Related papers: Risk-sensitive Nonzero-sum Stochastic Differential…

This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis…

Towards characterizing the optimization landscape of games, this paper analyzes the stability of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to…

Considering infinite-horizon, discrete-time, linear quadratic, N-player dynamic games with scalar dynamics, a graphical representation of feedback Nash equilibrium solutions is provided. This representation is utilised to derive conditions…

The works of (Daskalakis et al., 2009, 2022; Jin et al., 2022; Deng et al., 2023) indicate that computing Nash equilibria in multi-player Markov games is a computationally hard task. This fact raises the question of whether or not…

We propose a deep neural network-based algorithm to identify the Markovian Nash equilibrium of general large $N$-player stochastic differential games. Following the idea of fictitious play, we recast the $N$-player game into $N$ decoupled…

We examine global non-asymptotic convergence properties of policy gradient methods for multi-agent reinforcement learning (RL) problems in Markov potential games (MPG). To learn a Nash equilibrium of an MPG in which the size of state space…

The mathematical characterization of social-distancing games in classical epidemic theory remains an important question, for their applications to both infectious-disease theory and memetic theory. We consider a special case of the dynamic…

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…

Mean field games (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric $n$-player games. We consider the finite-state, infinite-horizon problem with ergodic cost. Assuming Markovian…

We study a class of dynamic decision problems of mean field type with time inconsistent cost functionals, and derive a stochastic maximum principle to characterize subgame perfect Nash equilibrium points. Subsequently, this approach is…

Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…

We analyze best response dynamics for finding a Nash equilibrium of an infinite horizon zero-sum stochastic linear quadratic dynamic game (LQDG) with partial and asymmetric information. We derive explicit expressions for each player's best…

The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…

We formulate a new class of two-person zero-sum differential games, in a stochastic setting, where a specification on a target terminal state distribution is imposed on the players. We address such added specification by introducing…

A Dynkin game is considered for stochastic differential equations with random coefficients. We first apply Qiu and Tang's maximum principle for backward stochastic partial differential equations to generalize Krylov estimate for the…

This paper aims at investigating the problem of fast convergence to the Nash equilibrium (NE) for N-Player noncooperative differential games. The proposed method is such that the players attain their NE point without steady-state…

We study a general formulation of the classical two-player Dynkin game in a discrete time Markovian setting. We identify an appropriate class of mixed strategies -- \textit{Markovian randomized stopping times} -- in which players stop at…

We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive…

We propose a toy model for a stochastic description of the competition between two athletes of unequal strength, whose average strength difference is represented by a parameter $d$. The athletes interact through the choice of their…

We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that…