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A Genetic Algorithm for the Structural Estimation of Games with Multiple Equilibria

Author

Listed:
  • VICTOR AGUIRREGABIRIA

    () (Department of Economics, Boston University)

  • PEDRO MIRA

    () (Centro de Estudios Monetarios y Financieros (CEMFI))

Abstract

This paper proposes an algorithm to obtain maximum likelihood estimates of structural parameters in discrete games with multiple equilibria. The method combines a genetic algorithm (GA) with a pseudo maximum likelihood (PML) procedure. The GA searches efficiently over the huge space of possible combinations of equilibria in the data. The PML procedure avoids the repeated computation of equilibria for each trial value of the parameters of interest. To test the ability of this method to get maximum likelihood estimates, we present a Monte Carlo experiment in the context of a game of price competition and collusion.

Suggested Citation

  • Victor Aguirregabiria & Pedro Mira, 2005. "A Genetic Algorithm for the Structural Estimation of Games with Multiple Equilibria," Boston University - Department of Economics - Working Papers Series WP2005-001, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2005-001
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, pages 1331-1370.
    4. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
    5. V. Joseph Hotz & Robert A. Miller & Seth Sanders & Jeffrey Smith, 1994. "A Simulation Estimator for Dynamic Models of Discrete Choice," Review of Economic Studies, Oxford University Press, pages 265-289.
    6. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    7. 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.
    8. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, 01.
    9. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
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    Cited by:

    1. Sumon Datta & K. Sudhir, 2013. "Does reducing spatial differentiation increase product differentiation? Effects of zoning on retail entry and format variety," Quantitative Marketing and Economics (QME), Springer, vol. 11(1), pages 83-116, March.
    2. Sumon Datta & K. Sudhir, 2012. "Does Reducing Spatial Differentiation Increase Product Differentiation? Effects of Zoning on Retail Entry and Format Variety," Cowles Foundation Discussion Papers 1851, Cowles Foundation for Research in Economics, Yale University, revised Sep 2012.
    3. Viauroux, Christelle, 2007. "Structural estimation of congestion costs," European Economic Review, Elsevier, vol. 51(1), pages 1-25, January.

    More about this item

    Keywords

    Empirical games; Maximum likelihood estimation; Multiple equilibria; Genetic algorithms;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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