On Equilibria of Non-compact Generalized Games

A fixed point theorem is first proved from which a theorem on the existence of maximal elements for LC-majorized correspondences defined on a non-compact set is obtained. Next, an equilibrium theorem for non-compact qualitative games with LC-majorized correspondences defined on a non-compact strategy set is proved and is applied to prove an equilibrium theorem for non-compact generalized games with LC-majorized correspondences defined on a non-compact strategy set. Our results generalize several previously published corresponding results.