Maximal element with applications to Nash equilibrium problems in Hadamard manifolds

ABSTRACT

The purpose of this paper is to study the existence of maximal elements with applications to Nash equilibrium problems for generalized games in Hadamard manifolds. By employing a KKM lemma, we establish a new maximal element theorem in Hadamard manifolds. As applications, some existence results of Nash equilibria for generalized games are derived. The results in this paper unify, improve and extend some known results from the literature.

KEYWORDS:

• Hadamard manifold
• maximal element
• Nash equilibrium
• generalized game

2010 MSC:

• 90C33
• 65K05
• 47J25
• 91E10

Acknowledgements

The authors would like to thank the referees for their valuable suggestions for improvement of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Social Science Fund of Jiangsu Province (No. 16GLB009) funded by the Office of the Philosophy and Social Science Planning of Jiangsu Province and by the Planning Foundation for Humanities and Social Sciences of Ministry of Education of China (No. 18YJA790058).