Subadditive and Homogeneous of Degree One Games Are Totally Balanced

A cooperative game with transferable utility is said to be homogeneous of degree one if for any integer m, the value of cloning m times all players at any given coalition, leads to m times the value of the original coalition. We show that this property coupled with sub-additivity, guarantee the non-emptyness of the core of the game and of all its subgames, namely the game is totally balanced. Examples for games stemming from the areas of retailing, and facility location are given. Subject classifications: Games/Group decisions: cooperative. Are of review: games, information and networks. ∗Faculty of Management, Tel Aviv University, Tel Aviv 69978, Israel. E-mail: [email protected] †Department of Statistics and the Center for the Study of Rationality, Hebrew University of Jerusalem, 91905 Jerusalem, Israel. E-mail: [email protected].