Abstract
The aim of this study is to identify and characterize the parts of an extensive form game that are “relevant” to determining whether the outcome of a certain strategy profile is an equilibrium outcome. We formally define what we mean by “relevant” and refer to the associated collection of information sets as essential. We apply this idea to a number of classic equilibrium concepts and discuss some implications of our approach.
Similar content being viewed by others
References
Fudenberg D, Tirole J (1991a) Game theory. MIT Press, Cambridge
Fudenberg D, Tirole J (1991b) Perfect Bayesian equilibrium and sequential equilibrium. J Econ Theory 53: 236–260
García-Jurado I, González-Díaz J (2006) The role of commitment in repeated games. Optimization 55: 541–553
Groenert V (2009) Trimmed equilibrium, Mimeo
Kalai E (2005) Partially-specified large games. Lect Notes Comp Sci 3828: 3–13
Kalai E (2006) Structural Robustness of Large Games. Tech. rep., CMS-EMS Discussion Paper 1431. Kellogg School of Management, Evanston
Kleppe J, Hendrickx R, Borm P, García-Jurado I, Fiestras-Janeiro G (2010) Transfers, contracts and strategic games. TOP 18: 481–492
Kreps DM, Wilson R (1982) Sequential equilibria. Econometrica 50: 863–894
Kuhn HW (1953) Extensive games and the problem of information. In: Kuhn H, Tucker A (eds) Contributions to the theory of games II. Princeton University Press, Princeton
Osborne MJ (1993) Candidate positioning and entry in a political competition. Games Econ Behav 5(1): 133–151
Selten R (1975) Reexamination of the perfectness concept for equilibrium points in extensive games. Int J Game Theory 4: 25–55
Wen-Tsun W, Jia-He J (1962) Essential equilibrium points of n-person non-cooperative games. Scientia Sinica 11: 1307–1322
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
González-Díaz, J., Briata, F., García-Jurado, I. et al. Essential collections for equilibrium concepts. Int J Game Theory 41, 517–552 (2012). https://doi.org/10.1007/s00182-011-0301-y
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00182-011-0301-y