Related papers: Large deviations for interacting particle dynamics…
The behaviour of multi-agent learning in competitive settings is often considered under the restrictive assumption of a zero-sum game. Only under this strict requirement is the behaviour of learning well understood; beyond this, learning…
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…
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…
We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…
We address payoff-based decentralized learning in infinite-horizon zero-sum Markov games. In this setting, each player makes decisions based solely on received rewards, without observing the opponent's strategy or actions nor sharing…
In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps and partial information. First, we prove a sufficient maximum…
We obtain global, non-asymptotic convergence guarantees for independent learning algorithms in competitive reinforcement learning settings with two agents (i.e., zero-sum stochastic games). We consider an episodic setting where in each…
In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…
This paper considers games where the utilities for agents are the sum of a term proportional to a social utility, and another term that is an individual cost or reward. The agents are assumed to be irrational in their perception of the…
Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
We establish a connection between tagged particles and size-biased empirical processes in interacting particle systems, in analogy to classical results on the propagation of chaos. In a mean-field scaling limit, the evolution of the…
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…
Coordination games admit two types of equilibria: pure equilibria, where all players successfully coordinate their actions, and mixed equilibria, where players frequently experience miscoordination. The existing literature shows that under…
The theory of large deviations has been applied successfully in the last 30 years or so to study the properties of equilibrium systems and to put the foundations of equilibrium statistical mechanics on a clearer and more rigorous footing. A…
Recently, the paper [12] introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This…
In this paper, we consider a distributed Bayesian Nash equilibrium (BNE) seeking problem in incomplete-information aggregative games, which is a generalization of Bayesian games and deterministic aggregative games. We handle the aggregation…
We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental…
We propose a zero-order optimization method for sequential min-max problems based on two populations of interacting particles. The systems are coupled so that one population aims to solve the inner maximization problem, while the other aims…
We present a fast numerical algorithm for large scale zero-sum stochastic games with perfect information, which combines policy iteration and algebraic multigrid methods. This algorithm can be applied either to a true finite state space…
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…