Cooperative games with additive multiple attributes

Abstract

This paper studies cooperative games in which players have multiple attributes. Such games are applicable to situations in which each player has a finite number of independent additive attributes in cooperative games and the payoffs of coalitions are endogenous functions of these attributes. The additive attributes cooperative game, which is a special case of the multiattribute cooperative game, is studied with respect to the core, the conditions for existence and boundedness and methods of transformation regarding a general cooperative game. A coalitional polynomial form is also proposed to discuss the structure of coalition. Moreover, a Shapley-like solution called the efficient resource (ER) solution for additive attributes cooperative games is studied via the axiomatical method, and the ER solution of two additive attribute games with equivalent total resources coincides with the Shapley value. Finally, some examples of additive attribute games are given.