Related papers: Almost Optimal Algorithms for Two-player Zero-Sum …

An ideal strategy in zero-sum games should not only grant the player an average reward no less than the value of Nash equilibrium, but also exploit the (adaptive) opponents when they are suboptimal. While most existing works in Markov games…

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…

Multi-agent robust reinforcement learning, also known as multi-player robust Markov games (RMGs), is a crucial framework for modeling competitive interactions under environmental uncertainties, with wide applications in multi-agent systems.…

In this work, we introduce the concept of non-negative weighted regret, an extension of non-negative regret \cite{anagnostides2022last} in games. Investigating games with non-negative weighted regret helps us to understand games with…

Regret minimization has proved to be a versatile tool for tree-form sequential decision making and extensive-form games. In large two-player zero-sum imperfect-information games, modern extensions of counterfactual regret minimization (CFR)…

We study decentralized learning in two-player zero-sum discounted Markov games where the goal is to design a policy optimization algorithm for either agent satisfying two properties. First, the player does not need to know the policy of the…

This paper studies a variant of two-player zero-sum matrix games, where, at each timestep, the row player selects row $i$, the column player selects column $j$, and the row player receives a noisy reward with expected value $A_{i,j}$, along…

We study the problem of learning Nash equilibria in offline two-player zero-sum Markov games. While existing approaches often rely on explicit pessimism to address distribution shift, we show that KL regularization alone suffices to…

We consider online no-regret learning in unknown games with bandit feedback, where each player can only observe its reward at each time -- determined by all players' current joint action -- rather than its gradient. We focus on the class of…

We study the game modification problem, where a benevolent game designer or a malevolent adversary modifies the reward function of a zero-sum Markov game so that a target deterministic or stochastic policy profile becomes the unique Markov…

Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…

Game theory is a very profound study on distributed decision-making behavior and has been extensively developed by many scholars. However, many existing works rely on certain strict assumptions such as knowing the opponent's private…

In this paper, a new method is proposed to compute the rolling Nash equilibrium of the time-invariant nonlinear two-person zero-sum differential games. The idea is to discretize the time to transform a differential game into a sequential…

An abundance of recent impossibility results establish that regret minimization in Markov games with adversarial opponents is both statistically and computationally intractable. Nevertheless, none of these results preclude the possibility…

Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…

The problem of two-player zero-sum Markov games has recently attracted increasing interests in theoretical studies of multi-agent reinforcement learning (RL). In particular, for finite-horizon episodic Markov decision processes (MDPs), it…

Self-play via online learning is one of the premier ways to solve large-scale two-player zero-sum games, both in theory and practice. Particularly popular algorithms include optimistic multiplicative weights update (OMWU) and optimistic…

We investigate Nash equilibrium learning in a competitive Markov Game (MG) environment, where multiple agents compete, and multiple Nash equilibria can exist. In particular, for an oligopolistic dynamic pricing environment, exact Nash…

Zero-sum games arise in a wide variety of problems, including robust optimization and adversarial learning. However, algorithms deployed for finding a local Nash equilibrium in these games often converge to non-Nash stationary points. This…

In this paper, we consider a distributed learning problem in a subnetwork zero-sum game, where agents are competing in different subnetworks. These agents are connected through time-varying graphs where each agent has its own cost function…