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Finite State Dynamic Games with Asymmetric Information: A Framework for Applied Work

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  • Fershtman, Chaim
  • Pakes, Ariel

Abstract

We present a framework for the applied analysis of dynamic games with asymmetric information. The framework consists of a definition of equilibrium, and an algorithm to compute it. Our definition of Applied Markov Perfect equilibrium is an extension of the definition of Markov Perfect equilibrium for games with asymmetric information; an extension chosen for its usefulness to applied research. Each agent conditions its strategy on the payoff or informationally relevant variables that are observed by that particular agent. The strategies are optimal given the beliefs on the evolution of these observed variables, and the rules governing the evolution of the observables are consistent with the equilibrium strategies. We then provide a simple algorithm for computing this equilibrium. The algorithm is easy to program and does not require computation of posterior distributions, explicit integration over possible future states, or information from all possible points in the state space. For specificity, we present our results in the context of a dynamic oligopoly game with collusion in which the outcome of firms? investments are random and only observed by the investing agent. We then use this example to illustrate the computational properties of the algorithm.

Suggested Citation

  • Fershtman, Chaim & Pakes, Ariel, 2005. "Finite State Dynamic Games with Asymmetric Information: A Framework for Applied Work," CEPR Discussion Papers 5024, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:5024
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    8. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 2004. "Learning to play Bayesian games," Games and Economic Behavior, Elsevier, vol. 46(2), pages 282-303, February.
    9. 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.
    10. 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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    13. Severin Borenstein & James B. Bushnell & Frank A. Wolak, 2002. "Measuring Market Inefficiencies in California's Restructured Wholesale Electricity Market," American Economic Review, American Economic Association, vol. 92(5), pages 1376-1405, December.
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    Cited by:

    1. Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2007. "Computational Methods for Oblivious Equilibrium," Research Papers 1969, Stanford University, Graduate School of Business.
    2. Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2007. "Markov Perfect Industry Dynamics with Many Firms," Research Papers 1919r, Stanford University, Graduate School of Business.
    3. Bernard Caillaud & Romain de Nijs, 2011. "Strategic loyalty reward in dynamic price Discrimination," Working Papers halshs-00622291, HAL.
    4. Bernard Caillaud & Romain de Nijs, 2011. "Strategic loyalty reward in dynamic price Discrimination," PSE Working Papers halshs-00622291, HAL.
    5. Lewis, Greg & Backus, Matthew, 2009. "An Estimable Demand System for a Large Auction Platform Market," Department of Economics, Working Paper Series qt8vk5j2kr, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    6. Mar Reguant, 2014. "Complementary Bidding Mechanisms and Startup Costs in Electricity Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(4), pages 1708-1742.
    7. Bernard Caillaud & Romain De Nijs, 2014. "Strategic Loyalty Reward in Dynamic Price Discrimination," Marketing Science, INFORMS, vol. 33(5), pages 725-742, September.
    8. Luís Cabral, 2005. "Collusion Theory: Where to Go Next?," Journal of Industry, Competition and Trade, Springer, vol. 5(3), pages 199-206, December.
    9. Patrick Bajari & Victor Chernozhukov & Han Hong & Denis Nekipelov, 2015. "Identification and Efficient Semiparametric Estimation of a Dynamic Discrete Game," NBER Working Papers 21125, National Bureau of Economic Research, Inc.
    10. 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.
    11. Ariel Pakes, 2008. "Theory and Empirical Work on Imperfectly Competitive Markets," NBER Working Papers 14117, National Bureau of Economic Research, Inc.

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    More about this item

    Keywords

    Dynamic games; Numerical analysis; Collusive behaviour; Cartels;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L40 - Industrial Organization - - Antitrust Issues and Policies - - - General

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