We adopt the largest consistent set defined by Chwe [J. of Econ. Theory 63 (1994), 299-235] to predict which coalition …, based on the assumption that players are cautious. For games with positive spillovers, many coalition structures may belong … to the largest consistent set. The grand coalition, which is the efficient coalition structure, always belongs to the …

sets: a set of matchings is a vNM farsightedly stable set if and only if it is a singleton subset of the core. Thus … cannot include matchings that are not in the core. Moreover, we show that our main result is robust to many-to-one matching … set and its element is in the strong core. …

A set of coalition structures P is farsightedly stable (i) if all possible deviations from any coalition structure p … belonging to P to a coalition structure outside P are deterred by the threat of ending worse off or equally well off, (ii) if … there exists a farsighted improvingpath from any coalition structure outside the set leading to some coalition structure in …