Best-Response Dynamics, Playing Sequences, And Convergence To Equilibrium In Random Games

Marco Pangallo, Torsten Heinrich, Yoojin Jang, Alex Scott, Bassel Tarbush, Samuel Wiese and Luca Mungo

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

Abstract: We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence—the order in which players update their actions—is essentially irrelevant in determining whether the dynamic converges to a Nash equilibrium in certain classes of games (e.g. in potential games) but, when evaluated across all possible games, convergence to equilibrium depends on the playing sequence in an extreme way. Our main asymptotic result shows that the best-response dynamic converges to a pure Nash equilibrium in a vanishingly small fraction of all (large) games when players take turns according to a fixed cyclic order. By contrast, when the playing sequence is random, the dynamic converges to a pure Nash equilibrium if one exists in almost all (large) games.

Keywords: Best-response dynamics; equilibrium convergence; random games (search for similar items in EconPapers)
JEL-codes: C62 C72 C73 D83 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2021-11
New Economics Papers: this item is included in nep-exp, nep-gth, nep-mic and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:amz:wpaper:2021-23

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