Dynamic game arises as a powerful paradigm for multi-robot planning, which safety constraint satisfaction is crucial. Constrained stochastic games are of particular interest, real-world robots need to operate and satisfy constraints under uncertainty. Existing methods solving handle chance using exponential penalties with hand-tuned weights. However, finding suitable penalty weight nontrivial r...

In this paper, we apply the idea of fictitious play to design deep neural networks (DNNs), and develop learning theory algorithms for computing Nash equilibrium asymmetric $N$-player non-zero-sum stochastic differential games, which refer as \emph{deep play}, a multi-stage process. Specifically at each stage, propose strategy letting individual player optimize her own payoff subject other playe...

The paper is concerned with two-person zero-sum mean-field linear-quadratic stochastic differential games over finite horizons. By a Hilbert space method, necessary condition and sufficient are derived for the existence of an open-loop saddle point. It shown that under condition, associated two Riccati equations admit unique strongly regular solutions, in terms which point can be represented as...

The theory of graph games with ω-regular winning conditions is the foundation for modeling and synthesizing reactive processes. In the case of stochastic reactive processes, the corresponding stochastic graph games have three players, two of them (System and Environment) behaving adversarially, and the third (Uncertainty) behaving probabilistically. We consider two problems for stochastic graph...