Private Monitoring and Communication in the Repeated Prisoner’s Dilemma

This paper provides a model of the repeated prisoner’s dilemma in which cheap-talk communication is necessary in order to achieve cooperative outcomes in a long-term relationship. The model is one of complete information. I consider a continuous time repeated prisoner’s dilemma game where informative signals about another player’s past actions arrive following a Poisson process; actions have to be held fixed for a certain time. I assume that signals are privately observed by players. I consider an environment where signals are noisy, and the correlation of signals is higher if both players cooperate. We show that, provided that players can change their actions arbitrary frequently, there exists an equilibrium with communication that strictly Pareto-dominates all equilibria without communication.

An epistemic approach to explaining cooperation in the finitely repeated Prisoner’s Dilemma

We use epistemic game theory to explore rationales behind cooperative behaviors in the finitely repeated Prisoner’s Dilemma. For a class of type structures that are sufficiently rich, the set of outcomes that can arise when each player i is rational and satisfies $$(m_i-1)$$ ( m i - 1 ) th order strong belief of rationality is the set of paths on which each player i defects in the last $$m_i$$ m i rounds. We construct one sufficiently rich type structure to elaborate on how different patterns of cooperative behaviors arise under sufficiently weak epistemic conditions. In this type structure, the optimality of forgiving the opponent’s past defection and the belief that one’s defection will be forgiven account for the richness of the set of behavior outcomes.

Checking Boxes for Making an Apology: Testing the Valuable Relationships Hypothesis by a New Method

A reconciliation signal may have evolved because it can reduce the uncertainty of defection, which might be caused by an error in a repeated prisoner’s dilemma situation. Ohtsubo and Watanabe (2009) proposed the “costly apology model” and argued that transgressors should make apologies in a costly way to convey sincerity to victims. Ohtsubo and Yagi (2015) showed that people are more likely to make a costly apology to valuable partners than to less valuable ones. The cost of apology was measured by the strength of willingness to suffer some inconvenience (e.g., cancellation of an important meeting) for it. Such a method of measuring costs is, however, dependent on culture, context, and the participants’ personal situations, and can only measure costs indirectly. We attempted to replicate the results of Ohtsubo and Yagi (2015) by using the checkbox method as a measurement of cost of apology. Among the factors expected to affect the number of checkboxes checked, the primary factor was the instrumentality of the friend, which replicated the results of Ohtsubo and Yagi (2015). Because the participants paid real costs of effort and time for fictitious mistakes, the costly apology might be triggered quickly and intuitively by a heuristic.

Flexibility and Reputation in Repeated Prisoner’s Dilemma Games

We study how three matching institutions, differing in how relationships are dissolved, affect cooperation in a repeated prisoner’s dilemma and how cooperation rates are affected by the presence of a reputation mechanism. Although cooperation is theoretically sustainable under all institutions, we show experimentally that cooperation rates are lowest under random matching, highest under fixed matching, and intermediate in a flexible matching institution, where subjects have the option to dissolve relationships. Our results also suggest important interactions between the matching institution and reputation mechanism. Under both the random matching and flexible matching institutions, both subjective (based on subjects’ ratings) and objective (based on subjects’ actions) reputation mechanisms lead to substantial increases in cooperative behavior. However, under fixed matching, only the subjective reputation mechanism leads to higher cooperation. We argue that these differences are due to different reputation mechanisms being more forgiving of early deviations from cooperation under certain matching institutions, which gives subjects the ability to learn the value of cooperation rather than getting stuck with a bad reputation and, consequently, uncooperative relationships. This paper was accepted by Yan Chen, decision analysis.

Zero-determinant strategies under observation errors in repeated games

Zero-determinant (ZD) strategies are a novel class of strategies in the repeated prisoner’s dilemma (RPD) game discovered by Press and Dyson. This strategy set enforces a linear payoff relationship between a focal player and the opponent regardless of the opponent’s strategy. In the RPD game, games with discounting and observation errors represent an important generalization, because they are better able to capture real life interactions which are often noisy. However, they have not been considered in the original discovery of ZD strategies. In some preceding studies, each of them has been considered independently. Here, we analytically study the strategies that enforce linear payoff relationships in the RPD game considering both a discount factor and observation errors. As a result, we first reveal that the payoffs of two players can be represented by the form of determinants as shown by Press and Dyson even with the two factors. Then, we search for all possible strategies that enforce linear payoff relationships and find that both ZD strategies and unconditional strategies are the only strategy sets to satisfy the condition. We also show that neither Extortion nor Generous strategies, which are subsets of ZD strategies, exist when there are errors. Finally, we numerically derive the threshold values above which the subsets of ZD strategies exist. These results contribute to a deep understanding of ZD strategies in society.