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Games 2016, 7(3), 19; doi:10.3390/g7030019

Optimal Decision Rules in Repeated Games Where Players Infer an Opponent’s Mind via Simplified Belief Calculation

Department of Evolutionary Studies of Biosystems, School of Advanced Sciences, SOKENDAI (The Graduate University for Advanced Studies), Hayama, Kanagawa 240-0193, Japan
Author to whom correspondence should be addressed.
Academic Editor: David Levine
Received: 23 May 2016 / Revised: 15 July 2016 / Accepted: 22 July 2016 / Published: 28 July 2016
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In strategic situations, humans infer the state of mind of others, e.g., emotions or intentions, adapting their behavior appropriately. Nonetheless, evolutionary studies of cooperation typically focus only on reaction norms, e.g., tit for tat, whereby individuals make their next decisions by only considering the observed outcome rather than focusing on their opponent’s state of mind. In this paper, we analyze repeated two-player games in which players explicitly infer their opponent’s unobservable state of mind. Using Markov decision processes, we investigate optimal decision rules and their performance in cooperation. The state-of-mind inference requires Bayesian belief calculations, which is computationally intensive. We therefore study two models in which players simplify these belief calculations. In Model 1, players adopt a heuristic to approximately infer their opponent’s state of mind, whereas in Model 2, players use information regarding their opponent’s previous state of mind, obtained from external evidence, e.g., emotional signals. We show that players in both models reach almost optimal behavior through commitment-like decision rules by which players are committed to selecting the same action regardless of their opponent’s behavior. These commitment-like decision rules can enhance or reduce cooperation depending on the opponent’s strategy. View Full-Text
Keywords: cooperation; direct reciprocity; repeated game; Markov decision process; heuristics cooperation; direct reciprocity; repeated game; Markov decision process; heuristics

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Nakamura, M.; Ohtsuki, H. Optimal Decision Rules in Repeated Games Where Players Infer an Opponent’s Mind via Simplified Belief Calculation. Games 2016, 7, 19.

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