Economic Theory

, Volume 42, Issue 1, pp 255–269 | Cite as

Computing sequential equilibria using agent quantal response equilibria

Symposium

Abstract

The limit of any convergent sequence of agent quantal response equilibria is a sequential equilibrium of an extensive game. Using a logarithmic transformation of action probabilities, it is numerically feasible and practical to compute such sequences, and thereby compute good approximations to sequential equilibrium assessments. This paper describes the algorithm to compute the sequences, and outlines the convergence and selection properties of the method.

Keywords

Computing Nash equilibrium Quantal response Homotopy methods 

JEL Classification

C63 C72 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allgower E.L., Georg K.: Numerical Continuation Methods: An Introduction. Springer, Berlin (1990)Google Scholar
  2. Banks J., Camerer C., Porter D.: Experimental tests of Nash refinements in signaling games. Games Econ Behav 4, 1–31 (1992)CrossRefGoogle Scholar
  3. Brandts J., Holt C.A.: Adjustment patterns and equilibrium selection in experimental signaling games. Int J Game Theory 22, 279–302 (1993)CrossRefGoogle Scholar
  4. Koller D., Megiddo N., von Stengel B.: Efficient computation of equilibria for extensive two-person games. Games Econ Behav 14, 247–259 (1996)CrossRefGoogle Scholar
  5. Kreps D., Wilson R.: Sequential equilibrium. Econometrica 50, 863–894 (1982)CrossRefGoogle Scholar
  6. McKelvey, R.D.: A Liapunov function for Nash equilibria. Caltech Social Science Working Paper 953 (1991)Google Scholar
  7. McKelvey R.D., Palfrey T.R.: An experimental study of the cenitpede game. Econometrica 60, 803–836 (1992)CrossRefGoogle Scholar
  8. McKelvey R.D., Palfrey T.R.: Quantal response equilibria for normal form games. Games Econ Behav 10, 6–38 (1995)CrossRefGoogle Scholar
  9. McKelvey R.D., Palfrey T.R.: Quantal response equilibria for extensive form games. Exp Econ 1, 9–41 (1998)Google Scholar
  10. McKelvey R.D., McLennan, A.M., Turocy, T.L.: Gambit: Software Tools for Game Theory (2008). http://gambit.sourceforge.net
  11. Miltersen, P.B., Sorensen, T.B.: Computing a quasi-perfect equilibrium of a two-player game. Econ Theory, this issue (2009)Google Scholar
  12. Selten R.: Reexamination of the perfectness concept for equilibrium points in extensive games. Int J Game Theory 4, 25–55 (1975)CrossRefGoogle Scholar
  13. Turocy T.L.: A dynamic homotopy interpretation of the logistic quantal response equilibrium correspondence. Games Econ Behav 51, 243–263 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of EconomicsTexas A&M UniversityCollege StationUSA

Personalised recommendations