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Bounds for best response functions in binary games

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Author Info

  • Kline, Brendan
  • Tamer, Elie

Abstract

This paper studies the identification of best response functions in binary games without making strong parametric assumptions about the payoffs. The best response function gives the utility maximizing response to a decision of the other players. This is analogous to the response function in the treatment–response literature, taking the decision of the other players as the treatment, except that the best response function has additional structure implied by the associated utility maximization problem. Further, the relationship between the data and the best response function is not the same as the relationship between the data and the response function in the treatment–response literature. We focus especially on the case of a complete information entry game with two firms. We also discuss the case of an entry game with many firms, non-entry games, and incomplete information. Our analysis of the entry game is based on the observation of realized entry decisions, which we then link to the best response functions under various assumptions including those concerning the level of rationality of the firms, including the assumption of Nash equilibrium play, the symmetry of the payoffs between firms, and whether mixed strategies are admitted.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 166 (2012)
Issue (Month): 1 ()
Pages: 92-105

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Handle: RePEc:eee:econom:v:166:y:2012:i:1:p:92-105

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Binary games; Entry games; Best response functions; Multiple equilibria; Mixed strategies; Nash equilibrium; Levels of rationality; Treatment effects; Peer effects;

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References

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  1. Aradillas-Lopez, Andres & Tamer, Elie, 2008. "The Identification Power of Equilibrium in Simple Games," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 261-310.
  2. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
  3. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
  4. Bresnahan, Timothy F & Reiss, Peter C, 1991. "Entry and Competition in Concentrated Markets," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 977-1009, October.
  5. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
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  7. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, 09.
  8. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  9. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
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  13. Bresnahan, Timothy F & Reiss, Peter C, 1990. "Entry in Monopoly Markets," Review of Economic Studies, Wiley Blackwell, vol. 57(4), pages 531-53, October.
  14. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  15. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 70(1), pages 147-165, January.
  16. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
  17. Reiss, Peter C, 1996. "Empirical Models of Discrete Strategic Choices," American Economic Review, American Economic Association, vol. 86(2), pages 421-26, May.
  18. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
  19. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
  20. Rosa L. Matzkin, 2008. "Identification in Nonparametric Simultaneous Equations Models," Econometrica, Econometric Society, vol. 76(5), pages 945-978, 09.
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  22. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
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Citations

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Cited by:
  1. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2013. "Random Coefficients in Static Games of Complete Information," Boston College Working Papers in Economics 835, Boston College Department of Economics.
  2. Marc HENRY & Ismael MOURIFIÉ, 2013. "Nonparametric Sharp Bounds For Payoffs In 2 × 2 Games," Working Papers tecipa-500, University of Toronto, Department of Economics.
  3. Andrew Chesher & Adam Rosen, 2012. "Simultaneous equations for discrete outcomes:coherence, completeness, and identification," CeMMAP working papers CWP21/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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