets x and P2 gets x. P2 can then accept the division, in which the is split according to P1's proposal, or reject the proposal, in which case neither player gets anything. The current paper reviews empirical research on ultimatum bargaining games. It covers early work starting with Guth et al. (1982), but largely fo- cuses on more recent work (post Roth (1995)). Taken together, the research suggests that P1's behavior in largely in accord with game theoretic income-maximization, but P2's behavior cannot be easily reconciled with standard game-theoretic assumptions. Rather, P2 seems to be driven by a sense of fairness, specifically, a desire to be treated fairly by P1. Both P1 and P2 behavior are in agree- ment with equity theory. The most important conclusion that falls out of this review is that players' motivations, which often are not the ones posited by traditional game theory (and neo-classical eco- nomics, in general), and their perceptions of others' motivations are of fundamental importance in understanding strategic interac- tion. Other ultimatum bargaining findings are reported as well. Future research directions are suggested throughout.

DOES FACT-FINDING PROMOTE SETTLEMENT? THEORY AND A TEST

Nonbinding recommendations, such as provided by fact-finders, are shown to significantly increase voluntary settlements in bargaining. Theoretically, it is unclear whether recommendations will increase settlement rates. A recommendation may reduce outcome uncertainty, thereby “chilling” bargaining and increasing dispute rates. On the other hand, a recommendation may give the parties a focal point around which an agreement is made. Which of these effects dominates is a question that we consider using theory and data from controlled bargaining experiments. The data show the dominance of a focal point effect for suggestions, highlighting their potential role in improving dispute settlement procedures.(JEL C78, C92, J52)

Giving in Dictator Games: Regard for Others or Regard by Others?

Recent bargaining experiments demonstrated an impact of anonymity and incomplete information on subjects' behavior. This has rekindled the question whether fair behavior is inspired by regard for others or is explained by external forces. To test for the importance of external pressure we compare a standard double blind dictator game to a treatment which provides no information about the source of dictator offers, and where recipients do not even know that they participate in an experiment. We find no differences between treatments. This suggests that those dictators who give are purely internally motivated, as asserted by models of other-regarding preferences.

Nominal bargaining power, selection protocol, and discounting in legislative bargaining

The comparative static predictions of the Baron and Ferejohn [Baron, D.P., and Ferejohn, J.A., (1989). Bargaining in legislatures, American Political Science Review 83 (4), 1181–1206] model better organize behavior in legislative bargaining experiments than Gamson's Law. Regressions similar to those employed in field data produce results seemingly in support of Gamson's Law (even when using data generated by simulating agents who behave according to the Baron–Ferejohn model), but this is determined by the selection protocol which recognizes voting blocks in proportion to the number of votes controlled. Proposer power is not nearly as strong as predicted in the closed rule Baron and Ferejohn model, as coalition partners refuse to take the small shares given by the continuation value of the game. Discounting pushes behavior in the direction predicted by Baron and Ferejohn but has a much smaller effect than predicted.

When Ignorance Is Bliss: Information Exchange and Inefficiency in Bargaining

Most theories of legal discovery assume that the sharing of information among disputing parties will lead to convergence of expectations and facilitate settlement. However, psychological research shows that shared information, if open to multiple interpretations, is likely to be interpreted egocentrically by the disputants, which can cause beliefs to diverge rather than converge. We present results from a bargaining experiment that demonstrate that information sharing leads to divergence of expectations and to settlement delays when the information exchanged is amenable to multiple interpretations. By contrast, when there is only one obvious interpretation, information sharing leads to convergence of expectations and speeds settlement. We show, further, that information sharing moderates the relationship between the size of the bargaining zone and the prospects for settlement.

Dividing Justly in Bargaining Problems with Claims: Normative Judgments and Actual Negotiations

Theoretical research on claims problems has concentrated on normative properties and axiomatizations of solution concepts. We complement these analyses by empirical evidence on the predictability of three classical solution concepts in a bankruptcy problem. We examine both people's impartial normative evaluations as well as their actual negotiation behavior in a bargaining with claims environment. We measure people's judgments on the normative attractiveness of solution concepts with the help of a survey and also observe actual agreements in a bargaining experiment with real money at stake. We find that the proportional solution is the normatively most attractive rule, whereas actual negotiation agreements are closest to the 'constrained equal award' solution.

Communication, Reputation, and Punishment in Sequential Bargaining Experiments

Experiments on sequential bargaining have shown that subjects' behavior is far from the equilibrium prediction. Whereas previous models explain these deviations by some kind of social preferences, we investigate an alternative interpretation of behavior based on the assumption of bounded rational self-interest. Our analyses reveal that, in line with this interpretation, bargaining outcomes depend on subjects' payoff consequences from punishment. However, after preplay communication, we find a much weaker effect of these payoff consequences and a tremendous increase in the number of equal splits. This communication effect can be attributed to reputation effects only to a minor degree, if at all.

Supporting Learning in Evolving Dynamic Environments

In dynamic decision environments such as direct sales, customer support, and electronically mediated bargaining, decision makers execute sequences of interdependent decisions under time pressure. Past decision support systems have focused on substituting for decision makers' cognitive deficits by relieving them of the need to explicitly account for sequential dependencies. However, these systems themselves are fragile to change and, further, do not enhance decision makers' own adaptive capacities. This study presents an alternative strategy that defines information systems requirements in terms of enhancing decision makers' adaptation. In so doing, the study introduces a simulation model of how decision makers learn patterns of sequential dependency. When a system was used to manage workflows in a way predicted by the model to enhance learning, decision makers in a bargaining experiment learned underlying patterns of sequential dependency that helped them adapt to new situations. This result is rare if not unique in the study of dynamic decision environments. It indicates that a shift, away from substituting for short-term deficits and toward enhancing pattern learning, can substantially improve the effectiveness of decision support in dynamic environments. Based on the specific findings in this study, this shift has important implications for designing information system workflows and potential future applications in interface design.

Settlement escrows: an experimental study of a bilateral bargaining game

This paper reports the results of a bargaining experiment. We follow the pre-trial bargaining model of Gertner and Miller (1995) under uncertainty and examine the effect of a litigation institution, called a settlement escrow, and uncertainty on the timing and quality of settlement outcomes. Our findings indicate that settlement rates are significantly higher when a settlement escrow is added to the bargaining process where there is asymmetric information. Quality of outcomes, measured as the percentage of the true damage that the outcome represents, is positively and significantly influenced by the addition of a settlement escrow.

Fairness, escalation, deference, and spite: strategies used in labor-management bargaining experiments with outside options

We review two recent cases of labor-management bargaining when outside options are in play and notice that structurally similar negotiations end differently. We hypothesize that behavioral factors are important and conduct an experiment. We find conflict is common when one side has an outside option despite relatively generous offers. We also find that firms who search for outside options, but do not take them, make more generous counteroffers than non-searching firms and that, overall, searching triggers concessions from unions unless the union has previously been hung out to dry by a firm who accepted an outside option.

A Cooperative Game for Siting Noxious Facilities: Theory and Experimental Design

The siting of noxious facilities is usually a reason for conflict: as a society we want them, but as individuals (and often as communities) we do not want them close by. Faced with this problem, economists have used several methods such as lotteries, auctions or insurance policies. However, all those mechanisms have theoretical shortcomings. Therefore, we propose a new approach based on voluntary exchange. In order to reduce transaction costs, we introduce an arbitrator that proposes surplus distribution and a host community. The main question in this paper is to determine which distributions it has to propose to quickly reach an agreement. To this end, a new asymmetric cooperative game is constructed and three classical solution concept are studied after adaptation to the asymmetric context of the game. Finally, we explore the predictive power of these solutions by implementing laboratory bargaining experiments.

Satisficing and fairness in ultimatum bargaining game experiments

We re-examine the subjects’ behavior in the ultimatum bargaining experiments studied by Roth et al. (1991, American Economic Review). In our model, un-modeled factors including rationality determine players’ initial aspirations, and a modified version of the case-based learning process governs subsequent adaptations. The calibration results of this paper show that ‘satisficing’ can explain the actual subjects’ behavior surprisingly well. More precisely, it is shown that 77.7% to 96.7% of the observed behavior is consistent with our model prediction. We also argue that the closer the initial aspiration levels are to the perfect equilibrium payoff, the lower the mean or modal offer tends to be in the actual experiments.

A Suggested Interpretation of Some Experimental Results on Preplay Communication

M. Rabin (1994, J. Econ. Theory63, 370–391) proposes a model of behavior in two-person complete-information games with preplay communication, using non-equilibrium notions in the spirit of rationalizability to derive lower bounds on players' expected payoffs when players have unlimited communication opportunities. This paper adapts Rabin's model so that it can be used to analyze the results of the experiments of R. Cooper et al. (1989, Rand J. Econ.20, 568–587) on structured preplay communication in the Battle of the Sexes and the results of the unstructured bargaining experiments of Roth, Malouf, and Murnighan. Adding empirically motivated restrictions that allow the model to predict the payoff effects of changes in bounded communication possibilities like those in the experiments, it is shown that the data from both experiments are generally consistent with Rabin's model, and with the predictions of the extended model. Journal of Economic Literature Classification Numbers: C70, C72, C78, C91.

Mental accounting and other-regarding behavior: Evidence from the lab

This paper uncovers a key determinant of the other-regarding behavior that permeates bargaining experiments. Examining a one-shot dictator game that has the first-mover dictate the split of an amount of money, dictators acting over earned money exhibited self-interested behavior in 76% of bargains. This result stands in stark contrast to the baseline experiment in which dictators acting over allocated money displayed self-interested behavior in only 26% of bargains. Self-interested behavior appeared at greater levels using an earnings protocol than any previous variation of the dictator game. While the distinction between earned and unearned wealth is likely context specific, the earnings protocol may be an important option for future laboratory research. Specifically, the earnings protocol may provide a closer correspondence between the laboratory and individual choices over personal assets.

Fairness, Escalation, Deference, and Spite: Strategies Used in Labor-Management Bargaining Experiments with Outside Options

Labor-management negotiations are an example of a situation in which outside options may play an important role in determining outcomes. In particular, firms may attempt to use outside options to extract concessions from unions. In reviewing two recent cases of bargaining between management and a union, we notice that although the situations appear similar, the negotiated outcomes are dramatically different. We hypothesize that behavioral factors may play a role. To test this conjecture, we construct a bargaining experiment. Our results suggest that outside options do affect bargaining behavior. First, we find that many fair offers are rejected and, in general, the rate of conflict is high. Second, firms who search for outside options, but do not take them, return to bargaining and make higher offers than if they had not searched. Third, overall the act of searching by firms tends to trigger concessions from unions except when the union has previously been hung out to dry by a firm accepting an outside option. In this case unions react spitefully.

The effects of power and message variables on compliance

The study investigated the empirical relationships among social power, message behavior, and compliance. A conceptualization of social power from power dependency theory was offered, and two models of the general relations among these constructs were advanced. They included a mediation model and a moderating model. These issues were investigated by having 108 subjects participate in a bargaining experiment where power was controlled by systematically varying each partner's alternatives, and participants' message behavior and outcomes were observed. Although power had non-trivial effects on message behavior, the data were generally inconsistent with the mediation model. The data were consistent with the moderator model which predicted that message effectiveness varies as a function of social power. Implications and limitations of the results are discussed.

Ultimatum Bargaining Behavior in Israel, Japan, Slovenia, and the United States: A Social Utility Analysis

We explain the main features of the results of the four-country ultimatum bargaining experiments of Roth et al. (1991), Amer. Econom. Rev.81, 1068–1095) by a social utility model. The specification of social utility of a player has two parts: a linear combination of the monetary payoffs of the proposer and the responder and payoff uncertainty. We find that, on average, responders have negative regard for proposers' earnings in all countries. Proposers have negative regard for responders' monetary earnings in countries where responders have high negative regard for proposers' earnings (USA and Slovenia). In countries where responders have low negative regard for proposers' earnings (Israel and Japan), proposers are expected payoff maximizers. Journal of Economic Literature Classification Numbers: A13, C19, C44, C72, C92, D63, D64.

Damage Caps, Motivated Anchoring, and Bargaining Impasse

This paper reports results from a bargaining experiment testing the effect on settlement rates of a damage cap set much higher than the value of the underlying claim. We presented 462 student subjects with materials outlining a personal injury lawsuit and permitted randomly assigned subject pairs to negotiate a pretrial settlement. We find that imposition of a $1 million cap reduced the settlement rate through a process termed “motivated anchoring,” in which a relatively high damage cap disproportionately anchors the plaintiff's estimate of the likely damage award. The result is a widened disparity in opposing litigants' judgments and less settlement. These results contrast with findings from previous experiments where a relatively low cap constrains the parties' judgments and produces more settlement. This pair of results suggests the effect of a cap will depend on its size relative to the stakes of the case.