Strategy optimization with its application to dynamic games

A metric space structure on the set of finite memory strategy profiles is proposed. The geometric meaning of this metric about the network structure is revealed. Based on this metric, a numerical method called hill climbing method is proposed to find the local “best” strategy profile. Two applications of this technique are introduced. First, we consider a dynamic game. The local Nash/sub-Nash equilibriums are defined, and then the problem of finding Nash/sub-Nash solutions to finite games over the set of μ-memory strategies are investigated. Second, the optimization of mixed-value logical dynamic control systems is studied, where the the strategies with initial conditions are considered. Several examples are included to demonstrate the efficiency of the method.