Some Relaxed Solutions of Minimax Inequality for Discontinuous Game
In this paper, we first prove the existence results of minimax inequality under some relaxed assumptions by virtue of KKMF principle or Fan-Browder fixed point theorem and propose the pseu-solution of minimax inequality. Mild continuity named pseudocontinuity and mild convexity are introduced for the existence results and generalize the present results in the literature. Some other cases of minimax inequality with pseudocontinuity are given in various ways. As applications, we introduce some pseu-Nash equilibrium for n-person noncooperative game and obtain some relaxed existence theorems.
KeywordsMinimax inequality KKMF lemma Pseudocontinuity Diagonal-quasi-concavity Pseu-solution pseu-Nash equilibrium
Mathematics Subject Classification (MSC2010):47H10 91A10
This research was supported by the National Natural Science Foundation of China (Grant No. 11401124 and No. 71461003), and the Natural Science Foundation of Guizhou Province (Grant No. QKH7424,7425). The authors acknowledge these supports.