IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpga/9901003.html
   My bibliography  Save this paper

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.
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9901/9901003.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    2. Maskin, Eric & Tirole, Jean, 1987. "A theory of dynamic oligopoly, III : Cournot competition," European Economic Review, Elsevier, vol. 31(4), pages 947-968, June.
    3. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Doraszelski, Ulrich & Satterthwaite, Mark, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," CEPR Discussion Papers 6212, C.E.P.R. Discussion Papers.
    3. , & ,, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    4. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
    5. 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.
    6. 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).
    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. Yoon, Jangsu, 2024. "Identification and estimation of sequential games of incomplete information with multiple equilibria," Journal of Econometrics, Elsevier, vol. 238(2).
    9. Ulrich Doraszelski & Mark Satterthwaite, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," Levine's Bibliography 321307000000000912, UCLA Department of Economics.
    10. 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.
    11. 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.
    12. 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.
    13. 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).
    14. 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.
    15. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
    16. 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.
    17. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    18. Gomes, Armando, 2015. "Multilateral negotiations and formation of coalitions," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 77-91.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Govindan, Srihari & Wilson, Robert, 2009. "Global Newton Method for stochastic games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 414-421, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
    2. Lau, Sau-Him Paul, 2001. "Aggregate Pattern of Time-dependent Adjustment Rules, II: Strategic Complementarity and Endogenous Nonsynchronization," Journal of Economic Theory, Elsevier, vol. 98(2), pages 199-231, June.
    3. John W. Patty, 2005. "Generic Difference of Expected Vote Share and Probability of Victory Maximization in Simple Plurality Elections with Probabilistic Voters," Public Economics 0502006, University Library of Munich, Germany.
    4. Do, Jihwan & Miklós-Thal, Jeanine, 2023. "Partial secrecy in vertical contracting," International Journal of Industrial Organization, Elsevier, vol. 90(C).
    5. Miettinen, Topi & Perea, Andrés, 2015. "Commitment in alternating offers bargaining," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 12-18.
    6. 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.
    7. Akihiko Matsui & Roger Lagunoff, 2001. "Are "Anti-Folk Theorems" in repeated games nongeneric?," Review of Economic Design, Springer;Society for Economic Design, vol. 6(3), pages 397-412.
    8. Luciano Fanti, 2015. "Environmental Standards and Cournot Duopoly: A Stability Analysis," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 61(4), pages 577-593, August.
    9. Vives, Xavier & Jun, Byoung, 2001. "Incentives in Dynamic Duopoly," CEPR Discussion Papers 2899, C.E.P.R. Discussion Papers.
    10. Chen, Yongmin & Rosenthal, Robert W., 1996. "Dynamic duopoly with slowly changing customer loyalties," International Journal of Industrial Organization, Elsevier, vol. 14(3), pages 269-296, May.
    11. Lisi, Domenico & Moscone, Francesco & Tosetti, Elisa & Vinciotti, Veronica, 2021. "Hospital quality interdependence in a competitive institutional environment: Evidence from Italy," Regional Science and Urban Economics, Elsevier, vol. 89(C).
    12. Seki, Erika, 2006. "Effects of rotation scheme on fishing behaviour with price discrimination and limited durability: Theory and evidence," Journal of Development Economics, Elsevier, vol. 80(1), pages 106-135, June.
    13. Halkos, George, 2009. "A Differential game approach in the case of a polluting oligopoly," MPRA Paper 23742, University Library of Munich, Germany.
    14. Ding, Zhanwen & Wang, Qiao & Cai, Chaoying & Jiang, Shumin, 2014. "Fictitious play with incomplete learning," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 1-8.
    15. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2006. "The Limits of ex post Implementation," Econometrica, Econometric Society, vol. 74(3), pages 585-610, May.
    16. Dockner, Engelbert J, 1992. "A Dynamic Theory of Conjectural Variations," Journal of Industrial Economics, Wiley Blackwell, vol. 40(4), pages 377-395, December.
    17. Mika Kato, 2016. "Jean Tirole, Nobel Prize Winner," Review of Political Economy, Taylor & Francis Journals, vol. 28(1), pages 23-44, January.
    18. Drew Fudenberg, 2015. "Tirole's Industrial Regulation and Organization Legacy in Economics," Scandinavian Journal of Economics, Wiley Blackwell, vol. 117(3), pages 771-800, July.
    19. Victor Aguirregabiria & Victor Aguirregabiria & Aviv Nevo & Aviv Nevo, 2010. "Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games," Working Papers tecipa-419, University of Toronto, Department of Economics.
    20. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov‐perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243, June.

    More about this item

    Keywords

    stochastic games; Markov Perfect equilibria; genericity.;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpga:9901003. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.