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Correlated Equilibrium and the Estimation of Static Discrete Games with Complete Information

Listed author(s):
  • Yang, Zhou

In order to understand strategic interactions among firms, we often need to estimate the parameters of static discrete games with complete information. This class of games is difficult to estimate because the possibility of multiple equilibria invalidates the use of methods such as MLE and GMM. We propose a two-step estimator to get around the issue of multiple equilibria by exploiting the fact that all of the Nash equilibria are contained in the set of correlated equilibria. In the first step, we estimate the conditional choice probabilities by which each possible outcome is realized. In the second step, we obtain the bounds on estimates of the parameters by minimizing the average distance between the set of correlated equilibria and the probability distribution that we obtained in the first step. Compared to previous approaches through which the issue of multiple equilibria has been tackled, our method has two important advantages. First, it explicitly takes into account the existence of mixed strategy equilibria. Second, it is computationally easy to implement: due to the inherent linearity of correlated equilibria, we can obtain the bounds estimates by solving a series of linear programming problems.

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File URL: https://mpra.ub.uni-muenchen.de/79395/1/MPRA_paper_79395.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 79395.

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Date of creation: 2006
Handle: RePEc:pra:mprapa:79395
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  1. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
  2. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
  3. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  4. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
  5. Timothy F. Bresnahan & Peter C. Reiss, 1990. "Entry in Monopoly Market," Review of Economic Studies, Oxford University Press, vol. 57(4), pages 531-553.
  6. Myerson, R B, 1986. "Acceptable and Predominant Correlated Equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 133-154.
  7. Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters,in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14 World Scientific Publishing Co. Pte. Ltd..
  8. Daniel A. Ackerberg & Gautam Gowrisankaran, 2006. "Quantifying equilibrium network externalities in the ACH banking industry," RAND Journal of Economics, RAND Corporation, vol. 37(3), pages 738-761, September.
  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.
  10. Michael J. Mazzeo, 2002. "Product Choice and Oligopoly Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 33(2), pages 221-242, Summer.
  11. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
  12. repec:rje:randje:v:37:y:2006:3:p:738-761 is not listed on IDEAS
  13. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics,in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier.
  14. Reiss, Peter C, 1996. "Empirical Models of Discrete Strategic Choices," American Economic Review, American Economic Association, vol. 86(2), pages 421-426, May.
  15. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
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