Best-response equilibrium: an equilibrium in finitely additive mixed strategies

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A generalization of mixed strategy equilibrium is proposed, where mixed strategies need only be finitely additive and payoff functions are not required to be integrable or bounded. This notion of best-response equilibrium is based on an extension of the idea that an equilibrium strategy is supported in the player’s set of best-response actions, but is applicable also when no best-response actions exist. It yields simple, natural equilibria in a number of well-known games where other kinds of mixed equilibrium are complicated, not compelling or do not exist.

Original languageEnglish
Pages (from-to)1317-1334
Number of pages18
JournalInternational Journal of Game Theory
Issue number4
StatePublished - Dec 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


  • Best-response equilibrium
  • Finitely additive probability
  • Mixed strategy


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