Hot vs. cold: Sequential responses and preference stability in experimental games

In experiments with two-person sequential games we analyzewhether responses to favorable and unfavorable actions dependon the elicitation procedure. In our hot treatment thesecond player responds to the first player s observed actionwhile in our cold treatment we follow the strategy method and have the second player decide on a contingent action foreach and every possible first player move, without firstobserving this move. Our analysis centers on the degree towhich subjects deviate from the maximization of their pecuniaryrewards, as a response to others actions. Our results show nodifference in behavior between the two treatments. We also findevidence of the stability of subjects preferences with respectto their behavior over time and to the consistency of theirchoices as first and second mover.

Game theory and reciprocity in some extensive form experimental games

We examine decision making in two-person extensive form game trees using nine treatments that vary matching protocol, payoffs, and payoff information. Our objective is to establish replicable principles of cooperative versus noncooperative behavior that involve the use of signaling, reciprocity, and backward induction strategies, depending on the availability of dominated direct punishing strategies and the probability of repeated interaction with the same partner. Contrary to the predictions of game theory, we find substantial support for cooperation under complete information even in various single-play treatments.

On some geometry and equivalence classes of normal form games

Equivalence classes of normal form games are defined using the geometryof correspondences of standard equilibiurm concepts like correlated, Nash,and robust equilibrium or risk dominance and rationalizability. Resultingequivalence classes are fully characterized and compared across differentequilibrium concepts for 2 x 2 games. It is argued that the procedure canlead to broad and game-theoretically meaningful distinctions of games aswell as to alternative ways of viewing and testing equilibrium concepts.Larger games are also briefly considered.

Games for groundwater governance: field experiments in Andhra Pradesh, India

Groundwater is a common-pool resource that is subject to depletion in many places around the world as a result of increased use of irrigation and water-demanding cash crops. Where state capacity to control groundwater use is limited, collective action is important to increase recharge and restrict highly water-consumptive crops. We present results of field experiments in hard rock areas of Andhra Pradesh, India, to examine factors affecting groundwater use. Two nongovernmental organizations (NGOs) ran the games in communities where they were working to improve watershed and water management. Results indicate that, when the links between crop choice and groundwater depletion is made explicit, farmers can act cooperatively to address this problem. Longer NGO involvement in the villages was associated with more cooperative outcomes in the games. Individuals with more education and higher perceived community social capital played more cooperatively, but neither gender nor method of payment had a significantly effect on individual behavior. When participants could repeat the game with communication, similar crop choice patterns were observed. The games provided an entry point for discussion on the understanding of communities of the interconnectedness of groundwater use and crop choice.

Leader corruption depends on power and testosterone

We used incentivized experimental games to manipulate leader power-the number of followers and the discretion leaders had to enforce their will. Leaders had complete autonomy in deciding payouts to themselves and their followers. Although leaders could make prosocial decisions to benefit the public good they could also abuse their power by invoking antisocial decisions, which reduced the total payouts to the group but increased leader's earnings. In Study 1 (N = 478), we found that both amount of followers and discretionary choices independently predicted leader corruption. In Study 2 (N = 240), we examined how power and individual differences (e.g., personality, hormones) affected leader corruption over time; power interacted with testosterone in predicting corruption, which was highest when leader power and baseline testosterone were both high. Honesty predicted initial level of leader antisocial decisions; however, honesty did not shield leaders from the corruptive effect of power.

Exposure to superfluous information reduces cooperation and increases antisocial punishment in reputation-based interactions

Human cooperation is often based on reputation gained from previous interactions with third parties. Such reputation can be built on generous or punitive actions, and both, one's own reputation and the reputation of others have been shown to influence decision making in experimental games that control for confounding variables. Here we test how reputation-based cooperation and punishment react to disruption of the cognitive processing in different kinds of helping games with observers. Saying a few superfluous words before each interaction was used to possibly interfere with working memory. In a first set of experiments, where reputation could only be based on generosity, the disruption reduced the frequency of cooperation and lowered mean final payoffs. In a second set of experiments where reputation could only be based on punishment, the disruption increased the frequency of antisocial punishment (i.e. of punishing those who helped) and reduced the frequency of punishing defectors. Our findings suggest that working memory can easily be constraining in reputation-based interactions within experimental games, even if these games are based on a few simple rules with a visual display that provides all the information the subjects need to play the strategies predicted from current theory. Our findings also highlight a weakness of experimental games, namely that they can be very sensitive to environmental variation and that quantitative conclusions about antisocial punishment or other behavioral strategies can easily be misleading.

Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.

Choice of partners in multiple two-person prisoner's dilemma games: An experimental study

We examine the effect of unilateral and mutual partner selection in the context of prisoner's dilemmas experimentally. Subjects play simultaneously several finitely repeated two-person prisoner's dilemma games. We find that unilateral choice is the best system. It leads to low defection and fewer singles than with mutual choice. Furthermore, with the unilateral choice setup we are able to show that intendingdefectors are more likely to try to avoid a match than intending cooperators. We compare our results of multiple games with single game PD-experiments and find no difference in aggregate behavior. Hence the multiple game technique is robust and might therefore be an important tool in the future for testing the use of mixed strategies.

Multiple prisoner's dilemma games with (out) an outside option: An experimental study

Experiments in which subjects play simultaneously several finite prisoner's dilemma supergames with and without an outside optionreveal that: (i) subjects use probabilistic start and endeffect behaviour, (ii) the freedom to choose whether to play the prisoner's dilemma game enhances cooperation, (iii) if the payoff for simultaneous defection is negative, subjects' tendency to avoid losses leads them to cooperate; while this tendency makes them stick to mutual defection if its payoff is positive.

Equilibrium selection through incomplete information in coordination games: An experimental study

We perform an experiment on a pure coordination game with uncertaintyabout the payoffs. Our game is closely related to models that have beenused in many macroeconomic and financial applications to solve problemsof equilibrium indeterminacy. In our experiment each subject receives anoisy signal about the true payoffs. This game has a unique strategyprofile that survives the iterative deletion of strictly dominatedstrategies (thus a unique Nash equilibrium). The equilibrium outcomecoincides, on average, with the risk-dominant equilibrium outcome ofthe underlying coordination game. The behavior of the subjects convergesto the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that subjects do not apply through"a priori" reasoning the iterated deletion of dominated strategies.Instead, they adapt to the responses of other players. Thus, the lengthof the learning phase clearly varies for the different signals. We alsotest behavior in a game without uncertainty as a benchmark case. The gamewith uncertainty is inspired by the "global" games of Carlsson and VanDamme (1993).

Accounting for risk aversion in repeated prisoners’ dilemma games: an experimental test

We apply experimental methods to study the role of risk aversion on players’ behavior in repeated prisoners’ dilemma games. Faced with quantitatively equal discount factors, the most risk-averse players will choose Nash strategies more often in the presence of uncertainty than when future profits are discounted in a deterministic way. Overall, we find that risk aversion relates negatively with the frequency of collusive outcomes.

Making sense of the experimental evidence on endogenous timing in duopoly markets

The prediction of asymmetric equilibria with Stackelberg outcomes is clearly the most frequent result in the endogenous timing literature. Several experiments have tried to validate this prediction empirically, but failed to find support for it. By contrast, the experiments find that simultaneous-move outcomes are modal and that behavior in endogenous timing games is quite heterogeneous. This paper generalizes Saloner’s (1987) and Hamilton and Slutsky’s (1990) endogenous timing games by assuming that players are averse to inequality in payoffs. We explore the theoretical implications of inequity aversion and compare them to the empirical evidence. We find that this explanation is able to organize most of the experimental evidence on endogenous timing games. However, inequity aversion is not able to explain delay in Hamilton and Slutsky’s endogenous timing games.

Equilibrium play and best response to (Stated) beliefs in constant sum games

We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our experiment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work.

Payoff levels, loss avoidance, and equilibrium selection in the Stag Hunt: an experimental study

Game theorists typically assume that changing a game’s payoff levels—by adding the same constant to, or subtracting it from, all payoffs—should not affect behavior. While this invariance is an implication of the theory when payoffs mirror expected utilities, it is an empirical question when the “payoffs” are actually money amounts. In particular, if individuals treat monetary gains and losses differently, then payoff–level changes may matter when they result in positive payoffs becoming negative, or vice versa. We report the results of a human–subjects experiment designed to test for two types of loss avoidance: certain–loss avoidance (avoiding a strategy leading to a sure loss, in favor of an alternative that might lead to a gain) and possible–loss avoidance (avoiding a strategy leading to a possible loss, in favor of an alternative that leads to a sure gain). Subjects in the experiment play three versions of Stag Hunt, which are identical up to the level of payoffs, under a variety of treatments. We find differences in behavior across the three versions of Stag Hunt; these differences are hard to detect in the first round of play, but grow over time. When significant, the differences we find are in the direction predicted by certain– and possible–loss avoidance. Our results carry implications for games with multiple equilibria, and for theories that attempt to select among equilibria in such games.