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Title:

Punishment with Uncertain Outcomes in the Prisoner’s Dilemma

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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 all...

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 Minimize

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Risky Punishment and Reward in the Prisoner’s Dilemma

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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...

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 Minimize

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Title:

Punishment with Uncertain Outcomes in the Prisoner’s Dilemma

Description:

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 all...

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 Minimize

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

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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 genera...

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 Minimize

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Title:

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

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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 g...

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 Minimize

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Title:

Pure Saddle Points and Symmetric Relative Payoff Games

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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 po...

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 Minimize

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Pure Saddle Points and Symmetric Relative Payoff Games

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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 po...

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 Minimize

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Title:

Unbeatable Imitation

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We show that for many classes of symmetric two-player games, the simple decision rule ""imitate-the-best"" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show that it can only be beaten by much in games that are of the rock-scissors-paper variety. Thus, in many i...

We show that for many classes of symmetric two-player games, the simple decision rule ""imitate-the-best"" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show that it can only be beaten by much in games that are of the rock-scissors-paper variety. Thus, in many interesting examples, like 2x2 games, Cournot duopoly, price competition, rent seeking, public goods games, common pool resource games, minimum effort coordination games, arms race, search, bargaining, etc., imitation cannot be beaten by much even by a very clever opponent. ; imitate-the-best, learning, symmetric games, relative payoffs, zero-sum games, rock-paper-scissors, finite population ESS, potential games, quasisubmodular games, quasisupermodular games, quasiconcave games, aggregative games Minimize

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Title:

Sick Pay Provision in Experimental Labor Markets

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Sick pay is a common provision in most labor contracts. This paper employs an experimental gift-exchange environment to explore two related questions using both managers and undergraduates as subjects. First, do workers reciprocate sick pay in the same way as they reciprocate wage payments? Second, do firms benefit from offering sick pay? Firms ...

Sick pay is a common provision in most labor contracts. This paper employs an experimental gift-exchange environment to explore two related questions using both managers and undergraduates as subjects. First, do workers reciprocate sick pay in the same way as they reciprocate wage payments? Second, do firms benefit from offering sick pay? Firms may benefit in two different ways: directly, from workers reciprocating higher sick pay with higher efforts; and indirectly, from self-selection of reciprocal workers into contracts with higher sick pay. Our main finding is that the direct effect is rather weak in terms of effort and negative in terms of profits. However, when there is competition among firms for workers, sick pay can become an important advantage. Consequently, competition leads to a higher provision of sick pay relative to a monopsonistic labor market. ; sick pay, sick leave, experiment, gift exchange Minimize

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Title:

Unbeatable Imitation

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We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable in the sense that, even against a very clever opponent, imitation is subject to a money pump if and only if the rel...

We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable in the sense that, even against a very clever opponent, imitation is subject to a money pump if and only if the relative payoff function of the game is of the rock-scissors-paper variety. For many interesting classes of games including examples like 2x2 games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games, we obtain an even stronger notion of the unbeatability of imitation. ; imitate-the-best, learning, symmetric games, relative payoffs, zero-sum games, rock-paper-scissors, finite population ESS, potential games, quasisubmodular games, quasisupermodular games, quasiconcave games, aggregative games Minimize

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