This paper reports laboratory data for games that are played only once. These games span the standard categories: static and dynamic games with complete and incomplete information. For each game, the treasure is a treatment in which behavior conforms nicely to predictions of the Nash equilibrium or relevant refinement. In each case, however, a change in the payoff structure produces a large inconsistency between theoretical predictions and observed behavior. These contradictions are generally consistent with simple intuition based on the interaction of payoff asymmetries and noisy introspection about others’ decisions.

This paper reports the results of a private-values auction experiment in which expected costs of deviating from the Nash equilibrium bidding function are asymmetric, with the implication that upward deviations will be more likely in one treatment than in the other. Overbidding is observed in both treatments, but is more prevalent in the treatment where the costs of overbidding are lower. We specify and estimate a noisy (quantal response) model of equilibrium behavior. Estimated noise and risk aversion parameters are highly significant and consistent across treatments. The resulting two-parameter model tracks both the average bids and the distribution of bids remarkably well. Alternative explanations of overbidding are also considered. The estimates of parameters from a nonlinear probability weighting function yield a formulation that is essentially equivalent to risk aversion in this context. A model in which players experience a "joy of winning " provides a reasonable fit of the data but does significantly worse than the risk aversion model. 1.

The quantal response equilibrium (QRE) notion of Richard D. McKelvey and Thomas R. Palfrey (1995) has recently attracted considerable attention, due in part to its widely documented ability to rationalize observed behavior in games played by experimental subjects. However, even with strong apriorirestrictions on unobservables, QRE imposes no falsifiable restrictions: it can rationalize any distribution of behavior in any normal form game. After demonstrating this, we discuss several approaches to testing QRE under additional maintained assumptions. (JEL C72, C52, C90) The quantal response equilibrium (QRE) notion of McKelvey and Palfrey (1995) can be viewed as an extension of standard random utility models of discrete (“quantal”) choice to strategic settings, or as a generalization of Nash equilibrium that allows noisy optimizing behavior while maintaining the internal consistency of rational expectations. Formally, QRE is based on the introduction of random perturbations to the payoffs associated with each action a player can take. 1 Realizations of these perturbations affect which action is the best response to the equilibrium distribution of opponents ’ behavior. 1We give a more complete discussion in the following section. The literature has considered generalizations of the QRE to extensive form games (McKelvey and Palfrey (1998)) and games with continuous strategy

Abstract. In experimental studies of behavior in 2 × 2 games with unique mixed strategy equilibria, observed choice frequencies are systematically different from mixed-strategy Nash predictions. This paper examines experimental results for a variety of such games, and shows that a structural econometric model which incorporates risk aversion into a quantal response equilibrium explains the data very well. Moreover, risk aversion estimates are stable across the different games and are close to those obtained from laboratory and field auction data, as well as from individual lottery choice experiments.

Experiments with real and computational agents are used to examine the impact of changing the level of a non-employment payoff on the evolution of cooperation between workers and employers participating in a sequential employment game with incomplete contracts. Workers either direct work offers to preferred employers or choose unemployment and receive the non-employment payoff. Subject to capacity limitations, employers either accept work offers from preferred workers or remain vacant and receive the nonemployment payoff. Matched workers and employers participate in an employment relationship modeled as a prisoner's dilemma game. In both types of experiments, increases in the non-employment payoff result in higher unemployment and vacancy rates while at the same time encouraging higher rates of cooperation among the workers and employers who do form matches. However, the behaviors exhibited by the computational agents are coordinated to a higher degree than the behaviors of the human subjects. This difference raises challenging questions for both human-subject and computational experimentalists. Keywords: Labor market; unemployment rate; vacancy rate; evolution of cooperation; efficiency wage; search and matching; endogenous interaction networks; evolutionary game; human-subject experiments; computational experiments; agentbased computational economics. 2 1.

This paper examines how the presence of a non-negligible fraction of reciprocally fair actors changes the provision of incentives through contracts. We provide experimental evidence that principals have a strong preference for less complete contracts although the standard self-interest model predicts that they should prefer the more complete contract. Our theoretical analysis shows that fairness concerns can explain this preference for less completeness. Fair principals keep their promises which provides strong pecuniary incentives through an incomplete contract. Selfish principals free-ride and exploit the agents. Counterintuitively, selfish agents are induced to work by an incomplete contract while fair agents shirk. Keywords: Fairness, Reciprocity, Incomplete Contracts, Incentives JEL Classification Numbers: C7, C9, D0, J3. * Paper written for the invited session "Fairness in Strategic Interactions" at the 14th Annual Congress of the European Economic Association in Santiago de Compostela, September 1-4, 1999. Alexander Klein and Susanne Kremhelmer provided excellent research assistance for the experiments discussed in this article. Financial support by Deutsche Forschungsgemeinschaft through grant SCHM-1196/4-1 is gratefully acknowledged. Ernst Fehr also gratefully acknowledges support from the Swiss National Science Foundation (project number 1214-05100.97) and the Network on the Evolution of Preferences and Social Norms of the MacArthur Foundation and the EU-TMR Research Network ENDEAR (FMRX-CTP98-0238). a Ernst Fehr, Institute for Empirical Research in Economics, University of Zurich, Bluemlisalpstrasse 10, CH-8006 Zurich, Switzerland. b Klaus M. Schmidt, Department of Economics, University of Munich, Ludwigstr. 28, D-80539 Muenchen, Germany, em...

We present experimental evidence that promises and threats mitigate the hold–up problem. While investors rely as much on their own threats as on their trading partner’s promises, the latter are more credible. Building on recent work in psychology and behavioral economics, we then present a simple model within which agents are concerned about both fairness and consistency. The model can account for several of our experimental findings. Its most striking implication is that fairmindedness strengthens the credibility of promises to behave fairly, but weakens the credibility of threats to punish unfair behavior. JEL classification: L14, C78.

In the basic ultimatum bargaining game two players, P 1 and P 2, must divide a pie (π). P 1 proposes a division in which he gets π − x and P 2 gets x. P 2 can then accept the division, in which the π is split according to P 1’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 Güth et al. (1982), but largely focuses on more recent work (post Roth (1995)). Taken together, the research suggests that P 1’s behavior in largely in accord with game theoretic income-maximization, but P 2’s behavior cannot be easily reconciled with standard game-theoretic assumptions. Rather, P 2 seems to be driven by a sense of fairness, specifically, a desire to be treated fairly by P 1. Both P 1 and P 2 behavior are in agreement with equity theory. The most important conclusion that falls out of this review is that players’ motivations, which often are not

We present an experiment that attempts to separate the two commonplace explanations for behavior in ultimatum games–subjects ’ concern for fairness versus the failure of subgame perfection as an equilibrium refinement. We employ a tournament structure of the bargaining interaction to eliminate the potential for fairness to influence behavior. Comparing the results of the tournament game with two control treatments affords us a clean test of subgame perfection as well as a measure fairness-induced play. We find after 10 iterations of play that about half of all non-subgame-perfect demands are due to fairness, and the rest to imperfect learning. However, as suggested by models of learning, we also confirm that the ultimatum game presents an especially difficult environment for learning subgame perfection. ∗ We are grateful to Larry Samuelson, Gary Bolton and Richard Zeckhauser helpful comments. Andreoni thanks the National Science Foundation for financial support.

Ken Binmore and Avner Shaked are highly respected economists, well-known for their analytical contributions and breadth of knowledge. Moreover, they have actively participated in experimental economics for many years. However, their critique of the current state of experimental economics in general, and of Ernst Fehr and Klaus Schmidt’s presentation of their theory of inequality aversion in particular, are deeply flawed. Moreover, their conception of the relationship between theory and experiment and their interpretation of the empirical evidence on otherregarding preferences are untenable. Binmore and Shaked set the problem as follows: Should we follow those experimental economists who seek recognition of their subject as a science by adopting the scientific standards that operate in neighboring disciplines like biology or psychology? Or should we... [treat] experimental results as just one more rhetorical tool to be quoted when convenient in seeking to convert others to whatever your own point of view may be? Binmore and Shaked in fact identify only one aspect of scientific standards on which experimentalists are purportedly wanting, their failure to adopt “a more skeptical attitude when far-reaching claims about human behavior are extrapolated from very slender data. ” We maintain that experimental economics has not been faulty in this respect.