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We investigate a two-player zero-sum stochastic differential game problem with the state process being constrained in a connected bounded closed domain, and the cost functional described by the solution of a generalized backward stochastic…
This paper studies singular mean field control problems and singular mean field stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some…
Stochastic games are a convenient formalism for modelling systems that comprise rational agents competing or collaborating within uncertain environments. Probabilistic model checking techniques for this class of models allow us to formally…
Mean field games (MFGs) describe the limit, as $n$ tends to infinity, of stochastic differential games with $n$ players interacting with one another through their common empirical distribution. Under suitable smoothness assumptions that…
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost…
We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic…
This study investigates differential games with motion-payoff uncertainty in continuous-time settings. We propose a framework where players update their beliefs about uncertain parameters using continuous Bayesian updating. Theoretical…
The value of a zero-sum differential games is known to exist, under Isaacs' condition, as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation. In this note we provide a self-contained proof based on the construction of…
We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…
This paper focuses on a kind of linear quadratic non-zero sum differential game driven by backward stochastic differential equation with asymmetric information, which is a natural continuation of Wang and Yu [IEEE TAC (2010) 55: 1742-1747,…
In this work, we present a novel characterization of approximate Nash equilibria in a class of convex games over the simplex. To achieve this, we regularize the utility functions using the Shannon entropy term, connect the solutions to the…
We study some ergodicity property of zero-sum stochastic games with a finite state space and possibly unbounded payoffs. We formulate this property in operator-theoretical terms, involving the solvability of an optimality equation for the…
We extend the construction of equilibria for linear-quadratic and mean-variance portfolio problems available in the literature to a large class of mean-field time-inconsistent stochastic control problems in continuous time. Our approach…
This paper considers the problem of designing optimal algorithms for reinforcement learning in two-player zero-sum games. We focus on self-play algorithms which learn the optimal policy by playing against itself without any direct…
Mean field games model equilibria in games with a continuum of players as limiting systems of symmetric $n$-player games with weak interaction between the players. We consider a finite-state, infinite-horizon problem with two cost criteria:…
In this paper, we investigate the noncooperative games of multi-agent systems. Different from existing noncooperative games, our formulation involves the high-order nonlinear dynamics of players, and the communication topologies among…
In this paper we study ergodic backward stochastic differential equations (EBSDEs) dropping the strong dissipativity assumption needed in the previous work. In other words we do not need to require the uniform exponential decay of the…
Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not…
This paper considers the problem of inverse reinforcement learning in zero-sum stochastic games when expert demonstrations are known to be not optimal. Compared to previous works that decouple agents in the game by assuming optimality in…
This paper proposes a novel approach for local convergence to Nash equilibrium in quadratic noncooperative games based on a distributed Lie-bracket extremum seeking control scheme. This is the first instance of noncooperative games being…