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Returns-based beliefs provide an explanation for the anomaly between the theory and empirics for the one-shot and finitely-repeated Prisoner's Dilemma games. Even in a fully specified game, there is strategic uncertainty as players attempt to coordinate their actions. Therefore players form subjective probabilities of the actions of their opponents. The authors provide a new method termed the 'Returns-based beliefs' approach of forming subjective probabilities that is based upon the expected returns of a particular strategy, in proportion to the total expected returns of all strategies. This method can be applied even in the absence of knowledge of the players' respective histories.
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