Autocratic strategies for alternating games

Abstract

Repeated games have a long tradition in the behavioral sciences and evolutionary biology. Recently, strategies were discovered that permit an unprecedented level of control over repeated interactions by enabling a player to unilaterally enforce linear constraints on payoffs. Here, we extend this theory of "zero-determinant" (or, more generally, "autocratic") strategies to alternating games, which are often biologically more relevant than traditional synchronous games. Alternating games naturally result in asymmetries between players because the first move matters or because players might not move with equal probabilities. In a strictly-alternating game with two players, $X$ and $Y$, we give conditions for the existence of autocratic strategies for player $X$ when (i) $X$ moves first and (ii) $Y$ moves first. Furthermore, we show that autocratic strategies exist even for (iii) games with randomly-alternating moves. Particularly important categories of autocratic strategies are extortionate and generous strategies, which enforce unfavorable and favorable outcomes for the opponent, respectively. We illustrate these strategies using the continuous Donation Game, in which a player pays a cost to provide a benefit to the opponent according to a continuous cooperative investment level. Asymmetries due to alternating moves could easily arise from dominance hierarchies, and we show that they can endow subordinate players with more autocratic strategies than dominant players.

28 pages; final version

References in corpus (2)

• Comparing reactive and memory-one strategies of direct reciprocity
• Critical dynamics in the evolution of stochastic strategies for the iterated Prisoner's Dilemma

Cited by in corpus (12)

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• Controlling conditional expectations by zero-determinant strategies
• Adapting paths against zero-determinant strategies in repeated prisoner's dilemma games
• On the implementation of zero-determinant strategies in repeated games
• Autocratic strategies in Cournot oligopoly game
• Unexploitable games and unbeatable strategies
• Properties of zero-determinant strategies in multichannel games
• Zero-determinant strategies in repeated continuously-relaxed games
• On the existence of fair zero-determinant strategies in the periodic prisoner's dilemma game