一个新的判定Nash平衡点存在的判定定理

推广了Fan-Glicksberg不动点定理,引入弱拟凹函数的定义,用弱拟凹函数代替拟凹函数,弱化Nash平衡点存在的条件,得出一个新的判定定理,并举例说明了它的实用性.

A New Existence Theorem for Nash Equilibrium Point

As a generalization of Fan-Glicksberg fixed point theorem, a new existence theorem of fixed point theorem for set-valued mapping is proved. And then, by introducing the concept of weakly quasiconcave function, and replacing quasiconcave function by weakly quasiconcave function, a new existence theorem of Nash equilibrium point for game theory is deduced. Lastly an example is given to prove that the new theory is more useful.