Split equilibrium problems for related games and applications to economic theory

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.

KEYWORDS:

• Fan-KKM theorem
• split Nash equilibrium problem
• convexity direction
• preserved mapping
• extended Bertrand duopoly model of price competition

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 49J40
• 49J52
• 91A10
• 91A25
• 91A80

Acknowledgements

The author is very grateful to Professor Christiane Tammer for her valuable communications and suggestions that have improved the presentation of this paper. The author thanks the anonymous reviewers for their suggestions and corrections.

Disclosure statement

No potential conflict of interest was reported by the author.