Payoffs-dependent Balancedness and Cores

We provide a result for non-emptiness of the core in NTU games. We use a payoffs-dependent balancedness condition, based on transfer rate mappings. Going beyond the non-emptiness of standard core, existence of some refined solution is proved, including specific core allocations and equilibrium-core allocations in parameterized collection of cooperative games. The proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to various extant results taken from game theory and economic theory are given.