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On the Existence of Markov Perfect Equilibria in Perfect Information Games

  • Hannu Salonen

    ()

    (Department of Economics and PCRC, University of Turku, 20014 Turku, Finland)

  • Hannu Vartiainen

    (HECER, P.O. Box 17 (Arkadiankatu 7), FI-00014 University of Helsinki)

We study the existence of pure strategy Markov perfect equilibria in two-person perfect information games. There is a state space X and each period player's possible actions are a subset of X. This set of feasible actions depends on the current state, which is determined by the choice of the other player in the previous period. We assume that X is a compact Hausdorff space and that the action correspondence has an acyclic and asymmetric graph. For some states there may be no feasible actions and then the game ends. Payoffs are either discounted sums of utilities of the states visited, or the utility of the state where the game ends. We give sufficient conditions for the existence of equilibrium e.g. in case when either feasible action sets are finite or when players' payoffs are continuously dependent on each other. The latter class of games includes zero-sum games and pure coordination games.

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Paper provided by Aboa Centre for Economics in its series Discussion Papers with number 68.

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Length: 22
Date of creation: Oct 2011
Date of revision:
Handle: RePEc:tkk:dpaper:dp68
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  1. Gale, Douglas, 1995. "Dynamic Coordination Games," Economic Theory, Springer, vol. 5(1), pages 1-18, January.
  2. Doraszelski, Ulrich & Escobar, Juan, 2008. "A Theory of Regular Markov Perfect Equilibria in Dynamic Stochastic Games: Genericity, Stability, and Purification," CEPR Discussion Papers 6805, C.E.P.R. Discussion Papers.
  3. Guilherme Carmona, 2005. "On Games Of Perfect Information: Equilibria, Ε–Equilibria And Approximation By Simple Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 491-499.
  4. Salonen, Hannu & Vartiainen, Hannu, 2010. "On the existence of undominated elements of acyclic relations," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 217-221, November.
  5. Hellwig, Martin & Leininger, Wolfgang & Reny, Philip J. & Robson, Arthur J., 1990. "Subgame perfect equilibrium in continuous games of perfect information: An elementary approach to existence and approximation by discrete games," Journal of Economic Theory, Elsevier, vol. 52(2), pages 406-422, December.
  6. Kuipers, J. & Flesch, J. & Schoenmakers, G. & Vrieze, K., 2009. "Pure subgame-perfect equilibria in free transition games," European Journal of Operational Research, Elsevier, vol. 199(2), pages 442-447, December.
  7. V. Bhaskar & George J. Mailath & Stephen Morris, 2012. "A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games," PIER Working Paper Archive 12-043, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  8. Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Game Theory and Information 9707002, EconWPA.
  9. Livshits, Igor, 2002. "On non-existence of pure strategy Markov perfect equilibrium," Economics Letters, Elsevier, vol. 76(3), pages 393-396, August.
  10. Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-28, May.
  11. Borgers, Tilman, 1989. "Perfect equilibrium histories of finite and infinite horizon games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 218-227, February.
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