Risky Punishment and Reward in the Prisoner’s Dilemma

We conduct a prisoner’s dilemma experiment with a punishment/reward stage, where punishments and rewards are risky. This is compared with a risk free treatment. We find that subjects do not change their behavior in the face of risky outcomes. Additionally, we measure risk attitude and the emotions of subjects. While we find a strong influence of emotions, individual risk aversion has no effect on the decision to punish or reward. This is good news for lab experiments who abstract from risky outcomes. From the perspective of social preferences, our results provide evidence for risk neutral inclusion of other player’s payoffs in the decisionmaker’s utility function.Prisoner’s dilemma, risk, punishment, reward, emotions, experiment

Punishment with Uncertain Outcomes in the Prisoner’s Dilemma

This paper experimentally investigates whether risk-averse individuals punish less if the outcome of punishment is uncertain than when it is certain. Our design includes three treatments: Baseline in which the one-shot prisoner’s dilemma game is played; Certain Punishment in which the prisoner’s dilemma game is followed by a punishment stage allowing subjects to decrease the other player’s payoff by 2 Euros; and Uncertain Punishment in which subjects could decrease the other player’s payoff with a 50% probability by 1 Euro and with a 50% probability by 3 Euros. We find that in all cases the risk-averse subjects are equally likely to cooperate in the prisoner’s dilemma and equally likely to punish in the second stage in either of the two punishment treatments.Experimental economics; prisoner’s dilemma; punishment; risk aversion; uncertainty

Punishment with Uncertain Outcomes in the Prisoner’s Dilemma

This paper experimentally investigates whether risk-averse individuals punish less if the outcome of punishment is uncertain than when it is certain. Our design includes three treatments: Baseline in which the one-shot prisoner’s dilemma game is played; Certain Punishment in which the prisoner’s dilemma game is followed by a punishment stage allowing subjects to decrease the other player’s payoff by 2 Euros; and Uncertain Punishment in which subjects could decrease the other player’s payoff with a 50% probability by 1 Euro and with a 50% probability by 3 Euros. We find that in all cases the risk-averse subjects are equally likely to cooperate in the prisoner’s dilemma and equally likely to punish in the second stage in either of the two punishment treatments.experiment, prisoner’s dilemma, punishment, risk aversion, uncertainty

Pure Strategy Equilibria in Symmetric Two-Player Zero-Sum Games

We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. Our findings extend to general two-player zero-sum games using the symmetrization of zero-sum games due to von Neumann. We point out that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of finite population evolutionary stable strategies.Symmetric two-player games, zero-sum games, Rock-Paper-Scissors, single-peakedness, quasiconcavity, finite population evolutionary stable strategy, saddle point, exact potential games

Once Beaten, Never Again: Imitation in Two-Player Potential Games

We show that in symmetric two-player exact potential games, the simple decision rule "imitate-if-better" cannot be beaten by any strategy in a repeated game by more than the maximal payoff difference of the one-period game. Our results apply to many interesting games including examples like 2x2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.Imitate-the-best, learning, exact potential games, symmetric games, relative payoffs, zero-sum games

Benevolent and Malevolent Ellsberg Games

Traditionally, real experiments testing subjective expected utility theory take for granted that subjects view the Ellsberg task as a one-person decision problem. We challenge this view: Instead of seeing the Ellsberg task as a one-person decision problem, it can be perceived as a two-player game. One player chooses among the bets. The second player determines the distribution of balls in the Ellsberg urn. The Nash equilibrium predictions of this game depend on the payoff of the second player, with the game ranging from a zero-sum one to a coordination game. Meanwhile, the predictions by ambiguity aversion models remain unchanged. Both situations are implemented experimentally and yield different results, in line with the game-theoretic prediction. Additionally, the standard scenario (without explicit mention of how the distribution is determined) leads to results similar to the zero-sum game, suggesting that subjects view the standard Ellsberg experiment as a game against the experimenter

Pure Saddle Points and Symmetric Relative Payoff Games

It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence are provided. We apply our theory to a rich collection of examples by noting that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of a finite population evolutionary stable strategies.symmetric two-player games, zero-sum games, Rock-Paper-Scissors, single-peakedness, quasiconcavity, finite population evolutionary stable strategy, increasing differences, decreasing differences, potentials, additive separability

Taking punishment into your own hands: An experiment on the motivation underlying punishment

In a punishment experiment, we separate the demand for punishment in general from a possible demand to conduct punishment personally. Subjects experience an unfair split of their earnings from a real effort task and have to decide on the punishment of the person who determines the distribution. First, it is established whether the allocator's payoff is reduced and, afterwards, subjects take part in a second price auction for the right to (physically) carry out the act of payoff reduction. This auction only resolves who will punish, not whether punishment takes place, so only subjects with a demand for personal punishment should bid

Price Competition in an Inflationary Environment

We study how inflation and deflation affect firms' ability to cooperate in an experimental Bertrand duopoly with differentiated products. We find that there is significantly less cooperation in the treatments with inflation and deflation compared to the no-inflation treatments. The difficulties to cooperate affect prices and welfare: Depending on the market structure, inflation and deflation lead to significantly lower (real) prices and higher welfare

Pure Saddle Points and Symmetric Relative Payoff Games

It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence are provided. We apply our theory to a rich collection of examples by noting that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of a finite population evolutionary stable strategies.symmetric two-player games; zero-sum games; Rock-Paper-Scissors; single-peakedness; quasiconcavity; finite population evolutionary stable strategy; increasing differences; decreasing differences; potentials; additive separability