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Open-ended learning in symmetric zero-sum games

David Balduzzi · Marta Garnelo · Yoram Bachrach · Wojciech Czarnecki · Julien Perolat · Max Jaderberg · Thore Graepel

Pacific Ballroom #158

Keywords: [ Multiagent Learning ] [ Game Theory and Mechanism Design ]


Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them winner' andloser'. If the game is approximately transitive, then self-play generates sequences of agents of increasing strength. However, nontransitive games, such as rock-paper-scissors, can exhibit strategic cycles, and there is no longer a clear objective -- we want agents to increase in strength, but against whom is unclear. In this paper, we introduce a geometric framework for formulating agent objectives in zero-sum games, in order to construct adaptive sequences of objectives that yield open-ended learning. The framework allows us to reason about population performance in nontransitive games, and enables the development of a new algorithm (rectified Nash response, PSROrN) that uses game-theoretic niching to construct diverse populations of effective agents, producing a stronger set of agents than existing algorithms. We apply PSROrN to two highly nontransitive resource allocation games and find that PSRO_rN consistently outperforms the existing alternatives.

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