Stationary consistent equilibrium coalition structures constitute the recursive core

Kóczy, Á. László (2015) Stationary consistent equilibrium coalition structures constitute the recursive core. JOURNAL OF MATHEMATICAL ECONOMICS, 61. pp. 104-110. ISSN 0304-4068

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Abstract

We study coalitional games where the coalitional payoffs depend on the embedding coalition structure. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core, a generalisation of the core to such games. In order to extend past results limited to totally recursive-balanced partition function form games we introduce a more permissive perfectness concept, subgame-consistency that only requires perfectness in selected subgames. Due to the externalities, the profitability of deviations depends on the partition formed by the remaining players: the stability of core payoff configurations is ensured by a combination of the pessimism of players going for certain profits only and the assumption that players base their stationary strategies on a made-up history punishing some of the possible deviators—and getting this sometimes right.

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