Incomplete stable structures in symmetric convex games
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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- Feinberg, Yossi, 1998. "An Incomplete Cooperation Structure for a Voting Game Can Be Strategically Stable," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 2-9, July.
- Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
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