We experimentally test the predictive success of three stationary concepts in two cyclic duopoly games. The concepts are Nash equilibrium, impulse-balance equilibrium and payoff-sampling equilibrium. In the experiment 11 independent subject groups, consisting out of six participants interacting over 200 rounds, were gathered for each game. The comparison of the three concepts with mixed strategies shows that the order of performance from best to worst is as follows: payoff-sampling equilibrium, impulse-balance equilibrium, and Nash equilibrium. In addition the data exhibit a weak but significant tendency over time in the direction of coordination at a pure strategy equilibrium.

A vast amount of empirical and theoretical research on public good games indicates that the threat of punishment can curb free-riding in human groups engaged in joint enterprises. Since punishment is often costly, however, this raises an issue of second-order free-riding: indeed, the sanctioning system itself is a common good which can be exploited. Most investigations, so far, considered peer punishment: players could impose fines on those who exploited them, at a cost to themselves. Only a minority considered so-called pool punishment. In this scenario, players contribute to a punishment pool before engaging in the joint enterprise, and without knowing who the free-riders will be. Theoretical investigations (Sigmund et al., Nature 466:861–863, 2010) have shown that peer punishment is more efficient, but pool punishment more stable. Social learning, i.e., the preferential imitation of successful strategies, should lead to pool punishment if sanctions are also imposed on second-order free-riders, but to peer punishment if they are not. Here we describe an economic experiment (the Mutual Aid game) which tests this prediction. We find that pool punishment only emerges if second-order free riders are punished, but that peer punishment is more stable than expected. Basically, our experiment shows that social learning can lead to a spontaneously emerging social contract, based on a sanctioning institution to overcome the free rider problem.

The Individual Evolutionary Learning (IEL) model explains human subjects’ behavior in a wide range of repeated games which have unique Nash equilibria. Using a variation of ‘better response’ strategies, IEL agents quickly learn to play Nash equilibrium strategies and their dynamic behavior is like that of humans subjects. In this paper we study whether IEL can also explain behavior in games with gains from coordination. We focus on the simplest such game: the 2 person repeated Battle of Sexes game. In laboratory experiments, two patterns of behavior often emerge: players either converge rapidly to one of the stage game Nash equilibria and stay there or learn to coordinate their actions and alternate between the two Nash equilibria every other round. We show that IEL explains this behavior if the human subjects are truly in the dark and do not know or believe they know their opponent’s payoffs. To explain the behavior when agents are not in the dark, we need to modify the basic IEL model and allow some agents to begin with a good idea about how to play. We show that if the proportion of inspired agents with good ideas is chosen judiciously, the behavior of IEL agents looks remarkably similar to that of human subjects in laboratory experiments.

This paper studies the dynamics by which individuals with heterogeneous preferences partition themselves into groups. A novel experimental environment is developed to capture the tension between increasing returns to group size and attaining a group policy closest to an ideal point. Subjects can move freely between locations, with group policy either fixed by location or determined by member vote. A primary goal is to assess which of two stability concepts common to the group formation literature predicts which groups agents sort into. The same set of Nash stable partitions exist in each condition, with the efficient, strong Nash stable state requiring subjects to form heterogeneous groups and compromise on policy. I find that subjects who are only able to move between locations with fixed policies always over-segregate, rather than build efficient heterogeneous groups. When mobility is combined with the ability to vote on local policy, most subjects reach the efficient partition. This shows outcomes cannot be determined by considering the existence of stable states alone and that consideration must also be given to subtle aspects of the system dynamics. Further, it suggests that experiments may play an important role in understanding these group formation dynamics.

We investigate a number of canonical predictions that arise from relational contract theory. Employing an experimental design with endogenous choice of contract type, we find considerable experimental support for several well-established predictions, including the importance of self-enforcement and individual rationality constraints for contractual performance; a preference for informal agreements when third-party verification of performance is coarse; and a tendency toward strategic ambiguity (Bernheim and Whinston Am Econ Rev 88(4):902–932, 1998). However, two findings that appear to be inconsistent with theory are that (1) contractually specified performance levels do not appear to respond to the discount factor though realized performance does; and (2) subjects often apply inefficient punishments following a deviation. By providing evidence on the strengths and weaknesses of standard relational contract theory, our study shows where there is room for improvement. We conjecture that incorporating social preferences and semi-grim strategies (Breitmoser Am Econ Rev 105(9):2882–2910, 2015) can potentially address the observed weaknesses.

We provide the first examination of all-pay auctions using continuous-time protocols, allowing subjects to adjust their bid at will, observe payoffs almost instantaneously, and gain more experience through repeated-play than in previous, discrete-time, implementations. Unlike our predecessors—who generally find overbidding—we observe underbidding relative to Nash equilibrium. To test the predictions of evolutionary models, we vary the number of bidders and prizes across treatments. If two bidders compete for a single prize, evolutionary models predict convergence to equilibrium. If three bidders compete for two prizes, evolutionary models predict non-convergent cyclical behavior. Consistent with evolutionary predictions, we observe cyclical behavior in both auctions and greater instability in two-prize auctions. These results suggest that evolutionary models can provide practitioners in the field with additional information about long-run aggregate behavior that is absent from conventional models.

We describe a common pool resource game in which players choose how much of the stock to extract in a sequential manner. There are two choices and one represents taking a larger proportion of the stock than the other. After a player makes a choice, the remaining stock grows at a constant rate. We consider a game with a finite number of alternating moves. It is shown that changes in the larger proportion of the stock that the players are allowed to take and the growth rate affect equilibrium, but have little effect on behavior in the laboratory. In addition to observing more cooperation than predicted, we observe that parameters that are strategically irrelevant affect behavior. The results of this research might help policy makers in developing adequate policies to prevent overexploitation of some natural renewable resources.

We consider payment schemes in experiments that model infinite-horizon games by using random termination. We compare paying subjects cumulatively for all periods of the game; with paying subjects for the last period only; with paying for one of the periods, chosen randomly. Theoretically, assuming expected utility maximization and risk neutrality, both the cumulative and the last period payment schemes induce preferences that are equivalent to maximizing the discounted sum of utilities. The last period payment is also robust under different attitudes toward risk. In comparison, paying subjects for one of the periods chosen randomly creates a present-period bias. We further provide experimental evidence from infinitely repeated prisoners’ dilemma games that supports the above theoretical predictions.

The structural Quantal Response Equilibrium (QRE) generalizes the Nash equilibrium by augmenting payoffs with random elements that are not removed in some limit. This approach has been widely used both as a theoretical framework to study comparative statics of games and as an econometric framework to analyze experimental and field data. The framework of structural QRE is flexible: it can be applied to arbitrary finite games and incorporate very general error structures. Restrictions on the error structure are needed, however, to place testable restrictions on the data (Haile et al., 2004). This paper proposes a reduced-form approach, based on quantal response functions that replace the best-response functions underlying the Nash equilibrium. We define a regular QRE as a fixed point of quantal response functions that satisfies four axioms: continuity, interiority, responsiveness, and monotonicity. We show that these conditions are not vacuous and demonstrate with an example that they imply economically sensible restrictions on data consistent with laboratory observations. The reduced-form approach allows for a richer set of regular quantal response functions, which has proven useful for estimation purposes.

We report on an experiment examining behavior and equilibrium selection in two similar, infinitely repeated games, Stag Hunt and Prisoner’s Dilemma under anonymous random matching. We are interested in the role that historical precedents may play for equilibrium selection between these two repeated games. We find that a precedent for efficient play in the repeated Stag Hunt game does not carry over to the repeated Prisoner’s Dilemma game despite the possibility that efficient play can be sustained as an equilibrium of the indefinitely repeated game. Similarly, a precedent for inefficient play in the repeated Prisoner’s Dilemma game does not extend to the repeated Stag Hunt game. We conclude that equilibrium selection between similar repeated games may have less to do with historical precedents and might instead depend more on strategic considerations associated with the different payoffs of these similar repeated games.

In a dyadic game, strategic asymmetric dominance occurs when a player's preference for one strategy A relative to another B is systematically increased by the addition of a third strategy Z, strictly dominated by A but not by B. There are theoretical and empirical grounds for believing that this effect should decline over repetitions, and other grounds for believing, on the contrary, that it should persist. To investigate this question experimentally, 30 participant pairs played 50 rounds of one symmetric and two asymmetric 3 × 3 games each having one strategy strictly dominated by one other, and a control group played 2 × 2 versions of the same games with dominated strategies removed. The strategic asymmetric dominance effect was observed in the repeated-choice data: dominant strategies in the 3 × 3 versions were chosen more frequently than the corresponding strategies in the 2 × 2 versions. Time series analysis revealed a significant decline in the effect over repetitions in the symmetric game only. Supplementary verbal protocol analysis helped to clarify the players’ reasoning and to explain the results.

This paper compares behavior under four different implementations of infinitely repeated games in the laboratory: the standard random termination method [proposed by Roth and Murnighan (J Math Psychol 17:189–198, 1978)] and three other methods that de-couple the expected number of rounds and the discount factor. Two of these methods involve a fixed number of repetitions with payoff discounting, followed by random termination [proposed by Sabater-Grande and Georgantzis (J Econ Behav Organ 48:37–50, 2002)] or followed by a coordination game [proposed in (Andersson and Wengström in J Econ Behav Organ 81:207–219, 2012; Cooper and Kuhn in Am Econ J Microecon 6:247–278, 2014a)]. We also propose a new method—block random termination—in which subjects receive feedback about termination in blocks of rounds. We find that behavior is consistent with the presence of dynamic incentives only with methods using random termination, with the standard method generating the highest level of cooperation. Subject behavior in the other two methods display two features: a higher level of stability in cooperation rates and less dependence on past experience. Estimates of the strategies used by subjects reveal that across implementations, even when the discount rate is the same, if interactions are expected to be longer defection increases and the use of the Grim strategy decreases.

We analyze experimentally two sender-receiver games with conflictive preferences. In the first game, the sender can choose to tell the truth, to lie, or to remain silent. The latter strategy is costly. In the second game, the receiver must decide additionally whether or not to costly punish the sender after having observed the history of the game. We investigate the existence of two kinds of social preferences: lying aversion and preference for truth-telling. In the first game, senders tell the truth more often than predicted by the sequential equilibrium analysis, they remain silent frequently, and there exists a positive correlation between the probability of being truthful and the probability of remaining silent. Our main experimental result for the extended game shows that those subjects who punish the sender with a high probability after being deceived are precisely those who send fewer but more truthful messages. Finally, we solve for the Perfect Bayesian Nash Equilibria of a reduced form of the baseline game with two types of senders. The equilibrium predictions obtained suggest that the observed excessive truth-telling in the baseline game can be explained by lying aversion but not by a preference for truth-telling.

This paper studies whether and how strategy revision opportunities affect levels of collusion in indefinitely repeated two-player games. Consistent with standard theory, we find that such opportunities do not affect strategy choices, or collusion levels, if the game is of strategic substitutes. In games of strategic complements, by contrast, revision opportunities lead to more collusion. We discuss alternative explanations for this result.

This paper considers some of the questions raised by the fact that people's behaviour—including their behaviour in experimental environments—has a stochastic component. The nature of this component may be crucial to the interpretation of the patterns of data we observe and the choice of statistical criteria for favouring one hypothesis at the expense of others. However, it is arguable that insufficient consideration has been given to the way(s) in which the stochastic element is modelled. The paper aims to explore some of the issues involved.

A well-known result from the theory of finitely repeated games states that if the stage game has a unique equilibrium, then there is a unique subgame perfect equilibrium in the finitely repeated game in which the equilibrium of the stage game is being played in every period. Here I show that this result does in general not hold anymore if players have social preferences of the form frequently assumed in the recent literature, for example in the inequity aversion models of Fehr and Schmidt (Quartely Journal of Economics 114:817–868, 1999) or Bolton and Ockenfels (American Economic Review 100:166–193, 2000). In fact, repeating the unique stage game equilibrium may not be a subgame perfect equilibrium at all. This finding should have relevance for all experiments with repeated interaction, whether with fixed, random or perfect stranger matching.

This paper experimentally investigates the provision of real-time feedback about school assignments during the preference reporting period in three widely employed mechanisms: deferred acceptance, top trading cycles, and the Boston mechanism. Adaptive models predict that greater sensitivity to tentative assignments during the reporting period will produce more equilibrium assignments in all three mechanisms. Consistent with adaptive predictions, real-time assignment feedback consistently increased equilibrium assignments but did not increase truthful reporting. These findings suggest that providing feedback about assignments during the preference reporting period could help student assignment mechanisms more reliably achieve policy goals.

Recent experiments have shown that voluntary punishment of free riders can increase contributions, mitigating the free-rider problem. But frequently punishers punish high contributors, creating “perverse” incentives which can undermine the benefits of voluntary punishment.

In our experiment, allowing punishment of punishing behaviors reduces punishment of high contributors, but gives rise to efficiency-reducing second-order “perverse” punishment. On balance, efficiency and contributions are slightly but not significantly enhanced.

There is mixed evidence on whether subjects coordinate on the efficient equilibrium in experimental stag hunt games under complete information. A design that generates an anomalously high level of coordination, Rankin et al. (Games Econo Behav 32(2):315–337, 2000), varies payoffs each period in repeated play rather than holding them constant. These payoff “perturbations” are eerily similar to those used to motivate the theory of global games, except the theory operates under incomplete information. Interestingly, that equilibrium selection concept is known to coincide with risk dominance, rather than payoff dominance. Thus, in theory, a small change in experimental design should produce a different equilibrium outcome. We examine this prediction in two treatments. In one, we use public signals to match Rankin et al. (2000)’s design; in the other, we use private signals to match the canonical example of global games theory. We find little difference between treatments, in both cases, subject play approaches payoff dominance. Our literature review reveals this result may have more to do with the idiosyncrasies of our complete information framework than the superiority of payoff dominance as an equilibrium selection principle.

Sequential multi-battle contests are predicted to induce lower expenditure than simultaneous contests. This prediction is a result of a “New Hampshire Effect”—a strategic advantage created by the winner of the first battle. Although our laboratory study provides evidence for the New Hampshire Effect, we find that sequential contests generate significantly higher (not lower) expenditure than simultaneous contests. This is mainly because in sequential contests, there is significant over-expenditure in all battles. We suggest sunk cost fallacy and utility of winning as two complementary explanations for this behavior and provide supporting evidence.