Uniformly supported approximate equilibria in families of games

Yehuda Levy

Journal of Mathematical Economics, 2022, vol. 98, issue C

Abstract: This paper considers uniformly bounded classes of non-zero-sum strategic-form games with large finite or compact action spaces. The central class of games considered is assumed to be defined via a semi-algebraic condition. We show that for each ɛ>0, the support size required for ɛ-equilibrium can be taken to be uniform over the entire class. As a corollary, the value of zero-sum games, as a function of a single-variable, is well-behaved in the limit. More generally, the result only requires that the collection of payoff functions considered, as functions of other players actions, have finite pseudo-dimension.

Keywords: Small-support equilibrium; Semi-algebraic classes; Vapnik–Chervonenkis dimension (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:98:y:2022:i:c:s0304406821001348

DOI: 10.1016/j.jmateco.2021.102571

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