Complete Sequential Equilibrium and Its Alternative

Jung, Hanjoon Michael (2009): Complete Sequential Equilibrium and Its Alternative. Unpublished.

Abstract

We propose a complete version of the sequential equilibrium (CSE) and its alternative solution concept (WCSE) for general finite-period games with observed actions. The sequential equilibrium (SE) is not a complete solution concept in that it might not be a Nash equilibrium in the general games that allow a continuum of types and strategies. The CSE is always a Nash equilibrium and is equivalent to the SE in finite games. So, the CSE is a complete solution concept in the general games as a version of the SE. The WCSE is a weak, but simple version of the CSE. It is also a complete solution concept and functions as an alternative solution concept to the CSE. Their relation with converted versions of the perfect equilibrium and the perfect Bayesian equilibrium are discussed

• Item Type: MPRA Paper
• Language: English
• Keywords: Complete Belief, Complete Sequential Equilibirum, Finite-period game, Solution Concept, Sequential Convergency, Sequential Equilibrium.
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

1.Ash, Robert B. (1972): "Real Analysis and Probability," Academic Press, New York.

2.Balder, Erik J. (1988): "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, 13, 265--276.

3.Billingsley, Patrick (1968): "Convergence of Probability Measures," Wiley, New York.

4.Crawford, Vincent P. and Sobel, Joel (1982): "Strategic Information Transmission," Econometrica, 50, 1431--1451.

5.Fudenberg, Drew and Tirole, Jean (1991a): "Perfect Bayesian Equilibrium and Sequential Equilibrium," Journal of Economic Theory, 53, 236--260.

6.Fudenberg, Drew and Tirole, Jean (1991b): "Game Theory," MIT Press, Massachusetts.

7.Harsanyi, John C. (1967--68): "Games with Incomplete Information Played by Bayesian Players," Part I--III, Management Science, 14, 159--182, 320--334, and 486--502.

8.Neveu, J. (1965): "Mathematical Foundations of the Calculus of Probability," Holden-Day, San Francisco.

9.Kreps, David M. and Wilson, Robert (1982): "Sequential Equilibria," Econometrica, 50, 863--894.

10.Kuhn, Harold W. (1950): "Extensive Games," Proceedings National Academy Sciences U.S.A., 36, 570--576.

11.Milgrom, Paul R. and Weber, Robert J. (1985): "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, 10, 619--632.

12.Myerson, Roger B. (1991): "Game Theory," Harvard University Press, Massachusetts.

13.Nash, John (1951): "Non-Cooperative Games," Annals of Mathematics, 54, 286--295.

14.Selten, R. (1975): "Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games," International Journal of Game Theory, 4, 25--55.

15.Uglanov, A. V. (1997): "Four Counterexamples to the Fubini Theorem," Mathematical Notes, 62, 104--107.