A note on discontinuity and approximate equilibria in games with infinitely many players

Shiran Rachmilevitch

Economics Letters, 2020, vol. 193, issue C

Abstract: Peleg (1969) showed that it is possible for a game with countably many players and finitely many pure strategies to have no Nash equilibrium. In his example not only Nash, but even perfect ϵ-equilibrium fails to exist. However, the example is based on tail utility functions, and these have infinitely many discontinuity points. I demonstrate non-existence of perfect ϵ-equilibrium under a milder form of discontinuity: I construct a game with countably many players, finitely many pure strategies and no perfect ϵ-equilibrium, in which one player has a utility function with a single discontinuity point, and the utility of every other player is not only continuous, but depends on finitely many coordinates.

Keywords: Approximate equilibrium; Discontinuous games; Infinite games; Equilibrium non-existence; Tail events (search for similar items in EconPapers)
JEL-codes: C71 C78 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:193:y:2020:i:c:s0165176520301816

DOI: 10.1016/j.econlet.2020.109267

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