Abstract
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.
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Brandt, F., Harrenstein, P. Characterization of dominance relations in finite coalitional games. Theory Decis 69, 233–256 (2010). https://doi.org/10.1007/s11238-009-9167-x
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DOI: https://doi.org/10.1007/s11238-009-9167-x