Existence of equilibrium in abstract economies with discontinuous payoffs and non - compact choice spaces *

This paper proves the equilibrium existence for abstract economies with non-compact infinitedimensional strategy spaces, infinitely many agents, and discontinuous payolT (utility) functions by using the quasi-variational inequality approach. The motivations come from economic applications showing that payoff functions are discontinuous in many cases and the set of feasible allocations generally is not compact in a given topology of the commodity space, a typical situation in infinite dimensional vector space. It will be noted that our results also extend a foundational quasi-variational inequality by relaxing the compactness and concavity conditions. Thus many existence theorems in the quasi-variational inequalities literature can also be generalized by our results.