Accessible outcomes versus absorbing outcomes

Kóczy and Lauwers, 2004 and Kóczy and Lauwers, 2007 show that the collection of absorbing outcomes, i.e., the coalition structure core, of a TU game, if non-empty, is a minimal dominant set. The paper complements the result in two respects. First, it is shown that the coalition structure core, if non-empty, can be reached from any outcome via a sequence of successive blocks in quadratic time. Second, we observe that an analogous result holds for accessible outcomes, namely, the collection of accessible outcomes, if non-empty, is a minimal dominant set. Moreover, we give an existence theorem for accessible outcomes, which implies that the minimal dominant set of a cohesive game is exactly the coalition structure core or the collection of accessible outcomes, either of which can be reached from any outcome in linear time.

► The coalition structure core can be reached from any outcome in quadratic time. ► The set of accessible outcomes, if non-empty, is a minimal dominant set. ► A cohesive game possesses an absorbing outcome or an accessible outcome. ► The minimal dominant set of a cohesive game can be reached in linear time.