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Genericity and Markovian Behavior in Stochastic Games

Author

Listed:
  • Hans Haller

    (Virginia Polytechnic Institute & State University)

  • Roger Lagunoff

    (Georgetown University)

Abstract

This paper examines Markov Perfect equilibria of general, finite state stochastic games. Our main result is that the number of such equilibria is finite for a set of stochastic game payoffs with full Lebesgue measure. We further discuss extensions to lower dimensional stochastic games like the alternating move game.

Suggested Citation

  • Hans Haller & Roger Lagunoff, 1999. "Genericity and Markovian Behavior in Stochastic Games," Game Theory and Information 9901003, University Library of Munich, Germany, revised 03 Jun 1999.
    • Handle: RePEc:wpa:wuwpga:9901003
    Note: Type of Document - Acrobat pdf file; prepared on IBM PC - PC- TEX; to print on Acrobat PDF Writer; pages: 25 ; figures: included.
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    References listed on IDEAS

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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, August.
    2. Maskin, Eric & Tirole, Jean, 1988. "Corrigendum to 'A Theory of Dynamic Oligopoly, III, Cournot Competition' (vol. 31, no. 4)," European Economic Review, Elsevier, vol. 32(7), pages 1567-1568, September.
    3. Anderson Robert M. & Zame William R., 2001. "Genericity with Infinitely Many Parameters," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-64, February.
    4. Govindan, Srihari & McLennan, Andrew, 2001. "On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms," Econometrica, Econometric Society, vol. 69(2), pages 455-471, March.
    5. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, I: Overview and Quantity Competition with Large Fixed Costs," Econometrica, Econometric Society, vol. 56(3), pages 549-569, May.
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    2. Ulrich Doraszelski & Mark Satterthwaite, 2003. "Foundations of Markov-Perfect Industry Dynamics. Existence, Purification, and Multiplicity," Discussion Papers 1383, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Doraszelski, Ulrich & Satterthwaite, Mark, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," CEPR Discussion Papers 6212, Centre for Economic Policy Research.
    4. , & ,, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    5. Peeters, R.J.A.P., 2004. "Hyperbolic discounting in stochastic games," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Ulrich Doraszelski & Mark Satterthwaite, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," Levine's Bibliography 321307000000000912, UCLA Department of Economics.
    7. Herings, P. J. J. & Polemarchakis, H., 2002. "Equilibrium and arbitrage in incomplete asset markets with fixed prices," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 133-155, April.
    8. Herings, P.J.J. & Houba, H, 2010. "The Condercet paradox revisited," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. P. Jean-Jacques Herings & Harold Houba, 2022. "Costless delay in negotiations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 69-93, July.
    10. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
    11. 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.
    12. Siu, Tak Kuen, 2008. "A game theoretic approach to option valuation under Markovian regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1146-1158, June.
    13. 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.
    14. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
    15. Tasos Kalandrakis, 2006. "Regularity of pure strategy equilibrium points in a class of bargaining games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 309-329, June.
    16. Yoon, Jangsu, 2024. "Identification and estimation of sequential games of incomplete information with multiple equilibria," Journal of Econometrics, Elsevier, vol. 238(2).
    17. Azad Gholami, Reza & Sandal, Leif K. & Ubøe, Jan, 2016. "Channel Coordination in a Multi-period Newsvendor Model with Dynamic, Price-dependent Stochastic Demand," Discussion Papers 2016/6, Norwegian School of Economics, Department of Business and Management Science.
    18. Haller, Hans & Lagunoff, Roger, 2010. "Markov Perfect equilibria in repeated asynchronous choice games," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1103-1114, November.
    19. Herings, P. Jean-Jacques & Peeters, Ronald & Schinkel, Maarten Pieter, 2005. "Intertemporal market division:: A case of alternating monopoly," European Economic Review, Elsevier, vol. 49(5), pages 1207-1223, July.
    20. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    21. Gomes, Armando, 2015. "Multilateral negotiations and formation of coalitions," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 77-91.
    22. Medio, Alfredo & Raines, Brian, 2007. "Backward dynamics in economics. The inverse limit approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1633-1671, May.
    23. Ruli Xiao, 2016. "Nonparametric Identification of Dynamic Games with Multiple Equilibria and Unobserved Heterogeneity," CAEPR Working Papers 2016-002, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    24. Govindan, Srihari & Wilson, Robert, 2009. "Global Newton Method for stochastic games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 414-421, January.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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