Computational Studies of Learning, Inference, and Assessment

Abstract

This thesis addresses two topics in evolutionary game theory. The first topic discusses how a player can infer other players’ strategies in the iterated prisoner’s dilemma game. We construct two methods for strategy inference. In the first method, we consider players with memory-one stochastic strategies in the iterated prisoner’s dilemma, with an assumption that they cannot directly access each other’s strategy but only observe the actual moves for a certain number of rounds. Based on the observation, the observer has to infer the resident strategy in a Bayesian way and chooses his or her own strategy accordingly. By examining the best-response relations, we argue that players can escape from full defection into a cooperative equilibrium supported by Win-Stay-Lose-Shift in a self-confirming manner, provided that the cost of cooperation is low and the observational learning supplies sufficiently large uncertainty. In the second method, the focal player infers the co-player’s strategy by applying the maximum likelihood estimation (MLE) to the observed sequence of actions. Our first finding is that the focal player’s inference is accurate when both players take only their last actions into consideration if the observed sequence is sufficiently long. To see the case in which inference must be inaccurate, we also set the focal player’s memory length to be shorter than the co-player’s. In this case, we choose a combination of Tit-for-tat and Anti-tit-for-tat (TA) as the co-player’s long-memory strategy. TA satisfies the following three conditions: 1) mutual cooperation is achieved when all player use the strategy, 2) the strategy exploits unconditional cooperation, and 3) a player using this strategy is not exploited repeatedly by any co-player. The short-memory player inaccurately infers TA as either Tit-for-tat, Win-Stay-Lose-Shift, or Grim trigger, depending on his or her own strategy. This work presents how a long-memory strategy is projected onto a short-memory one by inference with information loss. In addition, we suggest that each of those three well-known strategies could be a facet of a single successful strategy with a higher cognitive capacity. The second topic discusses the characteristics of cooperative stationarily stable strategies (CESS) with ternary reputations. In this topic, we introduce the third reputation, ‘Neutral’ (N), to the existing ‘Good’ (G) and ‘Bad’ (B) reputations and find CESSs. We categorize the CESSs into three types according to the proportions of the three reputations in equilibrium. We found that the proportion of N is finite in one of the three types. This result suggests that cooperation can be maintained with only ‘G’ but also in the presence of multiple reputations (‘G’ and ‘N’).