Equivalence between the Existence Theorems on Nash Equilibrium, Core and Hybrid Equilibrium *

Summary: This paper provides the equivalence between the existence theorems on Nash equilibrium, core, and hybrid equilibrium. It completes the equivalence by show ing that Scarf’s core theorem implies Kakutani’s fixed point theorem. Such equivalence leaves with us a long list of open problems for future research, one of which is to derive Kakutani’s fixed point theorem (1941) directly from Nash’s theorem (1951).