Abstract
Empirical models of strategic games are central to much analysis in marketing and economics. However, two challenges in applying these models to real-world data are that such models often admit multiple equilibria and that they require strong informational assumptions. The first implies that the model does not make unique predictions about the data, and the second implies that results may be driven by strong a priori assumptions about the informational setup. This article summarizes recent work that seeks to address both issues and suggests some avenues for future research.
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Notes
See Doraszelski and Pakes (2007) for a broad review.
This would build on Grieco (2014), which allows for the possibility that multiple equilibria are played in the data within the context of a static discrete game.
All the solution homotopy methods (Judd, Renner and Schmedders 2012) have the potential to be very useful in this respect.
An early example of empirical research that incorporates learning into games is provided by Gardete and Pedro (2013).
Lee and Pakes (2009) explore the implications for equilibrium selection of best reply and fictitious play learning processes within the context of a static game of bank ATM allocation.
See Gureckis and Love (2013) for a review of reinforcement learning.
References
Aguirregabiria, V. & MagesanA. (2012). Identification and estimation of dynamics games when players’ beliefs are not in equilibrium. Working paper, University of Toronto.
Bajari, P., Hong, H., Krainer, J., & Nekipelov, D. (2010a). Estimating static models of strategic interactions. Journal of Business and Economic Statistics, 28(4).
Bajari, P., Hong, H., & Ryan, S. (2010b). Identification and estimation of discrete games of complete information. Econometrica, 78(5), 1529–1568.
Berry, S., Levinsohn, J., & Pakes, A. (1999). Voluntary export restraints on automobiles: evaluating a trade policy. American Economic Review, 89(3), 400–430.
Besanko, D., Doraszelski, U., Kryukov, Y., & Satterthwaite, M. (2010a). Learning-by-doing, organizational forgetting, and industry dynamics. Econometrica, 78(2), 453–508.
Besanko, D., Doraszelski, U., Lauren, L., & Satterthwaite, M. (2010b). On the role of demand and strategic uncertainty in capacity investment and disinvestment dynamics. International Journal of Industrial Organization, 28(4), 383–389.
Besanko, D., Doraszelski, U., Lauren, L., & Satterthwaite, M. (2010c). Lumpy capacity investment and disinvestment dynamics. Operations Research, 58(4), 1178–1193.
Besanko, D., Doraszelski, U., & Kryukov, Y. (2013). The economics of predation: what drives pricing when there is learning-by-doing?”American. Economic Review, 104(3), 868–897.
Borkovsky, R., Doraszelski, U., & Kryukov, S. (2010). A user’s guide to solving dynamic stochastic games using the homotopy method. Operations Research, 58(4), 1116–1132.
Borkovsky, R., Doraszelski, U., & Kryukov, S. (2012). A dynamic quality ladder duopoly with entry and exit: exploring the equilibrium correspondence using the homotopy method. Quantitative Marketing and Economics, 10(2), 197–229.
Bresnahan, T. F., & Reiss, P. C. (1991). Empirical models of discrete games. Journal of Econometrics, 48(1–2), 57–82.
Camerer, C., & Ho, T.-H. (1999). Experience-weighted attraction learning in normal form games. Econometrica, 67, 837–874.
Camerer, C., Ho, T.-H., & Chong, J.-K. (2002). Sophisticated learning and strategic teaching. Journal of Economic Theory, 104, 137–188.
Ciliberto, F., & Tamer, E. (2009). Market structure and multiple equilibria in airline markets. Econometrica, 77(6), 1791–1828.
Doraszelski, U. & Pakes, A. (2007). A framework for applied dynamic analysis in IO. In: J. J. Heckman and E. Leamer (eds.), Handbook of Industrial Organization (Ch. 60), North Holland.
Doraszelski, U., & Satterthwaite, M. (2010). Computable Markov-perfect industry dynamics. Rand Journal of Economics, 41(2), 215–243.
Doraszelski, U., Lewis, G., Pakes, A. (2014). Just starting out: learning and price competition in a new market. Working paper, Harvard University.
Echenique, F., & Komunjer, I. (2009). Testing models with multiple equilibria by quantile methods. Econometrica, 77(4), 1281–1298.
Ellickson, P. B., & Misra, S. (2011). Estimating discrete games. Marketing Science, 30(6), 997–1010.
Erev, I., & Roth, A. (1998). Predicting how people play games: reinforcement learning in experimental games with unique, mixed strategy equilibria. The American Economic Review, 88(4), 848–881.
Ericson, R., & Pakes, A. (1995). Markov-perfect industry dynamics: a framework for empirical work. Review of Economic Studies, 62, 53–82.
Fershtman, C., & Pakes, A. (2012). Dynamic games with asymmetric information: a framework for empirical work. The Quarterly Journal of Economics, 127(4), 1611–1661.
Fudenberg, D., & Levine, D. (1998). The Theory of Learning in Games. Cambridge: MIT.
Gardete, Pedro M. (2013). Peer effects in buying behavior: evidence from in-flight purchases. Working paper, Stanford University.
Gedge, C., Roberts, J., & Sweeting, A. (2013). An empirical model of dynamic limit pricing: the airline industry. Working paper, University of Maryland and Duke University.
Grieco, P. (2014). Discrete games with flexible information structures: an application to local grocery markets. RAND Journal of Economics, 45(2), 303–340.
Gureckis, T.M. and Love, B.C. (2013) Reinforcement learning: a computational perspective. working paper, New York University.
Judd, K., Renner, P., & Schmedders, K. (2012). Finding all pure strategy equilibria in games with continuous strategies. Quantitative Economics, 3(2), 289–331.
Lee, R. & Pakes, A. (2009). Multiple equilibria and selection by learning in an applied setting. Economic Letters.
Mathevet, L. (2013). An axiomatic approach to bounded rationality in repeated interactions: theory and experiments. Working paper, New York University.
Milgrom, P., & Roberts, J. (1982). Limit pricing and entry under incomplete information: an equilibrium analysis. Econometrica, 50(2), 443–459.
Misra, S. (2013). Markov Chain Monte Carlo for incomplete information discrete games. Quantitative Marketing and Economics, 11(1), 117–153.
Narayanan, S. (2013). Bayesian estimation of discrete games of complete information. Quantitative Marketing and Economics, 11(1), 39–81.
Pakes, A., & McGuire, P. (1994). Computing Markov-perfect Nash equilibria: numerical implications of a dynamic differentiated product model. Rand Journal of Economics, 25(4), 555–589.
Roth, A., & Erev, I. (1995). Learning in extensive-form games: experimental data and simple dynamic models in the intermediate term. Games and Economic Behavior, 8, 164–212.
Sweeting, A. (2009). The strategic timing of radio commercials: an empirical analysis using multiple equilibria. RAND Journal of Economics, 40(4).
Tamer, E. (2003). Incomplete simultaneous discrete response model with multiple equilibria. Review of Economic Studies, 147-165.
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Ron N. Borkovsky, Paul B. Ellickson and Brett R. Gordon were the co-chairs of the session at the 9th Triennial Choice Symposium.
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Borkovsky, R.N., Ellickson, P.B., Gordon, B.R. et al. Multiplicity of equilibria and information structures in empirical games: challenges and prospects. Mark Lett 26, 115–125 (2015). https://doi.org/10.1007/s11002-014-9308-z
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DOI: https://doi.org/10.1007/s11002-014-9308-z