# Payoff-dependent balancedness and cores (revised version)

Working paper

Publisher:

Elsevier

Year:

2007

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoﬀ-dependent balancedness, based on transfer rate mappings. We also deﬁne a new equilibrium condition on transfer rates and we prove the existence of core payoﬀ vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parametrized cooperative games is introduced. this new setting and its associated equilibrium-core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium-core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to results taken from game theory and economic theory are given.