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On the Geometry of Nash and Correlated Equilibria with Cumulative Prospect Theoretic Preferences

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  • Soham R. Phade

    (Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, California 94720)

  • Venkat Anantharam

    (Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, California 94720)

Abstract

It is known that the set of all correlated equilibria of an n -player non-cooperative game is a convex polytope and includes all of the Nash equilibria. Furthermore, the Nash equilibria all lie on the boundary of this polytope. We study the geometry of both these equilibrium notions when the players have cumulative prospect theoretic (CPT) preferences. The set of CPT correlated equilibria includes all of the CPT Nash equilibria, but it need not be a convex polytope. We show that it can, in fact, be disconnected. However, all of the CPT Nash equilibria continue to lie on its boundary. We also characterize the sets of CPT correlated equilibria and CPT Nash equilibria for all 2 × 2 games, with the sets of correlated and Nash equilibria in the classical sense being a special case.

Suggested Citation

  • Soham R. Phade & Venkat Anantharam, 2019. "On the Geometry of Nash and Correlated Equilibria with Cumulative Prospect Theoretic Preferences," Decision Analysis, INFORMS, vol. 16(2), pages 142-156, June.
    • Handle: RePEc:inm:ordeca:v:16:y:2019:i:2:p:142-156
    DOI: 10.1287/deca.2018.0378
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    References listed on IDEAS

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    Cited by:

    1. Soham R. Phade & Venkat Anantharam, 2020. "Black-Box Strategies and Equilibrium for Games with Cumulative Prospect Theoretic Players," Papers 2004.09592, arXiv.org.
    2. Theodore T. Allen & Olivia K. Hernand & Abdullah Alomair, 2020. "Optimal Off-line Experimentation for Games," Decision Analysis, INFORMS, vol. 17(4), pages 277-298, December.
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    4. Ali Yekkehkhany & Timothy Murray & Rakesh Nagi, 2021. "Stochastic Superiority Equilibrium in Game Theory," Decision Analysis, INFORMS, vol. 18(2), pages 153-168, June.
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