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Nash Equilibrium Payoffs in Mixed Strategies

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Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 12))

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Abstract

We consider non zero sum two players differential games. We study Nash equilibrium payoffs and publicly correlated equilibrium payoffs. If players use deterministic strategies, it has been proved that the Nash equilibrium payoffs are precisely the reachable and consistent payoffs. Referring to repeated games, we introduce mixed strategies which are probability distributions over pure strategies. We give a characterization of the set of Nash equilibrium payoffs in mixed strategies. Unexpectedly, this set is larger than the closed convex hull of the set of Nash equilibrium payoffs in pure strategies. Finally, we study the set of publicly correlated equilibrium payoffs for differential games and show that it is the same as the set of Nash equilibrium payoffs using mixed strategies.

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Authors and Affiliations

  1. UMR CNRS 3192 Lab-STICC, Institut TELECOM, TELECOM Bretagne, Technopole Brest Iroise, CS 83818, 29238, Brest Cedex, France

    Anne Souquière

  2. Laboratoire de Mathématiques, Université de Bretagne Occidentale, UMR 6205, 6 Avenue Victor Le Gorgeu, CS 93837, 29238, Brest Cedex, France

    Anne Souquière

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  1. Anne Souquière
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Correspondence to Anne Souquière .

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Editors and Affiliations

  1. , CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris, 75775, France

    Pierre Cardaliaguet

  2. Wilfrid Laurier University, University Ave W 75, Waterloo, N2L 3C5, Ontario, Canada

    Ross Cressman

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Souquière, A. (2013). Nash Equilibrium Payoffs in Mixed Strategies. In: Cardaliaguet, P., Cressman, R. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8355-9_7

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