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 was recently reformulated 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. Consequently, when there are multiple continuation paths, the farsighted stable set can yield unreasonable predictions. We restrict coalitions to hold common, history independent expectations that incorporate maximality regarding the continuation path. This leads to two related solution concepts: the rational expectations farsighted stable set and the strong rational expectations farsighted stable set. We apply these concepts to simple games and to pillage games to illustrate the consequences of imposing rational expectations for farsighted stability.