Rational Expectations and Farsighted Stability
In the study of farsighted coalitional behavior, a central role is played by the von Neumann-Morgenstern (1944) stable set and its modification that incorporates farsightedness. Such a modification was first proposed by Harsanyi (1974) and has recently been re-formulated by Ray and Vohra (2015). The farsighted stable set is based on a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional ‘moves’ in which each coalition that is involved in the sequence eventually stands to gain. However, it does not require that each coalition make a maximal move, i.e., one that is not Pareto dominated (for the members of the coalition in question) by another. Nor does it restrict coalitions to hold common expectations regarding the continuation path from every state. Consequently, when there are multiple continuation paths the farsighted stable set can yield unreasonable predictions. We resolve this difficulty by requiring all coalitions to have common rational expectations about the transition from one outcome to another. This leads to two related concepts: the rational expectations farsighted stable set (REFS) and the strong rational expectations farsighted stable set (SREFS). We apply these concepts to simple games and to pillage games to illustrate the consequences of imposing rational expectations for farsighted stability.
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- Ana Mauleon & Vincent Vannetelbosch, 2004.
"Farsightedness and Cautiousness in Coalition Formation Games with Positive Spillovers,"
Theory and Decision,
Springer, vol. 56(3), pages 291-324, 05.
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- Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954.
- John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
- Vannetelbosch, Vincent J. & Mauleon, Ana & Vergote, Wouter, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
- MAULEON, Ana & VANNETELBOSCH, Vincent J. & VERGOTE, Wouter, "undated". "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," CORE Discussion Papers RP 2337, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- MAULEON, Ana & VANNETELBOSCH, Vincent & VERGOTE, Wouter, 2008. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," CORE Discussion Papers 2008016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Vincent Vannetelbosch & Ana Mauleon & Wouter Vergote, 2008. "Von Neumann-Morgenstern Farsightedly Stable Sets in Two-Sided Matching," Working Papers 2008.29, Fondazione Eni Enrico Mattei.
- Ana, MAULEON & Vincent, VANNETELBOSCH & Wouter, VERGOTE, 2008. "Von Neuman-Morgenstern farsightedly stable sets in two-sided matching," Discussion Papers (ECON - Département des Sciences Economiques) 2008013, Université catholique de Louvain, Département des Sciences Economiques.
- Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May. Full references (including those not matched with items on IDEAS)
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