Linear values for interior operator games

Interior operator games were introduced by Bilbao et al. (2005) as additive games restricted by antimatroids. In that paper several interesting cooperative games were shown as examples of interior operator games. The antimatroid is a known combinatorial structure which represents, in the game theory context, a dependence system among the players. The aim of this paper is to study a family of values which are linear functions and satisfy reasonable conditions for interior operator games. Two classes of these values are considered assuming particular properties.

► We define the family of linear values for interior operator games. ► We describe the linear values as a convex set of linear functions. ► Linear values obtaining core solutions are described. ► Random-order linear values are studied. ► The centers of all these families are calculated.