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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,…
This paper studies mean field games for multi-agent systems with control-dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal…
We prove that finding an $\epsilon$-approximate Nash equilibrium is PPAD-complete for constant $\epsilon$ and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions. As…
We study a portfolio optimization problem for competitive agents with CRRA utilities and a common finite time horizon. The utility of an agent depends not only on her absolute wealth and consumption but also on her relative wealth and…
In this paper, we present a framework for multi-agent learning in a nonstationary dynamic network environment. More specifically, we examine projected gradient play in smooth monotone repeated network games in which the agents'…
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…
Power system operators and electric utility companies often impose a coincident peak demand charge on customers when the aggregate system demand reaches its maximum. This charge incentivizes customers to strategically shift their peak usage…
We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper…
We provide the first fully polynomial time approximation scheme (FPTAS) for computing an approximate mixed-strategy Nash equilibrium in tree-structured graphical multi-hypermatrix games (GMhGs). GMhGs are generalizations of normal-form…
We consider multi-agent decision making, where each agent optimizes its cost function subject to constraints. Agents' actions belong to a compact convex Euclidean space and the agents' cost functions are coupled. We propose a distributed…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
This paper shows the existence of $\mathcal{O}(\frac{1}{n^\gamma})$-Nash equilibria in $n$-player noncooperative sum-aggregative games in which the players' cost functions, depending only on their own action and the average of all players'…
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…
Algorithms and models based on game theory have nowadays become prominent techniques for the design of digital controllers for critical systems. Indeed, such techniques enable automatic synthesis: given a model of the environment and a…
We study the performance of the gradient play algorithm for stochastic games (SGs), where each agent tries to maximize its own total discounted reward by making decisions independently based on current state information which is shared…
The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…
We consider $\epsilon$-equilibria notions for constant value of $\epsilon$ in $n$-player $m$-actions games where $m$ is a constant. We focus on the following question: What is the largest grid size over the mixed strategies such that…
This work proposes a policy learning algorithm for seeking generalised feedback Nash equilibria (GFNE) in $N_P$-player noncooperative dynamic games. We consider linear-quadratic games with stochastic dynamics and design a best-response…
This paper considers the design of fully distributed Nash equilibrium seeking strategies for multi-agent games. To develop fully distributed seeking strategies, two adaptive control laws, including a node-based control law and an edge-based…
This paper is related to nonzero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The…