Characterization of dominance relations in finite coalitional games

Journal article

McGarvey (1953) has shown that any irreflexive and anti-symmetric relation can be obtained as a relation induced by majority rule. We address the analogous issue for dominance relations of finite cooperative games with non-transferable utility (coalitional NTU games). We find any irreflexive relation over a finite set can be obtained as the dominance relation of some finite coalitional NTU game. We also show that any such dominance relation is induced by a non-cooperative game through β-effectivity. Dominance relations obtainable through α-effectivity, however, have to comply with a more restrictive condition, which we refer to as the edge-mapping property.

Authors: Brandt, F; Harrenstein, B

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Theory and Decision
• Volume: 69
• Issue: 2
• Pages: 233-256
• Publication date: 2010-08-01
• DOI: 10.1007/s11238-009-9167-x
• EISSN: 1573-7187
• ISSN: 0040-5833
• Keywords: Dominance; Cooperative Game Theory; Non-Transferable Utility