连续时间Dynkin博弈的纳什均衡点存在性的一个新证明

A New Method on the Existence of the Nash Equilibrium for Continuous Time Stochastic Games with Stopping Times

针对一类连续时间的以停止时间作为参与人行动策略的博弈,采用了新的利用FanKy定理的方法证明了该博弈的纳什均衡点的存在性,并且也对该博弈存在纳什均衡点的条件进行一定程度上的改进.另外,将该方法应用到了一个具体的博弈期权,得到了该期权价格的存在性.

In this thesis, the existence of the Nash equilibrim for continuous time stochastic games with stopping times is studied. If the profit/cost stochastic processes are satisfied with some continuity conditions and proper martingale properties, from comparing the stopping time and different strategies, it can beproved that this kind of game is satisfied with conditions of Fan Ky theorem. So the existence of Nash equilibrium point can be obtained. Finally, this method is applied into a practical example, under the general assumption of American option the existence of the price of game options can be proved.