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Incomplete Stable Structures in Symmetric Convex Games
Slikker,M. Norde,H.W.
Slikker,M.
Norde,H.W.
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.
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Pagination: 37
Date
2000
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Publisher
Operations research
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Keywords
symmetric convex game, undirected graph, link formation, incomplete stable structure, C71 - Cooperative Games, C72 - Noncooperative Games
Citation
Slikker, M & Norde, H W 2000 'Incomplete Stable Structures in Symmetric Convex Games' CentER Discussion Paper, vol. 2000-97, Operations research, Tilburg.