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Markov Perfect Equilibria in Repeated Asynchronous Choice Games

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Author Info

  • Roger Lagunoff

    (Georgetown University)

  • Hans Haller

    (Virginia Polytechnic Institute and State University)

Abstract

This paper examines the issue of multiplicity of equilibria in alternating move repeated games with two players. Such games are canonical models of environments with repeated, asynchronous choices due to inertia or replacement. We focus our attention on Markov Perfect equilibria (MPE). These are Perfect equilibria in which individuals condition their actions on payoff-relevant state variables. Our main result is that the number of Markov Perfect equilibria is generically finite with respect to stage game payoffs. This holds despite the fact that the stochastic game representation of the alternating move repeated game is "non-generic" in the larger space of state dependent payoffs. We also compare the MPE to non-Markovian equilibria and to the (trivial) MPE of standard repeated games. Unlike the latter, it is often true when moves are asynchronous that Pareto inferior stage game equilibrium payoffs cannot be supported in MPE. Also, MPE can be constructed to support cooperation in a Prisoner's Dilemma despite limited possibilities for constructing punishments.

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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 9707006.

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Date of creation: 05 Jul 1997
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Handle: RePEc:wpa:wuwpga:9707006

Note: Type of Document - LaTex; prepared on IBM PC ; to print on HP;
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Web page: http://128.118.178.162

Related research

Keywords: repeated games; asynchronous choice; turn-taking games; stochastic games; Markov Perfect equilibria; genericity;

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References

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  1. Roger Lagunoff & Akihiko Matsu, . ""Asynchronous Choice in Repeated Coordination Games''," CARESS Working Papres 96-10, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
  3. Hans Haller & Roger Lagunoff, 1999. "Genericity and Markovian Behavior in Stochastic Games," Game Theory and Information 9901003, EconWPA, revised 03 Jun 1999.
  4. Park, I.U., 1993. "Generic Finiteness of Equilibrium Outcome Distribution for Sender Receiver Cheap-Talk Games," Papers 269, Minnesota - Center for Economic Research.
  5. Robert Wilson, 2010. "Computing Equilibria of n-person Games," Levine's Working Paper Archive 402, David K. Levine.
  6. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, vol. 103(2), pages 334-350, April.
  7. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
  8. Maskin, Eric & Tirole, Jean, 1987. "A theory of dynamic oligopoly, III : Cournot competition," European Economic Review, Elsevier, vol. 31(4), pages 947-968, June.
  9. Eric Maskin & Jean Tirole, 2010. "A Theory of Dynamic Oligopoly, 1: Overview and Quantity Competition with Large Fixed Costs," Levine's Working Paper Archive 397, David K. Levine.
  10. Yoon, Kiho, 2001. "A Folk Theorem for Asynchronously Repeated Games," Econometrica, Econometric Society, vol. 69(1), pages 191-200, January.
  11. Prajit K. Dutta, 1997. "A Folk Theorem for Stochastic Games," Levine's Working Paper Archive 1000, David K. Levine.
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Cited by:
  1. Sibdari, Soheil & Pyke, David F., 2014. "Dynamic pricing with uncertain production cost: An alternating-move approach," European Journal of Operational Research, Elsevier, vol. 236(1), pages 218-228.
  2. Andrew McLennan & Hülya Eraslan, 2010. "Uniqueness of Stationary Equilibrium Payoffs in Coalitional Bargaining," Economics Working Paper Archive 562, The Johns Hopkins University,Department of Economics.
  3. Takashi Kamihigashi & Taiji Furusawa, 2010. "Global Dynamics in Repeated Games with Additively Separable Payoffs," Discussion Paper Series DP2010-04, Research Institute for Economics & Business Administration, Kobe University, revised Jun 2010.
  4. V. Bhaskar & Fernando Vega-Redondo, 1998. "Asynchronous Choice and Markov Equilibria:Theoretical Foundations and Applications," Game Theory and Information 9809003, EconWPA.
  5. Takashi Kamihigashi & Taiji Furusawa, 2006. "Immediately Reactive Equilibria in Infinitely Repeated Games with Additively Separable Continuous Payoffs," Discussion Paper Series 199, Research Institute for Economics & Business Administration, Kobe University.
  6. Takashi Kamihigashi & Taiji Furusawa, 2007. "Global Dynamics in Infinitely Repeated Games with Additively Separable Continuous Payoffs," Discussion Paper Series 210, Research Institute for Economics & Business Administration, Kobe University.

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