Abstract
People often deviate from their individual Nash equilibrium strategy in game experiments based on the prisoner’s dilemma (PD) game and the public goods game (PGG), whereas conditional cooperation, or conformity, is supported by the data from these experiments. In a complicated environment with no obvious “dominant” strategy, conformists who choose the average strategy of the other players in their group could be able to avoid risk by guaranteeing their income will be close to the group average. In this paper, we study the repeated PD game and the repeated m-person PGG, where individuals’ strategies are restricted to the set of conforming strategies. We define a conforming strategy by two parameters, initial action in the game and the influence of the other players’ choices in the previous round. We are particularly interested in the tit-for-tat (TFT) strategy, which is the well-known conforming strategy in theoretical and empirical studies. In both the PD game and the PGG, TFT can prevent the invasion of non-cooperative strategy if the expected number of rounds exceeds a critical value. The stability analysis of adaptive dynamics shows that conformity in general promotes the evolution of cooperation, and that a regime of cooperation can be established in an AllD population through TFT-like strategies. These results provide insight into the emergence of cooperation in social dilemma games.
Highlights
Classical game theory relies on the assumption of perfect rationality, but in practice, people often deviate from their individual Nash equilibrium (NE)
When one of p1 and p2 equals to 1, |E(S1)−E(S2)| must be less than T − S, which is the maximal payoff difference between outcomes in the one-shot prisoner’s dilemma (PD) game [10,11]
We study the repeated PD game and the repeated m-person public goods game (PGG) by restricting individual strategies to the set of conforming strategies
Summary
Classical game theory relies on the assumption of perfect rationality (i.e., players always act in a way to maximize their payoff), but in practice, people often deviate from their individual Nash equilibrium (NE). Conforming behavior has been applied to analyze strategies in the repeated PD game and PGG.
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