Incomplete Stable Structures in Symmetric Convex Games
AbstractWe 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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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2000-97.
Date of creation: 2000
Date of revision:
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Web page: http://center.uvt.nl
symmetric convex game; undirected graph; link formation; incomplete stable structure;
Other versions of this item:
- Slikker, Marco & Norde, Henk, 2004. "Incomplete stable structures in symmetric convex games," Games and Economic Behavior, Elsevier, vol. 48(1), pages 171-200, July.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
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- Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154855, Tilburg University.
- Roger B. Myerson, 1976. "Graphs and Cooperation in Games," Discussion Papers 246, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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., 1990. "On game theoretic models and solution concepts," Open Access publications from Tilburg University urn:nbn:nl:ui:12-155350, Tilburg University.
- Slikker, M. & Norde, H.W., 2004. "Symmetric Convex Games and Stable Structures," Discussion Paper 2004-114, Tilburg University, Center for Economic Research.
- Slikker, Marco & Gilles, Robert P. & Norde, Henk & Tijs, Stef, 2005. "Directed networks, allocation properties and hierarchy formation," Mathematical Social Sciences, Elsevier, vol. 49(1), pages 55-80, January.
- Slikker, M. & Gilles, R.P. & Norde, H.W. & Tijs, S.H., 2000. "Directed Communication Networks," Discussion Paper 2000-84, Tilburg University, Center for Economic Research.
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