非连续非拟凹博弈的Nash均衡存在性

Existence of Nash equilibrium in discontinuous and non quasiconcave games

法国数学家Rabia Nessah于2011年提出了一个Nash均衡存在性定理。该定理证明了对于一个有界的、紧的并且拟凹的广义弱转移连续博弈,一定存在一个Nash均衡。为了提高Nessah的定理的普遍适用性,减弱定理的条件,通过构造一个衡量拟凹程度大小标准的函数,引入了一个新的弱转移连续函数的概念,减弱了Nessah的定理对支付函数拟凹性的设定,并在此基础上得到了一个在非拟凹条件下,判断Nash均衡是否存在的新的定理,结果一般化了Nessah的定理。为寻找Nash均衡增加了新的理论基础和新的方向。

In 2011, the French mathematician Rabia Nessah proposed a Nash equilibrium existence theorem. Thetheorem has proved that a bounded, compact quasiconcave and generalized weak transfer continuous game has a Nashequilibrium certainly. In order to improve universal applicability of the Nessah＇s theorem and reduce the theorem＇sconditions, the author introduces a new concept called as a-weakly transfer continuous to reduce the assumption ofquasicancavity of payoff functions in Nessah＇s theorem by constructing a new function of measuring the degree ofquasiconcavity. On this basis the author obtains a new theorem of the existence of Nash equilibrium under the condition ofnonquasiconcavity. The result generalizes Nessah＇s theorem mentioned above. It adds a new theoretical basis anddirection for looking for Nash equilibrium.