The Frequency of Convergent Games under Best-Response Dynamics

Torsten Heinrich and Samuel Wiese

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

Abstract: Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of n-player, m-strategy games. These are perfectly predictable as they must converge to the Nash equilibrium. We then consider a wider class of games that converge under a best-response dynamic, in which each player chooses their optimal pure strategy successively. We show that the frequency of convergent games goes to zero as the number of players or the number of strategies goes to infinity. In the 2-player case, we show that for large games with at least 10 strategies, convergent games with multiple pure strategy Nash equilibria are more likely than games with a unique Nash equilibrium. Our novel approach uses an n-partite graph to describe games.

Keywords: Pure Nash equilibrium; best-response dynamics; random games (search for similar items in EconPapers)
Pages: 17 pages
Date: 2020-11
New Economics Papers: this item is included in nep-gth, nep-isf and nep-mic
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Persistent link: https://EconPapers.repec.org/RePEc:amz:wpaper:2020-24

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