IDEAS home Printed from https://ideas.repec.org/p/red/sed010/680.html

Oblivious Equilibrium in Dynamic Discrete Games

Author

Listed:
  • Joao Macieira

    (Virginia Tech)

Abstract

The recently introduced concept of oblivious equilibrium aims at approximating Markov-Perfect Nash Equilibria (MPNE) when its calculation is computationally prohibitive in Ericson-Pakes-style games with many players. This paper extends the oblivious equilibrium concept to dynamic discrete-choice games. In contrast to Ericson-Pakes models, we find that there is a unique oblivious under independence of state transitions across players. We demonstrate that the distance between this equilibrium and any MPNE converges in probability to zero as the number of game players goes to infinity. Unlike previous work, our convergence result requires neither a "light tail" condition nor the absence of aggregate states in the dynamic game.

Suggested Citation

  • Joao Macieira, 2010. "Oblivious Equilibrium in Dynamic Discrete Games," 2010 Meeting Papers 680, Society for Economic Dynamics.
    • Handle: RePEc:red:sed010:680
    as

    Download full text from publisher

    File URL: https://red-files-public.s3.amazonaws.com/meetpapers/2010/paper_680.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    2. Thierry Magnac & David Thesmar, 2002. "Identifying Dynamic Discrete Decision Processes," Econometrica, Econometric Society, vol. 70(2), pages 801-816, March.
    3. 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.
    4. 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.
    5. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    6. J. Rust & J. F. Traub & H. Wozniakowski, 2002. "Is There a Curse of Dimensionality for Contraction Fixed Points in the Worst Case?," Econometrica, Econometric Society, vol. 70(1), pages 285-329, January.
    7. Doraszelski, Ulrich, 2003. "An R&D Race with Knowledge Accumulation," RAND Journal of Economics, The RAND Corporation, vol. 34(1), pages 20-42, Spring.
    8. 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.
    9. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
    10. Aguirregabiria, Victor, 2012. "A method for implementing counterfactual experiments in models with multiple equilibria," Economics Letters, Elsevier, vol. 114(2), pages 190-194.
    11. 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.
    12. 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.
    13. 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.
    14. Patrick Bajari & Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan, 2009. "A Simple Nonparametric Estimator for the Distribution of Random Coefficients," NBER Working Papers 15210, National Bureau of Economic Research, Inc.
    15. V. Joseph Hotz & Robert A. Miller & Seth Sanders & Jeffrey Smith, 1994. "A Simulation Estimator for Dynamic Models of Discrete Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 265-289.
    16. Victor Aguirregabiria & Pedro Mira & Hernan Roman, 2007. "An Estimate Dynamic Model of Entry, Exit, and Growth in Oligopoly Retail Markets," American Economic Review, American Economic Association, vol. 97(2), pages 449-454, May.
    17. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    18. Patrick Bajari & Jeremy T. Fox & Stephen P. Ryan, 2007. "Linear Regression Estimation of Discrete Choice Models with Nonparametric Distributions of Random Coefficients," American Economic Review, American Economic Association, vol. 97(2), pages 459-463, May.
    19. Yanyou Chen & Daniel Yi Xu, 2023. "A Structural Empirical Model of R&D, Firm Heterogeneity, and Industry Evolution," Journal of Industrial Economics, Wiley Blackwell, vol. 71(2), pages 323-353, June.
    20. Paul Ellickson & Beresteanu Arie, 2005. "The Dynamics of Retail Oligopolies," 2005 Meeting Papers 829, Society for Economic Dynamics.
    21. Jaap H. Abbring & Jeffrey R. Campbell, 2010. "Last-In First-Out Oligopoly Dynamics," Econometrica, Econometric Society, vol. 78(5), pages 1491-1527, September.
    22. 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.
    23. Jaap H. Abbring & Jeffrey R. Campbell & Nan Yang, 2010. "Simple Markov-perfect industry dynamics," Working Paper Series WP-2010-21, Federal Reserve Bank of Chicago.
    24. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    25. Aguirregabiria, Victor & Ho, Chun-Yu, 2010. "A dynamic game of airline network competition: Hub-and-spoke networks and entry deterrence," International Journal of Industrial Organization, Elsevier, vol. 28(4), pages 377-382, July.
    26. 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.
    27. 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.
    28. 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.
    29. 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.
    30. Minjae Song, 2011. "A Dynamic Analysis Of Cooperative Research In The Semiconductor Industry," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(4), pages 1157-1177, November.
    31. Victor Aguirregabiria & Gustavo Vicentini, 2006. "Dynamic Spatial Competition Between Multi-Store Firms," Working Papers tecipa-253, University of Toronto, Department of Economics.
    32. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    33. Gautam Gowrisankaran, 1999. "A Dynamic Model of Endogenous Horizonal Mergers," RAND Journal of Economics, The RAND Corporation, vol. 30(1), pages 56-83, Spring.
    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. 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.
    2. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov‐perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243, June.
    3. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    4. Jason R. Blevins, 2025. "Identification and Estimation of Continuous-Time Dynamic Discrete Choice Games," Papers 2511.02701, arXiv.org.
    5. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    6. Santos, Carlos Daniel, 2009. "Recovering the sunk costs of R&D: the moulds industry case," LSE Research Online Documents on Economics 28689, London School of Economics and Political Science, LSE Library.
    7. , & ,, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    8. 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.
    9. Haizhen Lin, 2015. "Quality Choice And Market Structure: A Dynamic Analysis Of Nursing Home Oligopolies," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1261-1290, November.
    10. Peter Arcidiacono & Paul B. Ellickson, 2011. "Practical Methods for Estimation of Dynamic Discrete Choice Models," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 363-394, September.
    11. 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.
    12. Yu Zheng & Juan Pantano, 2012. "Using Subjective Expectations Data to Allow for Unobserved Heterogeneity in Hotz-Miller Estimation Strategies," 2012 Meeting Papers 940, Society for Economic Dynamics.
    13. Peter Arcidiacono & Robert A. Miller, 2011. "Conditional Choice Probability Estimation of Dynamic Discrete Choice Models With Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 79(6), pages 1823-1867, November.
    14. Srisuma, Sorawoot & Linton, Oliver, 2012. "Semiparametric estimation of Markov decision processes with continuous state space," Journal of Econometrics, Elsevier, vol. 166(2), pages 320-341.
    15. Joao Macieira, 2007. "Extending the Frontier: A Structural Model of Investment and Technological Competition in the Supercomputer Industry," Working Papers e07-10, Virginia Polytechnic Institute and State University, Department of Economics.
    16. 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.
    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. Hanming Fang & Yang Wang, 2015. "Estimating Dynamic Discrete Choice Models With Hyperbolic Discounting, With An Application To Mammography Decisions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(2), pages 565-596, May.
    19. Daniel Ackerberg, 2009. "A new use of importance sampling to reduce computational burden in simulation estimation," Quantitative Marketing and Economics (QME), Springer, vol. 7(4), pages 343-376, December.
    20. Doraszelski, Ulrich & Satterthwaite, Mark, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," CEPR Discussion Papers 6212, C.E.P.R. Discussion Papers.

    More about this item

    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:red:sed010:680. 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: Christian Zimmermann (email available below). General contact details of provider: https://edirc.repec.org/data/sedddea.html .

    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.