A social dilemmaappears when defection is individually favored than cooperation although the latter is collectively optimal  . A class of successful strategies of direct reciprocity were recently found for the iterated prisoner's dilemma Yi et al., J. Theor. Biol. (2017) and for the three-person iterated public goods game Murase and Baek, J. Theor. Biol. (2018)%DIFDELCMD < ]%%% . A successful strategyforms a cooperative Nash equilibrium in the presence of implementation errorwhile 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 the successful strategies , the rationale behind them have not been fully understood  . In this paper, we wish to provide a better understanding for the successful strategies by converting them into automata with a minimal number of states. Each of the states becomes interpretable in this representation, whereby one can gain insight into the underlying mechanism .
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 %DIFDELCMD < ]%%% 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 .
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A social dilemmaappears when defection is individually favored than cooperation although the latter
In a social dilemma, cooperation
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, yet individually each group member prefers to defect
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Yi et al., J. Theor. Biol. (2017)
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three-person iterated public goods game
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Murase and Baek, J. Theor. Biol. (2018)
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. A successful strategyforms
iterated three-person public-goods game: By a successful strategy, we mean that it constitutes
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in the presence of implementation errorwhile
under implementation error, with
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the successful strategies
each successful strategy
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have
has
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for the iterated public-goods game because the list has hundreds of entries to deal with every relevant history of previous interactions
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wish to provide a better understanding for the successful strategies by converting them into automata
propose a method to convert such history-based representation into an automaton
R
Each of the states becomes interpretable in this representation, whereby one can gain insight into the underlying mechanism
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