Coalitional stability with a credibility constraint

Following Chwe (1994) we introduce a similar notion of coalitional stability for proper simple games with the additional desirable property that a coalition moves to an outcome stable with respect to this notion only when the outcome is not dominated by another stable outcome. We call a set of outcomes stable with respect to this notion a credibly consistent set. We examine the issue of the existence and non-emptiness of such sets and investigate their relation to some other solution concepts prevalent in the literature concerning coalitional stability.