Game theory is playing more and important roles in understanding complex systems investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic stochastic differential games, but contrast to most of existing studies, coefficient matrices are assumed be unknown both players, consequently it necessary study adapti...

Abstract We study optimal strategies in two-player stochastic games that are played on a finite graph, equipped with general payoff function. The existence of do not make use memory and randomisation is desirable property vastly simplifies the algorithmic analysis such games. Our main theorem gives sufficient condition for maximizer to possess simple strategy. imposed function, saying does depe...

We define the first nontrivial polynomially recognizable subclass of P-matrixGeneralized Linear Complementarity Problems (GLCPs) with a subexponential pivot rule. No such classes/rules were previously known. We show that a subclass of Shapley turn-based stochastic games, subsuming Condon’s simple stochastic games, is reducible to the new class of GLCPs. Based on this we suggest the new strongly...

This paper is concerned with a new type of differential game problems of forward-backward stochastic systems. There are three distinguishing features: Firstly, our game systems are forward-backward doubly stochastic differential equations, which is a class of more general game systems than other forward-backward stochastic game systems without doubly stochastic terms; Secondly, forward equation...

Our purpose is to discuss stochastic algorithms to learn equilibria in games, and their time of convergence. To do so, we consider a general class of stochastic algorithms that converge weakly (in the sense of weak convergence for stochastic processes) towards solutions of particular ordinary differential equations, corresponding to their mean-field approximations. Tuning parameters in these al...