Essential collections for equilibrium concepts. (English) Zbl 1259.91023
Summary: 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.
Keywords:
extensive games; equilibrium concepts; relevant information sets; essential collections; reduced game; virtual equilibriumReferences:
| [1] | Fudenberg D, Tirole J (1991a) Game theory. MIT Press, Cambridge · Zbl 0596.90015 |
| [2] | Fudenberg D, Tirole J (1991b) Perfect Bayesian equilibrium and sequential equilibrium. J Econ Theory 53: 236–260 · Zbl 0717.90108 · doi:10.1016/0022-0531(91)90155-W |
| [3] | García-Jurado I, González-Díaz J (2006) The role of commitment in repeated games. Optimization 55: 541–553 · Zbl 1156.91318 · doi:10.1080/02331930600815991 |
| [4] | Groenert V (2009) Trimmed equilibrium, Mimeo |
| [5] | Kalai E (2005) Partially-specified large games. Lect Notes Comp Sci 3828: 3–13 · doi:10.1007/11600930_2 |
| [6] | Kalai E (2006) Structural Robustness of Large Games. Tech. rep., CMS-EMS Discussion Paper 1431. Kellogg School of Management, Evanston |
| [7] | Kleppe J, Hendrickx R, Borm P, García-Jurado I, Fiestras-Janeiro G (2010) Transfers, contracts and strategic games. TOP 18: 481–492 · Zbl 1233.91010 · doi:10.1007/s11750-009-0074-7 |
| [8] | Kreps DM, Wilson R (1982) Sequential equilibria. Econometrica 50: 863–894 · Zbl 0483.90092 · doi:10.2307/1912767 |
| [9] | 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 · Zbl 0050.14303 |
| [10] | Osborne MJ (1993) Candidate positioning and entry in a political competition. Games Econ Behav 5(1): 133–151 · Zbl 0825.90825 · doi:10.1006/game.1993.1007 |
| [11] | Selten R (1975) Reexamination of the perfectness concept for equilibrium points in extensive games. Int J Game Theory 4: 25–55 · Zbl 0312.90072 · doi:10.1007/BF01766400 |
| [12] | Wen-Tsun W, Jia-He J (1962) Essential equilibrium points of n-person non-cooperative games. Scientia Sinica 11: 1307–1322 · Zbl 0141.36103 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
