Incomplete Stable Structures in Symmetric Convex Games

CentER Working Paper No. 2000-97

37 Pages Posted: 3 Dec 2000

See all articles by Marco Slikker

Marco Slikker

Eindhoven University of Technology (TUE) - School of Industrial Engineering

Henk Norde

Tilburg University - Center For Economic Research; Tilburg University - Department of Econometrics & Operations Research

Date Written: October 2000

Abstract

We study the model of link formation that was introduced by Aumann and Myerson (1988) and focus on symmetric convex games with transferable utilities. We show that with at most five players the full cooperation structure results according to a subgame perfect Nash equilibrium. Moreover, if the game is strictly convex then every subgame perfect Nash equilibrium results in a structure that is payoff equivalent to the full cooperation structure. Subsequently, we analyze a game with six players that is symmetric and strictly convex. We show that there exists a subgame Nash equilibrium that results in an incomplete structure in which two players are worse off than in the full cooperation structure, whereas four players are better off. Independent of the initial order any pair of players can end up being exploited.

Keywords : symmetric convex game, undirected graph, link formation, incomplete stable structure

JEL Classification: C71, C72

Suggested Citation

Slikker, Marco and Norde, Henk W., Incomplete Stable Structures in Symmetric Convex Games (October 2000). CentER Working Paper No. 2000-97, Available at SSRN: https://ssrn.com/abstract=249029 or http://dx.doi.org/10.2139/ssrn.249029

Marco Slikker

Eindhoven University of Technology (TUE) - School of Industrial Engineering ( email )

P.O. Box 513
5600 MB Eindhoven
Netherlands

Henk W. Norde (Contact Author)

Tilburg University - Center For Economic Research ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 3245 (Phone)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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