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Uniformly supported approximate equilibria in families of games

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  • Levy, Yehuda John

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.

Suggested Citation

  • Levy, Yehuda John, 2022. "Uniformly supported approximate equilibria in families of games," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    • Handle: RePEc:eee:mateco:v:98:y:2022:i:c:s0304406821001348
    DOI: 10.1016/j.jmateco.2021.102571
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    References listed on IDEAS

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    6. Guillaume Vigeral, 2013. "A Zero-Sum Stochastic Game with Compact Action Sets and no Asymptotic Value," Dynamic Games and Applications, Springer, vol. 3(2), pages 172-186, June.
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    8. Yehuda John Levy, 2016. "Projections and functions of Nash equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 435-459, March.
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