A Solution to the Non-Cooperative Equilibrium Problem for Two and Three Players Using the Fixed-Point Technique

The aims of this paper are (a) to introduce the concept of the 0-complete m-metric spaces, (b) to obtain the results for (Formula presented.) -Caristi mapping using Kirk’s approach, (c) to investigate the problem of non-cooperative equilibrium (abbreviated as NCE) in two- and three-person games in the structure of game theory and find the solution by employing coupled and tripled fixed-point results within the framework of 0-complete m-metric spaces (m-metric spaces, respectively), and (d) to establish some coupled fixed-point results which extend the scope of metric fixed point theory. We provide some examples to support the concepts and results presented in this paper. As an application of our results in this paper, we obtain the existence of a solution for a nonlinear integral equation.