Equilibrium in abstract economies without ordered preferences

We extend a theorem of G. Debreu on the existence of equilibrium in a generalized N-person game (‘A Social Equilibrium Existence Theorem’). Applying standard techniques the result can be used to prove the existence of equilibrium in economies with interdependent preferences, price-dependent preferences and preferences which may be both non-transitive and non-complete. This generalizes a recent theorem of A. Mas-Colell.