Full characterization of the nonnegative core of some cooperative games

We propose a method to design cost allocation contracts that help maintain the stability of strategic alliances among firms by using cooperative game theory. The partners of the alliance increase their efficiency by sharing their assets. We introduce a new sufficient condition for total balancedness of regular games, and a full characterization of their nonnegative core. A regular game is defined by a finite number of resources owned by the players. The initial cost of a player is a function of the vector of quantities of the resources that the player owns. The characteristic function value of a coalition is a symmetric real function of the vectors of its members. Within this class we focus on centralizing aggregation games, meaning that the formation of a coalition is equivalent to aggregating its players into one artificial player whose cost is an intermediate value of the costs of the aggregated players. We prove that under a certain decreasing variation condition, a centralizing aggregation game is totally balanced and its nonnegative core is fully characterized. We present a few nonconcave games in operations management that their nonnegative core is fully characterized, by showing that they satisfy the conditions presented in this article.