Study Of Dynamic Games With Random Effects

In this paper, we mainly research the stochastic problem. Focusing on games in extensive form, on connected graph and differential game, we try to get the way of how to introduce stochastic elements. By introducing the stochastic matrix to describe the stochastic interference, we construct the algorithm and give an illustration to explain the main points at last.On the first chapter, we mainly research the finite game in extensive form. Focusing on three different cooperative forms, which are non-cooperation, complete cooperation and partial cooperation, we introduce the stochastic matrix and construct the algorithm as well as illustrations. At last, we discuss the existence of the subgame perfect Nash equilibrium on games with stochastic games in extensive form.On the second chapter, we firstly define how to extend the traditional game to game on connected graph, and then study the existence of the absolute equilibrium on this kind of game. By introducing the stochastic matrix on game with weight-payoffs, we construct the algorithm and illustrations. At last, we explain the existence of the absolute equilibrium on graph-game with stochastic interference.The last chapter mainly describes the differential game. On the base of the differential game, we introduce stochastic matrix as well as stochastic covariance matrix to define the stochastic elements, and then discuss the form of the solution. At last, we show the application of the stochastic differential game by an applicable example.