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Ergodic Problems in Differential Games

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Advances in Dynamic Game Theory

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 9))

Abstract

We present and study a notion of ergodicity for deterministic zero-sum differential games that extends the one in classical ergodic control theory to systems with two conflicting controllers.We show its connections with the existence of a constant and uniform long-time limit of the value function of finite horizon games, and characterize this property in terms of Hamilton-Jacobi-Isaacs equations.We also give several sufficient conditions for ergodicity and describe some extensions of the theory to stochastic differential games.

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Author information

Authors and Affiliations

  1. UMR 60-85, Université de Rouen, 76821, Mont-Saint Aignan Cedex, France

    Olivier Alvarez

  2. Dipartimento di Matematica Pura ed Applicata, Università di Padova, via Belzoni 7, 35131, Padova, Italy

    Martino Bardi

Authors
  1. Olivier Alvarez
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  2. Martino Bardi
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Editor information

Editors and Affiliations

  1. Department of Economics and Business, University of Southern Denmark, Campusvej 55, DK-5230 Odense, Denmark

    Steffen Jørgensen

  2. Laboratoire de Mathématiques, Université de Bretagne Occidentale, 6 Avenue Le Georgeu, 29200 Brest, France

    Marc Quincampoix

  3. Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA

    Thomas L. Vincent

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Alvarez, O., Bardi, M. (2007). Ergodic Problems in Differential Games. In: Jørgensen, S., Quincampoix, M., Vincent, T.L. (eds) Advances in Dynamic Game Theory. Annals of the International Society of Dynamic Games, vol 9. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4553-3_7

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