Article ID: | iaor20032942 |
Country: | United States |
Volume: | 20 |
Issue: | 1 |
Start Page Number: | 197 |
End Page Number: | 212 |
Publication Date: | Feb 1995 |
Journal: | Mathematics of Operations Research |
Authors: | Gilboa I., Schmeidler D. |
The representation of a cooperative transferable utility game as a linear combination of unanimity games may be viewed as an isomorphism between not-necessarily additive set functions on the players space and additive ones on the coalitions space. (Or, alternatively, between nonadditive probability measures on a state space and additive ones on the space of events.) We extend the unanimity-basis representation to general (infinite) spaces of players, study spaces of games which satisfy certain properties and provide some conditions for sigma-additivity of the resulting additive set function (on the space of coalitions). These results also allow us to extend some representations of the Choquet integral from finite to infinite spaces.