Related papers: On noncooperative $n$-player principal eigenvalue …

This paper studies a stochastic utility maximization game under relative performance concerns in finite agent and infinite agent settings, where a continuum of agents interact through a graphon (see definition below). We consider an…

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…

Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in…

Multi-leader multi-follower games are a class of hierarchical games in which a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium…

Under what conditions do the behaviors of players, who play a game repeatedly, converge to a Nash equilibrium? If one assumes that the players' behavior is a discrete-time or continuous-time rule whereby the current mixed strategy profile…

We study a sequence of symmetric $n$-player stochastic differential games driven by both idiosyncratic and common sources of noise, in which players interact with each other through their empirical distribution. The unique Nash equilibrium…

Inspired by the path coordination problem arising from robo-taxis, warehouse management, and mixed-vehicle routing problems, we model a group of heterogeneous players responding to stochastic demands as a congestion game under Markov…

A multi-player competitive Dynkin stopping game is constructed. Each player can either exit the game for a fixed payoff, determined a priori, or stay and receive an adjusted payoff depending on the decision of other players. The single…

We consider the problem of minimizing the asymptotic exit rate with which the controlled-diffusion process of a stochastically perturbed multi-channel dynamical system exits from a given bounded open domain. In particular, for a class of…

This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…

Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented…

Nash equilibrium is a central concept in game theory. Several Nash solvers exist, yet none scale to normal-form games with many actions and many players, especially those with payoff tensors too big to be stored in memory. In this work, we…

We consider a general class of nonzero-sum $N$-player stochastic games with impulse controls, where players control the underlying dynamics with discrete interventions. We adopt a verification approach and provide sufficient conditions for…

Consider a set of agents who play a network game repeatedly. Agents may not know the network. They may even be unaware that they are interacting with other agents in a network. Possibly, they just understand that their payoffs depend on an…

Coordinating communication and control is a key component in the stability and performance of networked multi-agent systems. While single user networked control systems have gained a lot of attention within this domain, in this work, we…

We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player…

We discuss similarities and differencies between systems of many interacting players maximizing their individual payoffs and particles minimizing their interaction energy. We analyze long-run behavior of stochastic dynamics of many…

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…

We introduce a new mean field kinetic model for systems of rational agents interacting in a game theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large…

In this paper, we study a non-zero-sum game with two players, where each of the players plays what we call Bermudan strategies and optimizes a general non-linear assessment functional of the pay-off. By using a recursive construction, we…