[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/6805.html
   My bibliography  Save this paper

A Theory of Regular Markov Perfect Equilibria in Dynamic Stochastic Games: Genericity, Stability, and Purification

Author

Listed:
  • Doraszelski, Ulrich
  • Escobar, Juan
Abstract
This paper develops a theory of regular Markov perfect equilibria in dynamic stochastic games. We show that almost all dynamic stochastic games have a finite number of locally isolated Markov perfect equilibria that are all regular. These equilibria are essential and strongly stable. Moreover, they all admit purification.

Suggested Citation

  • 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.
    • Handle: RePEc:cpr:ceprdp:6805
    as

    Download full text from publisher

    File URL: https://cepr.org/publications/DP6805
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. 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.
    3. Doraszelski, Ulrich & Pakes, Ariel, 2007. "A Framework for Applied Dynamic Analysis in IO," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 30, pages 1887-1966, Elsevier.
    4. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    5. Victor Aguirregabiria & Pedro Mira, 2002. "Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models," Econometrica, Econometric Society, vol. 70(4), pages 1519-1543, July.
    6. Che‐Lin Su & Kenneth L. Judd, 2012. "Constrained Optimization Approaches to Estimation of Structural Models," Econometrica, Econometric Society, vol. 80(5), pages 2213-2230, September.
    7. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 497-529.
    8. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-769, May.
    9. Daron Acemoglu & James A. Robinson, 2001. "A Theory of Political Transitions," American Economic Review, American Economic Association, vol. 91(4), pages 938-963, September.
    10. Bergemann, Dirk & Valimaki, Juuso, 1996. "Learning and Strategic Pricing," Econometrica, Econometric Society, vol. 64(5), pages 1125-1149, September.
    11. V. Bhaskar, 1998. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 135-149.
    12. V. Bhaskar & George J. Mailath & Stephen Morris, 2008. "Purification in the Infinitely-Repeated Prisoners' Dilemma," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 515-528, July.
    13. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    14. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    15. Govindan, Srihari & Reny, Philip J. & Robson, Arthur J., 2003. "A short proof of Harsanyi's purification theorem," Games and Economic Behavior, Elsevier, vol. 45(2), pages 369-374, November.
    16. Ariel Pakes & Paul McGuire, 1994. "Computing Markov-Perfect Nash Equilibria: Numerical Implications of a Dynamic Differentiated Product Model," RAND Journal of Economics, The RAND Corporation, vol. 25(4), pages 555-589, Winter.
    17. C. Lanier Benkard, 2004. "A Dynamic Analysis of the Market for Wide-Bodied Commercial Aircraft," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 581-611.
    18. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    19. Doraszelski, Ulrich & Satterthwaite, Mark, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," CEPR Discussion Papers 6212, C.E.P.R. Discussion Papers.
    20. Hans Haller & Roger Lagunoff, 2000. "Genericity and Markovian Behavior in Stochastic Games," Econometrica, Econometric Society, vol. 68(5), pages 1231-1248, September.
    21. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    22. Pesendorfer, Martin & Schmidt-Dengler, Philipp, 2003. "Identification and Estimation of Dynamic Games," CEPR Discussion Papers 3965, C.E.P.R. Discussion Papers.
    23. Martin Pesendorfer & Philipp Schmidt-Dengler, 2008. "Asymptotic Least Squares Estimators for Dynamic Games -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 901-928.
    24. Erkan Erdem & James Tybout, 2003. "Trade Policy and Industrial Sector Responses: Using Evolutionary Models to Interpret the Evidence," NBER Working Papers 9947, National Bureau of Economic Research, Inc.
    25. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
    26. Pakes, Ariel & McGuire, Paul, 2001. "Stochastic Algorithms, Symmetric Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Econometrica, Econometric Society, vol. 69(5), pages 1261-1281, September.
    27. Doraszelski, Ulrich & Kryukov, Yaroslav & Borkovsky, Ron N., 2008. "A User's Guide to Solving Dynamic Stochastic Games Using the Homotopy Method," CEPR Discussion Papers 6733, C.E.P.R. Discussion Papers.
    28. Aguirregabiria, Victor & Ho, Chun-Yu, 2012. "A dynamic oligopoly game of the US airline industry: Estimation and policy experiments," Journal of Econometrics, Elsevier, vol. 168(1), pages 156-173.
    29. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, June.
    30. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    31. Ulrich Doraszelski & Mark Satterthwaite, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," Levine's Bibliography 321307000000000912, UCLA Department of Economics.
    32. Ronald L. Goettler & Christine A. Parlour & Uday Rajan, 2005. "Equilibrium in a Dynamic Limit Order Market," Journal of Finance, American Finance Association, vol. 60(5), pages 2149-2192, October.
    33. Bernheim, B. Douglas & Ray, Debraj, 1989. "Markov perfect equilibria in altruistic growth economies with production uncertainty," Journal of Economic Theory, Elsevier, vol. 47(1), pages 195-202, February.
    34. Gautam Gowrisankaran & Robert J. Town, 1997. "Dynamic Equilibrium in the Hospital Industry," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(1), pages 45-74, March.
    Full references (including those not matched with items on IDEAS)

    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. Joao Macieira, 2010. "Oblivious Equilibrium in Dynamic Discrete Games," 2010 Meeting Papers 680, Society for Economic Dynamics.
    2. Ulrich Doraszelski & Mark Satterthwaite, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," Levine's Bibliography 321307000000000912, UCLA Department of Economics.
    3. 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.
    4. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    5. Doraszelski, Ulrich & Satterthwaite, Mark, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," CEPR Discussion Papers 6212, C.E.P.R. Discussion Papers.
    6. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov‐perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243, June.
    7. Carlos Daniel Santos, 2009. "Recovering the Sunk Costs of R&D: the Moulds Industry Case," CEP Discussion Papers dp0958, Centre for Economic Performance, LSE.
    8. C. Lanier Benkard & Przemyslaw Jeziorski & Gabriel Y. Weintraub, 2013. "Oblivious Equilibrium for Concentrated Industries," NBER Working Papers 19307, National Bureau of Economic Research, Inc.
    9. Johannes Van Biesebroeck & Aamir Hashmi, 2007. "Market Structure and Innovation: A Dynamic Analysis of the Global Automobile Industry," 2007 Meeting Papers 362, Society for Economic Dynamics.
    10. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    11. Peter Arcidiacono & Patrick Bayer & Jason R. Blevins & Paul B. Ellickson, 2016. "Estimation of Dynamic Discrete Choice Models in Continuous Time with an Application to Retail Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(3), pages 889-931.
    12. Ulrich Doraszelski & Kenneth L. Judd, 2012. "Avoiding the curse of dimensionality in dynamic stochastic games," Quantitative Economics, Econometric Society, vol. 3(1), pages 53-93, March.
    13. Doraszelski, Ulrich & Kryukov, Yaroslav & Borkovsky, Ron N., 2008. "A User's Guide to Solving Dynamic Stochastic Games Using the Homotopy Method," CEPR Discussion Papers 6733, C.E.P.R. Discussion Papers.
    14. Govindan, Srihari & Wilson, Robert, 2009. "Global Newton Method for stochastic games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 414-421, January.
    15. Gabriel Y. Weintraub & C. Lanier Benkard & Benjamin Van Roy, 2010. "Computational Methods for Oblivious Equilibrium," Operations Research, INFORMS, vol. 58(4-part-2), pages 1247-1265, August.
    16. Hu, Yingyao & Shum, Matthew, 2012. "Nonparametric identification of dynamic models with unobserved state variables," Journal of Econometrics, Elsevier, vol. 171(1), pages 32-44.
    17. C. Lanier Benkard & Przemyslaw Jeziorski & Gabriel Y. Weintraub, 2015. "Oblivious equilibrium for concentrated industries," RAND Journal of Economics, RAND Corporation, vol. 46(4), pages 671-708, October.
    18. Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2007. "Computational Methods for Oblivious Equilibrium," Research Papers 1969, Stanford University, Graduate School of Business.
    19. Jason R. Blevins & Ahmed Khwaja & Nathan Yang, 2018. "Firm Expansion, Size Spillovers, and Market Dominance in Retail Chain Dynamics," Management Science, INFORMS, vol. 64(9), pages 4070-4093.
    20. Linli Xu & Jorge M. Silva-Risso & Kenneth C. Wilbur, 2018. "Dynamic Quality Ladder Model Predictions in Nonrandom Holdout Samples," Management Science, INFORMS, vol. 64(7), pages 3187-3207, July.

    More about this item

    Keywords

    Computation; Dynamic stochastic games; Essentiality; Estimation; Finiteness; Genericity; Markov perfect equilibrium; Purifiability; Regularity; Repeated games;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • 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:cpr:ceprdp:6805. 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: the person in charge (email available below). General contact details of provider: https://www.cepr.org .

    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.