Related papers: On Approximate Nash Equilibria in Mean Field Games
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…
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…
We investigate mean-field games from the point of view of a large number of indistinguishable players which eventually converges to infinity. The players are weakly coupled via their empirical measure. The dynamics of the states of the…
In this paper we focus on noncooperative games with uncertain constraints coupling the agents' decisions. We consider a setting where bounded deviations of agents' decisions from the equilibrium are possible, and uncertain constraints are…
We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…
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…
Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…
We investigate the convergence of symmetric stochastic differential games with interactions via control, where the volatility terms of both idiosyncratic and common noises are controlled. We apply the stochastic maximum principle, following…
In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their…
This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to…
We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…
We study techniques to incentivize self-interested agents to form socially desirable solutions in scenarios where they benefit from mutual coordination. Towards this end, we consider coordination games where agents have different intrinsic…
This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions…
We develop a probabilistic framework to approximate Nash equilibria in symmetric $N$-player games in the large population regime, via the analysis of associated mean field games (MFGs). The approximation is achieved through the analysis of…
We consider learning approximate Nash equilibria for discrete-time mean-field games with nonlinear stochastic state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator,…
A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE…
Computing an equilibrium in congestion games can be challenging when the number of players is large. Yet, it is a problem to be addressed in practice, for instance to forecast the state of the system and be able to control it. In this work,…
This paper addresses the problem of learning a Nash equilibrium in $\gamma$-discounted multiplayer general-sum Markov Games (MG). A key component of this model is the possibility for the players to either collaborate or team apart to…
We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players $n$. Our main result states that for $n$-player binary-action games and for constant $\varepsilon$, the query complexity of an…
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…