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Split Equilibrium Problems for Related Games and Applications to Economic Theory

Author

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  • Jinlu Li

    (Department of Mathematics, Shawnee State University, Portsmouth, OH 45662, USA)

Abstract

In this paper we introduce the concept of split Nash equilibrium problems associated with two related noncooperative strategic games. Then we apply the Fan–KKM theorem to prove the existence of solutions to split Nash equilibrium problems of related noncooperative strategic games, in which the strategy sets of the players are nonempty closed and convex subsets in Banach spaces. As an application of this existence to economics, an example is provided that studies the existence of split Nash equilibrium of utilities of two related economies. As applications, we study the existence of split Nash equilibrium in the dual (playing twice) extended Bertrand duopoly model of price competition.

Suggested Citation

  • Jinlu Li, 2018. "Split Equilibrium Problems for Related Games and Applications to Economic Theory," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-20, December.
    • Handle: RePEc:wsi:igtrxx:v:20:y:2018:i:04:n:s0219198918500056
    DOI: 10.1142/S0219198918500056
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