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In this paper we introduce the concept of split Nash equilibrium problemsassociated with two related noncooperative strategic games. Then we apply theFan-KKM theorem to prove the existence of solutions to split Nash equilibriumproblems of related noncooperative strategic games, in which the strategy setsof the players are nonempty closed and convex subsets in Banach spaces. Asapplication of this existence to economics, an example is provided to study theexistence of split Nash equilibrium of utilities of two related economies. Asapplications, we study the existence of split Nash equilibrium in the dualextended Bertrant duopoly model of price competition

Split Nash Equilibria for Related Games and Applications to Economics