Existence of solution to n-person noncooperative games and minimax regret equilibria with set payoffs

Abstract

In this paper, by virtue of the Kakutani–Fan–Glicksberg fixed point theorem and a nonlinear scalarization function, we first obtain an existence theorem of general n-person noncooperative games problems with set payoffs. Then, we also obtain existence theorems of minimax regret equilibria and ϵ-minimax regret equilibria with scalar set payoffs. Some examples are given to illustrate our results.

Keywords:

• Fixed point theorem
• n-person noncooperative games
• minimax regret equilibria
• set payoffs

2010 Mathematics Subject Classification:

• 49J35

Acknowledgments

The authors are grateful to the anonymous referees for their valuable comments and suggestions, which improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 11901511) and supported by the Center for General Education, China Medical University, Taichung, Taiwan.