Equilibrium Points in Games with Ordered Outcomes

A general method for a description of equilibrium points in games with ordered outcomes is proposed. This method is based on a construction of complete family of homomorphisms from a given game with ordered outcomes into games with payoff functions. Using this method, we obtain a description of the set of equilibrium points and Nash equilibrium points for mixed extension of game with vector payoffs. The main result is a finding of equilibrium points in mixed extension of a finite game with ordered outcomes.