Theory and Decision

, Volume 69, Issue 2, pp 233–256 | Cite as

Characterization of dominance relations in finite coalitional games

  • Felix Brandt
  • Paul Harrenstein


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.


Cooperative game theory Non-transferable utility Dominance 


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Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.Ludwig-Maximilians-Universität MünchenMünchenGermany

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