Accessible outcomes versus absorbing outcomes

• Published in: Mathematical social sciences Vol. 62; no. 1; pp. 65 - 70
• Main Author: Yang, Yi-You
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2011; Elsevier
• Series: Mathematical Social Sciences
• Subjects: Coalitions; Game theory; Pay-off; Utility functions
• ISSN: 0165-4896; 1879-3118
• DOI: 10.1016/j.mathsocsci.2011.04.008

Kóczy and Lauwers (2004, 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.