Coalition formation and history dependence

Farsighted formulations of coalitional formation, for instance by Harsanyi (1974) and Ray and Vohra (2015), have typically been based on the von Neumann-Morgenstern (1944) stable set. These farsighted stable sets use 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. Dutta and Vohra (2017) point out that these solution concepts do not require coalitions to make optimal moves. Hence, these solution concepts can yield unreasonable predictions. Dutta and Vohra (2017) restricted coalitions to hold common, history independent expectations that incorporate optimality regarding the continuation path. This paper extends the Dutta-Vohra analysis by allowing for history dependent expectations. The paper provides characterization results for two solution concepts corresponding to two versions of optimality. It demonstrates the power of history dependence by establishing non-emptyness results for all finite games as well as transferable utility partition function games. The paper also provides partial comparisons of the solution concepts to other solutions.