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Unique Ergodicity of Deterministic Zero-Sum Differential Games

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  • Antoine Hochart

    (Universidad Adolfo Ibáñez)

Abstract

We study the ergodicity of deterministic two-person zero-sum differential games. This property is defined by the uniform convergence to a constant of either the infinite-horizon discounted value as the discount factor tends to zero, or equivalently, the averaged finite-horizon value as the time goes to infinity. We provide necessary and sufficient conditions for the unique ergodicity of a game. This notion extends the classical one for dynamical systems, namely when ergodicity holds with any (suitable) perturbation of the running payoff function. Our main condition is symmetric between the two players and involve dominions, i.e., subsets of states that one player can make approximately invariant.

Suggested Citation

  • Antoine Hochart, 2021. "Unique Ergodicity of Deterministic Zero-Sum Differential Games," Dynamic Games and Applications, Springer, vol. 11(1), pages 109-136, March.
    • Handle: RePEc:spr:dyngam:v:11:y:2021:i:1:d:10.1007_s13235-020-00355-y
    DOI: 10.1007/s13235-020-00355-y
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    References listed on IDEAS

    as
    1. Dmitry Khlopin, 2018. "Tauberian Theorem for Value Functions," Dynamic Games and Applications, Springer, vol. 8(2), pages 401-422, June.
    2. 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.
    3. repec:dau:papers:123456789/10880 is not listed on IDEAS
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