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Rational Expectations and Farsighted Stability

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  • Dutta, Bhaskar

    (University of Warwick)

  • Vohra, Rajiv

    (Brown University)

Abstract

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.

Suggested Citation

  • Dutta, Bhaskar & Vohra, Rajiv, 2015. "Rational Expectations and Farsighted Stability," CRETA Online Discussion Paper Series 05, Centre for Research in Economic Theory and its Applications CRETA.
  • Handle: RePEc:wrk:wcreta:05
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    File URL: https://warwick.ac.uk/fac/soc/economics/research/centres/creta/papers/manage/creta05a-bhaskar_dutta.pdf
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    References listed on IDEAS

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    1. Ana Mauleon & Vincent Vannetelbosch, 2004. "Farsightedness and Cautiousness in Coalition Formation Games with Positive Spillovers," Theory and Decision, Springer, pages 291-324.
    2. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954.
    3. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, pages 1472-1495.
    4. Vannetelbosch, Vincent J. & Mauleon, Ana & Vergote, Wouter, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society.
    5. Ana Mauleon & Vincent Vannetelbosch, 2004. "Farsightedness and Cautiousness in Coalition Formation Games with Positive Spillovers," Theory and Decision, Springer, pages 291-324.
    6. 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.
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    1. repec:eee:ecolet:v:156:y:2017:i:c:p:42-47 is not listed on IDEAS

    More about this item

    Keywords

    stable sets ; farsightedness ; consistency ; maximality ; rational expectations ; simple games ; pillage games. JEL Classification Numbers: C71 ; D72 ; D74;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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