A dynamical neural network approach for solving stochastic two-player zero-sum games

This paper aims at solving a stochastic two-player zero-sum Nash game problem studied in Singh and Lisser (2019). The main contribution of our paper is that we model this game problem as a dynamical neural network (DNN for short). In this paper, we show that the saddle point of this game problem is the equilibrium point of the DNN model, and we study the globally asymptotically stable of the DNN model. In our numerical experiments, we present the time-continuous feature of the DNN model and compare it with the state-of-the-art convex solvers, i.e., Splitting conic solver (SCS for short) and Cvxopt. Our numerical results show that our DNN method has two advantages in dealing with this game problem. Firstly, the DNN model can converge to a better optimal point. Secondly, the DNN method can solve all problems, even when the problem size is large.