Superadditive Market Games

ABSTRACT We study a class of cooperative games, referred to as superadditive market games (SMG). Each SMG is characterized by a set of players, an initial endowment distribution, and a common production function that is superadditive (and meets certain regularity conditions). Due to superadditivity, players may desire to cooperate by pooling their endowments to jointly produce. We investigate kind production functions, namely production functions whose derived SMGs always have nonempty cores, regardless of initial endowment distributions. We show that a production function is kind if and only if its Walrasian core (the set of Walrasian equilibrium price vectors of a properly defined exchange economy) is always nonempty. We prove that a concave production function is kind if and only if it is homogeneous, and a convex production function is kind if and only if it satisfies a property that resembles the balancedness condition for classical cooperative games. Applying our results to newsvendor games, linear production games, and EOQ games easily reproduces several well‐known results and also generates some new results.