Quantitative Marketing and Economics

, Volume 10, Issue 1, pp 1–26 | Cite as

Enriching interactions: Incorporating outcome data into static discrete games

Article

Abstract

When modeling the behavior of firms, marketers and micro-economists routinely confront complex problems of strategic interaction. In competitive environments, firms make strategic decisions that not only depend on the features of the market, but also on their beliefs regarding the reactions of their rivals. Structurally modeling these interactions requires formulating and estimating a discrete game, a task which, until recently, was considered intractable. Fortunately, two-step estimation methods have cracked the problem, fueling a growing literature in both marketing and economics that tackles a host of issues from the optimal design of ATM networks to the choice of pricing strategy. However, most existing methods have focused on only the discrete choice of actions, ignoring a wealth of information contained in post-choice outcome data and severely limiting the scope for performing informative counterfactuals or identifying the deep structural parameters that drive strategic decisions. The goal of this paper is to provide a method for incorporating post-choice outcome data into static discrete games of incomplete information. In particular, our estimation approach adds a selection correction to the two-step games approach, allowing the researcher to use revenue data, for example, to recover the costs associated with alternative actions. Alternatively, a researcher might use R&D expenses to back out the returns to innovation.

Keywords

Discrete games Selection Incomplete information EDLP Pricing strategy Two step estimators 

Keywords

C1 C7 M31 L81 

References

  1. Aguirregabiria, V., & Mira, P. (2002). Swapping the nested fixed point algorithm: a class of estimators for discrete Markov decision models. Econometrica, 70(4), 1519–1543.CrossRefGoogle Scholar
  2. Aguirregabiria, V., & Mira, P. (2007). Sequential estimation of dynamic discrete games. Econometrica, 75(1), 1–53.CrossRefGoogle Scholar
  3. Ahn, H., & Powell, J. L. (1993). Semiparametric estimation of censored selection models with a nonparametric selection mechanism. Journal of Econometrics, 58, 3–29.CrossRefGoogle Scholar
  4. Bajari, P., Benkard, L., & Levin, J. (2007). Estimating dynamic models of imperfect competition. Econometrica, 75(5), 1331–1370.CrossRefGoogle Scholar
  5. Bajari, P., Hong, H., Krainer, J., & Nekipelov, D. (2010). Estimating static models of strategic interactions. Journal of Economics and Business Statistics, 28(4), 469–482.CrossRefGoogle Scholar
  6. Berry, S. (1992). Estimation of a model of entry in the airline industry. Econometrica, 60(4), 889–917.CrossRefGoogle Scholar
  7. Berry, S., Levinsohn, J., & Pakes, A. (1995). Automobile prices in market equilibrium. Econometrica, 63(4), 841–890.CrossRefGoogle Scholar
  8. Bresnahan, T., & Reiss, P. (1991a). Empirical models of discrete games. Journal of Econometrics, 48, 57–81.CrossRefGoogle Scholar
  9. Bresnahan, T., & Reiss, P. (1991b). Entry and competition in concentrated markets. Journal of Political Economy, 99, 977–1009.CrossRefGoogle Scholar
  10. Dahl, G. (2002). Mobility and the return to education: Testing a Roy model with multiple markets. Econometrica, 70(6), 2367–2420.CrossRefGoogle Scholar
  11. Draganska, M., Mazzeo, M., & Seim, K. (2009). Beyond plain vanilla: Modeling product assortment choices in the ice cream market. Quantitative Marketing and Economics, 7(2), 105–146.CrossRefGoogle Scholar
  12. Dubin, J., & McFadden, D. (1984). An econometric analysis of residential electric appliance holdings and consumption. Econometrica, 52, 345–362.CrossRefGoogle Scholar
  13. Ellickson, P., & Misra, S. (2008). Supermarket pricing strategies. Marketing Science, 27(5), 811–828.CrossRefGoogle Scholar
  14. Ellickson, P., & Misra, S. (2011). Estimating discrete games. Marketing Science (forthcoming).Google Scholar
  15. Ellickson, P., Misra, S., & Nair, H. (2011). Repositioning dynamics and pricing strategy. Simon School of Business Working Paper No. FR 11-07.Google Scholar
  16. Fox, J. (2007). Semiparametric estimation of multinomial discrete choice models using a subset of choices. RAND Journal of Economics, 38(4), 1002–1019.CrossRefGoogle Scholar
  17. Hanemann, W. M. (1984). Discrete/Continuous models of consumer demand. Econometrica, 52(3), 541–561.CrossRefGoogle Scholar
  18. Hartmann, W. R. (2010). Demand estimation with social interactions and the implications for targeted marketing. Marketing Science, 29(4), 585–601.CrossRefGoogle Scholar
  19. Heckman, J. J. (1974). Shadow prices, market wages, and labor supply. Econometrica, 42, 679–693.CrossRefGoogle Scholar
  20. Heckman, J. J. (1979). Sample selection bias as a specification error. Econometrica, 47(1), 153–161.CrossRefGoogle Scholar
  21. Heckman, J. J., & Honore, B. (1990). The empirical content of the Roy model. Econometrica, 58(5), 1121–1149.CrossRefGoogle Scholar
  22. Heckman, J. J., & Robb, R. (1985). Alternative methods for evaluating the impact of interventions. In J. J. Heckman, & B. Singer (Eds.), Longitudinal analysis of labor market data (pp. 156–245). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  23. Heckman, J. J., & Robb, R. (1986). Alternative methods for solving the problem of selection bias in evaluating the impact of treatments on outcomes. In H. Wainer (Ed.), Drawing inferences from self-selected samples. New York: Springer.Google Scholar
  24. Ho, K. (2009). Insurer-provider networks in the medical care market. American Economic Review, 99(1), 393–430.CrossRefGoogle Scholar
  25. Hotz, V.J., Miller, R.A., Sanders, S., & Smith, J. (1994). A simulation estimator for dynamic models of discrete choice. Review of Economic Studies, 61(2), 265–289.CrossRefGoogle Scholar
  26. Lal, R., & Rao, R. (1997). Supermarket competition: The case of every day low pricing. Marketing Science, 16(1), 60–81.CrossRefGoogle Scholar
  27. Mazzeo, M. (2002). Competitive outcomes in product-differentiated oligopoly. Review of Economics and Statistics, 84(4), 716–728.CrossRefGoogle Scholar
  28. Newey, W. K., & McFadden, D. (1994). Large sample estimation and hypothesis testing. In D. McFadden, & R. Engle (Eds.), Handbook of econometrics (Vol. 4, pp. 2113–2245). North-Holland, Amsterdam, The Netherlands: Elsevier.Google Scholar
  29. Orhun, Y. (2006). Spatial differentiation in the supermarket industry. Working paper, GSB Chicago.Google Scholar
  30. Pakes, A., Ostrovsky, M., & Berry, S. (2007). Simple estimators for the parameters of discrete dynamic games (with entry-exit examples). RAND Journal of Economics, 38(2), 373–399.CrossRefGoogle Scholar
  31. Pakes, A., Porter, J., Ho, K., & Ishii, J. (2006). Moment inequalities and their application. Working paper, Harvard University.Google Scholar
  32. Pesendorfer, M., & Schmidt-Dengler, P. (2007). Asymptotic least squares estimators for dynamic games. Review of Economic Studies, 75, 901–928.CrossRefGoogle Scholar
  33. Pesendorfer, M., & Schmidt-Dengler, P. (2010). Sequential estimation of dynamic discrete games: A comment. Econometrica, 78(2), 833–842.CrossRefGoogle Scholar
  34. Reiss, P., & Spiller, P. (1989). Competition and entry in small airline markets. Journal of Law and Economics, 32(2), S179–202.CrossRefGoogle Scholar
  35. Roy, A. D. (1951). Some thoughts on the distribution of earnings. Oxford Economic Papers, 3(2), 135–146.Google Scholar
  36. Rust, J. (1987). Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher. Econometrica, 55(5), 999–1033.CrossRefGoogle Scholar
  37. Rust, J. (1994). Estimation of dynamic structural models, problems and prospects: Discrete decision processes. In C. Sims (Ed.), Advances in econometrics: Sixth world congress (Vol. 2, Chap. 4, pp. 119–170). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  38. Seim, K. (2006). An empirical model of firm entry with endogenous product-type choices. RAND Journal of Economics, 37(3), 619–640.CrossRefGoogle Scholar
  39. Su, C. L., & Judd, K. L. (2007). Constrained optimization approaches to estimation of structural models. Working paper, CMS-EMS, Kellogg School of Management.Google Scholar
  40. Sweeting, A. (2009). The strategic timing of radio commercials: An empirical analysis using multiple equilibria. RAND Journal of Economics, 40(4), 710–742.CrossRefGoogle Scholar
  41. Vella, F. (1998). Estimating models with sample selection bias: A survey. Journal of Human Resources, 33, 127–172.CrossRefGoogle Scholar
  42. Vitorino, M. A. (2007). Empirical entry games with complementarities: An application to the shopping center industry. Working paper, Chicago GSB.Google Scholar
  43. Zhu, T., & Singh, V. (2009). Spatial competition and endogenous location choices: An application to discount retailing. Quantitative Marketing and Economics, 7(1), 1–35.CrossRefGoogle Scholar
  44. Zhu, T., Singh, V., & Manuszak, M. (2009). Market structure and competition in the retail discount industry. Journal of Marketing Research, 46(4), 453–466.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.William E. Simon School of Business AdministrationUniversity of RochesterRochesterUSA

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