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A Discounted Stochastic Game with No Stationary Equilibria: The Case of Absolutely Continuous Transitions

  • Yehuda (John) Levy

We present a discounted stochastic game with a continuum of states, finitely many players and actions, such that although all transitions are absolutely continuous w.r.t. a fixed measure, it possesses no stationary equilibria. This absolute continuity condition has been assumed in many equilibrium existence results, and the game presented here complements a recent example of ours of a game with no stationary equilibria but which possess deterministic transitions. We also show that if one allows for compact action spaces, even games with state-independent transitions need not possess stationary equilibria.

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Paper provided by The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem in its series Discussion Paper Series with number dp612.

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Length: 21 pages
Date of creation: Jun 2012
Date of revision:
Handle: RePEc:huj:dispap:dp612
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  1. Yehuda (John) Levy, 2012. "A Cantor Set of Games with No Shift-Homogeneous Equilibrium Selection," Discussion Paper Series dp607, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  2. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
  3. Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Nash Equilibrium," Discussion Paper Series dp596r, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised May 2012.
  4. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
  5. Chakrabarti, Subir K., 1999. "Markov Equilibria in Discounted Stochastic Games," Journal of Economic Theory, Elsevier, vol. 85(2), pages 294-327, April.
  6. Horst, Ulrich, 2005. "Stationary equilibria in discounted stochastic games with weakly interacting players," Games and Economic Behavior, Elsevier, vol. 51(1), pages 83-108, April.
  7. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, June.
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