![]() ![]() ![]() George Berkeley says that a man who believes in no future state has no reason to postpone his own private interest or pleasure to doing his duty 1. This result thus suggests a comprehensible way to choose an appropriate action at each step towards cooperation based on a situational judgement, which is mapped from the history of interactions. In this automaton, each state can be interpreted as the player’s internal judgement of the situation, such as trustworthiness of the co-players and the need to redeem oneself after defection. Our main finding is that a successful strategy for the iterated three-person public-goods game can be represented as a 10-state automaton by this method. ![]() In this paper, we propose a method to convert such history-based representation into an automaton with a minimal number of states. Although we have a list of actions prescribed by each successful strategy, the rationale behind them has not been fully understood for the iterated public-goods game because the list has hundreds of entries to deal with every relevant history of previous interactions. A class of successful strategies of direct reciprocity were recently found for the iterated prisoner’s dilemma and for the iterated three-person public-goods game: By a successful strategy, we mean that it constitutes a cooperative Nash equilibrium under implementation error, with assuring that the long-term payoff never becomes less than the co-players’ regardless of their strategies, when the error rate is small. In a social dilemma, cooperation is collectively optimal, yet individually each group member prefers to defect. ![]()
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