Coalition Formation among Farsighted Agents
2. Coalition Formation
3. Farsightedly Stable Sets of Coalition Structures
- ∀ , ∀ such that is obtainable from p via , such that we do not have for all and for some .
- ∄ such that satisfies Conditions (i) and (ii).
4. Coalition Formation with Positive Spillovers
- Hart, S.; Kurz, M. Endogenous formation of coalitions. Econometrica 1983, 51, 1047–1064. [Google Scholar] [CrossRef]
- Chwe, M.S. Farsighted coalitional stability. J. Econ. Theory 1994, 63, 299–325. [Google Scholar] [CrossRef]
- Xue, L. Coalitional stability under perfect foresight. Econ. Theory 1998, 11, 603–627. [Google Scholar] [CrossRef]
- Barbera, S.; Gerber, A. On coalition formation: Durable coalition structures. Math. Soc. Sciences 2003, 45, 185–203. [Google Scholar] [CrossRef]
- Mariotti, M. A model of agreements in strategic form games. J. Econ. Theory 1997, 74, 196–217. [Google Scholar] [CrossRef]
- Bloch, F. Sequential formation of coalitions in games with externalities and fixed payoff division. Games Econ. Behav. 1996, 14, 90–123. [Google Scholar] [CrossRef]
- Ray, D.; Vohra, R. A Theory of endogenous coalition structures. Games Econ. Behav. 1999, 26, 286–336. [Google Scholar] [CrossRef]
- Konishi, H.; Ray, D. Coalition formation as a dynamic process. J. Econ. Theory 2003, 110, 1–41. [Google Scholar] [CrossRef][Green Version]
- Herings, P.J.J.; Mauleon, A.; Vannetelbosch, V. Rationalizability for social environments. Games Econ. Behav. 2004, 49, 135–156. [Google Scholar] [CrossRef]
- Herings, P.J.J.; Mauleon, A.; Vannetelbosch, V. Farsightedly stable networks. Games Econ. Behav. 2009, 67, 526–541. [Google Scholar] [CrossRef]
- Hafalir, I.E. Efficiency in coalition games with externalities. Games Econ. Behav. 2007, 61, 242–258. [Google Scholar] [CrossRef]
- Von Neumann, J.; Morgenstern, O. Theory of Games and Economic Behavior; Princeton University Press: Princeton, NJ, USA, 1944. [Google Scholar]
- Diamantoudi, E.; Xue, L. Farsighted stability in hedonic games. Soc. Choice Welfare 2003, 21, 39–61. [Google Scholar] [CrossRef]
- Mauleon, A.; Vannetelbosch, V. Farsightedness and cautiousness in coalition formation games with positive spillovers. Theory Decis. 2004, 56, 291–324. [Google Scholar] [CrossRef]
- Page, F.H., Jr.; Wooders, M. Strategic basins of attraction, the path dominance core, and network formation games. Games Econ. Behav. 2009, 66, 462–487. [Google Scholar] [CrossRef]
- Page, F.H., Jr.; Wooders, M. Networks and clubs. J. Econ. Behav. Organ. 2007, 64, 406–425. [Google Scholar] [CrossRef]
- Jackson, M.O.; van den Nouweland, A. Strongly stable networks. Games Econ. Behav. 2005, 51, 420–444. [Google Scholar] [CrossRef]
- Bogomolnaia, A.; Jackson, M.O. The stability of hedonic coalition structures. Games Econ. Behav. 2002, 38, 201–230. [Google Scholar] [CrossRef]
- Bloch, F. Non-cooperative models of coalition formation in games with spillovers. In New Directions in the Economic Theory of the Environment; Carraro, C., Siniscalco, D., Eds.; Cambridge University Press: Cambridge, UK, 1997; pp. 311–352. [Google Scholar]
- Yi, S.S. Stable coalition structures with externalities. Games Econ. Behav. 1997, 20, 201–237. [Google Scholar] [CrossRef]
- 1.Xue  has proposed the solution concepts of optimistic or conservative stable standards of behavior. It strengthens the farsightedness notion of the largest consistent set. A farsighted individual considers only the final outcomes that might result when making choices. But, an individual with perfect foresight considers also how final outcomes can be reached. That is, possible deviations along the way to the final outcomes should be considered. Barbera and Gerber  have proposed a solution concept for hedonic coalition formation games: durability. This concept assumes some form of maxmin behavior on the part of farsighted players.
- 2.For the coalitional contingent threat situation, Mariotti  has defined an equilibrium concept: the coalitional equilibrium. Central to his concept is the notion of coalitional strategies and the similarity with subgame perfection (except that coalitions are formally treated as players).
- 3.Konishi and Ray  have studied a model of dynamic coalition formation where players evaluate the desirability of a move in terms of its consequences on the entire discounted stream of payoffs.
- 4.Myopic notions of stability make assumptions about what a deviating coalition conjectures about the reaction of the non-deviating players. Hart and Kurz’s  notion of δ-stability assumes that non-deviating players do not move, while their notion of γ-stability supposes that former partners of the deviating players form singletons after the deviation. Hafalir  has investigated other rules of behavior where deviators hold the conjecture that either non-deviating players minimize the payoff of the deviating coalition, or non-deviating players merge, or non-deviating players will take the deviation as given and try to maximize their own payoff. For farsighted notions of stability such assumptions matter less to the extent that a deviating coalition considers the possibility that, once it deviates, another coalition might react, a third coalition might in turn react, and so on without limit. The behavior of reacting coalitions is endogenous.
- 5.Page and Wooders  have introduced the notion of path dominance core. In general, the path dominance core is contained in each farsightedly stable set. Page and Wooders  have analyzed the problem of club formation as a game of network formation and have identified stable club networks if players behave farsightedly in choosing their club memberships. They have found that, if there are too few clubs so that the average number of players per club is larger than the optimal club size, then the path dominance core is empty. Unlike myopic players, farsighted players may switch their club memberships to overcrowded clubs, temporarily becoming worse off, if they believe that switching might induce other members to leave those overcrowded clubs to make them ultimately better off. Thus, a non-empty path dominance core may fail to exist while a non-empty farsightedly stable set always exists.
- 6.Jackson and van den Nouweland  have proposed the myopic notion of strong stability which is the adaptation of δ-stability for network formation models.
- 7.Bogomolnaia and Jackson  have studied the partitioning of a society into coalitions in pure hedonic games, that is, in situations where the payoff to a player depends only on the composition of members of the coalition to which she belongs. They have looked for sufficient conditions for the existence of stable partitions if players are myopic. Diamantoudi and Xue  have analyzed the stability of partitions if players are farsighted. They have shown that, if a hedonic game satisfies the top-coalition property and preferences are strict, then the largest consistent set contains only the top-coalition partition and coincides with the unique von Neumann-Morgenstern farsightedly stable set. Hence, a singleton set consisting of the top-coalition partition is a farsightedly stable set.
- 8.Ray and Vohra  have provided a justification for the assumption of an equal sharing rule. In an infinite-horizon model of coalition formation among symmetric players with endogenous bargaining, they have shown that in any equilibrium without delay there is equal sharing.
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Herings, P.J.-J.; Mauleon, A.; Vannetelbosch, V. Coalition Formation among Farsighted Agents. Games 2010, 1, 286-298. https://doi.org/10.3390/g1030286
Herings PJ-J, Mauleon A, Vannetelbosch V. Coalition Formation among Farsighted Agents. Games. 2010; 1(3):286-298. https://doi.org/10.3390/g1030286Chicago/Turabian Style
Herings, P. Jean-Jacques, Ana Mauleon, and Vincent Vannetelbosch. 2010. "Coalition Formation among Farsighted Agents" Games 1, no. 3: 286-298. https://doi.org/10.3390/g1030286