Automata representation of successful strategies for social dilemmas

Abstract

In a social dilemma, cooperation is collectively optimal, yet individually each group member prefers to defect. 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. 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. In this paper, we propose a method to convert such history-based representation into an automaton with a minimal number of states. 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 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. 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.

arXiv comment11 pages, 7 figures

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Cited by in corpus (5)

• Five rules for friendly rivalry in direct reciprocity
• Evolution of direct reciprocity in group-structured populations
• Local stability of cooperation in a continuous model of indirect reciprocity
• Grouping promotes both partnership and rivalry with long memory in direct reciprocity
• Friendly-rivalry solution to the iterated $n$-person public-goods game