The prevalence of chaotic dynamics in games with many players

J. Farmer, James Sanders and Tobias Galla

INET Oxford Working Papers from Institute for New Economic Thinking at the Oxford Martin School, University of Oxford

Abstract: We study adaptive learning in a typical p-player game. The payoffs of the games are randomly generated and then held fixed. The strategies of the players evolve through time as the players learn. The trajectories in the strategy space display a range of qualitatively different behaviors, with attractors that include unique fixed points, multiple fixed points, limit cycles and chaos. In the limit where the game is complicated, in the sense that the players can take many possible actions, we use a generating-functional approach to establish the parameter range in which learning dynamics converge to a stable fixed point. The size of this region goes to zero as the number of players goes to infinity, suggesting that complex non-equilibrium behavior, exemplified by chaos, may be the norm for complicated games with many players.

Pages: 22 pages
Date: 2017-04
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Related works:
Working Paper: The prevalence of chaotic dynamics in games with many players (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:amz:wpaper:2017-05

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