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Finding Nash equilibria in two-player zero-sum imperfect-information games remains a central challenge in multi-agent reinforcement learning. Recent multi-round regularization methods offer a promising direction, yet existing approaches…

People choose their strategies through a trial-and-error learning process in which they gradually discover that some strategies work better than others. The process can be modelled as an evolutionary game dynamics system, which may be…

We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…

We present the concept of a Generalized Feedback Nash Equilibrium (GFNE) in dynamic games, extending the Feedback Nash Equilibrium concept to games in which players are subject to state and input constraints. We formalize necessary and…

A class of nonzero-sum stochastic dynamic games with imperfect information structure is investigated. The game involves an arbitrary number of players, modeled as homogeneous Markov decision processes, aiming to find a sequential Nash…

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…

We study reinforcement learning for two-player zero-sum Markov games with simultaneous moves in the finite-horizon setting, where the transition kernel of the underlying Markov games can be parameterized by a linear function over the…

This paper explores distributed Nash equilibrium seeking problems for games in which the players have limited knowledge on other players' actions. In particular, the involved players are considered to be high-order integrators with their…

Autonomous racing extends beyond the challenge of controlling a racecar at its physical limits. Professional racers employ strategic maneuvers to outwit other competing opponents to secure victory. While modern control algorithms can…

Existing methods for learning Stackelberg equilibria typically assume that the followers' (variational, generalized) Nash equilibrium is unique. However, in the presence of multiple equilibria, without a selection convention, the problem…

Although it has been known since the 1970s that a globally optimal strategy profile in a common-payoff game is a Nash equilibrium, global optimality is a strict requirement that limits the result's applicability. In this work, we show that…

This work studies Nash equilibrium seeking for a class of stochastic aggregative games, where each player has an expectation-valued objective function depending on its local strategy and the aggregate of all players' strategies. We propose…

We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave…

The Nash equilibrium problem is a widely used tool to model non-cooperative games. Many solution methods have been proposed in the literature to compute solutions of Nash equilibrium problems with continuous strategy sets, but, besides some…

This paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances. Our proposed distributionally robust safe policy maximizes the probability of a system remaining in a…

Distributed Nash equilibrium (NE) seeking problem for multi-coalition games has attracted increasing attention in recent years, but the research mainly focuses on the case without agreement demand within coalitions. This paper considers a…

In this paper, we consider game problems played by (multi)-integrator agents, subject to external disturbances. We propose Nash equilibrium seeking dynamics based on gradient-play, augmented with a dynamic internal-model based component,…

This paper proposes a distributed algorithm to find the Nash equilibrium in a class of non-cooperative convex games with partial-decision information. Our method employs a distributed projected gradient play approach alongside consensus…

We study the open question of how players learn to play a social optimum pure-strategy Nash equilibrium (PSNE) through repeated interactions in general-sum coordination games. A social optimum of a game is the stable Pareto-optimal state…

In this paper, we study closed-loop strong equilibrium strategies for the time-inconsistent control problem with higher-order moments formulated by [Wang et al. SIAM J. Control. Optim., 63 (2025), 1560--1589]. Since time-inconsistency makes…