Characterization of dominance relations in finite coalitional games
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McGarvey (Econometrica, 21(4), 608–610, 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.
KeywordsCooperative game theory Non-transferable utility Dominance
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