A GENERALIZED F-CONTRACTION MAPPING FOR COUPLED FIXED POINT THEOREMS AND AN APPLICATION TO A TWO-PERSON GAME

To relate the existence of equilibria to the existence of fixed points is the main aim of this paper. Game theory is to study a situation under some conflict among certain agents (or players). Each one seeks for their own minimum loss in such situation. Moreover, game can be divided into two main broad categories characterized as cooperative or non-cooperative manner. In other words, cooperative game allows agents to collaborate, but non-cooperative does not. Due to the equivalence of the existence of a solution of a non-cooperative equilibrium and a couple fixed point, the existence problem of the non-cooperative equilibrium of two person games is clarified by applying some coupled fixed point theorems in partial metric spaces. © 2022 Journal of Nonlinear Functional Analysis