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This paper studies a class of strongly monotone games involving non-cooperative agents that optimize their own time-varying cost functions. We assume that the agents can observe other agents' historical actions and choose actions that best…
The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act…
The paper studies the convergence properties of (continuous) best-response dynamics from game theory. Despite their fundamental role in game theory, best-response dynamics are poorly understood in many games of interest due to the…
In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…
Multiagent learning settings are inherently more difficult than single-agent learning because each agent interacts with other simultaneously learning agents in a shared environment. An effective approach in multiagent reinforcement learning…
We investigate the repeated prisoner's dilemma game where both players alternately use reinforcement learning to obtain their optimal memory-one strategies. We theoretically solve the simultaneous Bellman optimality equations of…
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…
This paper introduces two metrics (cycle-based and memory-based metrics), grounded on a dynamical game-theoretic solution concept called sink equilibrium, for the evaluation, ranking, and computation of policies in multi-agent learning. We…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
Learning in games considers how multiple agents maximize their own rewards through repeated games. Memory, an ability that an agent changes his/her action depending on the history of actions in previous games, is often introduced into…
Repeated games consider a situation where multiple agents are motivated by their independent rewards throughout learning. In general, the dynamics of their learning become complex. Especially when their rewards compete with each other like…
In single-agent Markov decision processes, an agent can optimize its policy based on the interaction with environment. In multi-player Markov games (MGs), however, the interaction is non-stationary due to the behaviors of other players, so…
Repeated games are difficult to analyze, especially when agents play mixed strategies. We study one-memory strategies in iterated prisoner's dilemma, then generalize the result to k-memory strategies in repeated games. Our result shows that…
This paper focuses on multi-agent stochastic differential games for jump-diffusion systems. On one hand, we study the multi-agent game for optimal investment in a jump-diffusion market. We derive constant Nash equilibria and provide…
Learning by experience in Multi-Agent Systems (MAS) is a difficult and exciting task, due to the lack of stationarity of the environment, whose dynamics evolves as the population learns. In order to design scalable algorithms for systems…
Reinforcement learning (RL) has recently achieved tremendous successes in many artificial intelligence applications. Many of the forefront applications of RL involve multiple agents, e.g., playing chess and Go games, autonomous driving, and…
In this paper, we examine the convergence landscape of multi-agent learning under uncertainty. Specifically, we analyze two stochastic models of regularized learning in continuous games -- one in continuous and one in discrete time with the…
We investigate multi-agent reinforcement learning for stochastic games with complex tasks, where the reward functions are non-Markovian. We utilize reward machines to incorporate high-level knowledge of complex tasks. We develop an…
Constrained Markov games offer a formal mathematical framework for modeling multi-agent reinforcement learning problems where the behavior of the agents is subject to constraints. In this work, we focus on the recently introduced class of…
Examining the behavior of multi-agent systems is vitally important to many emerging distributed applications - game theory has emerged as a powerful tool set in which to do so. The main approach of game-theoretic techniques is to model…