Automata representation of successful strategies for social dilemmas

TL;DR

This paper introduces a method to convert complex history-based strategies in social dilemmas into minimal automata, revealing that successful three-player public-goods game strategies can be represented with just 10 states, enhancing interpretability.

Contribution

It presents a novel automaton-based representation of successful strategies in social dilemmas, simplifying complex history-dependent strategies into minimal, interpretable models.

Findings

Successful strategies can be represented as 10-state automata.

States correspond to internal judgments like trustworthiness.

Automaton representation aids understanding of strategic decision-making.

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.