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Motivated by models of epidemic control in large populations, we consider a Stackelberg mean field game model between a principal and a mean field of agents evolving on a finite state space. The agents play a non-cooperative game in which…
Mean-field reinforcement learning has become a popular theoretical framework for efficiently approximating large-scale multi-agent reinforcement learning (MARL) problems exhibiting symmetry. However, questions remain regarding the…
We study the existence of strong solutions for mean-field forward-backward stochastic differential equations (FBSDEs) with measurable coefficients and their implication on the Nash equilibrium of a multi-population mean-field game. More…
The model of congestion games is widely used to analyze games related to traffic and communication. A central property of these games is that they are potential games and hence posses a pure Nash equilibrium. In reality it is often the case…
Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications,…
A growing body of literature in networked systems research relies on game theory and mechanism design to model and address the potential lack of cooperation between self-interested users. Most game-theoretic models applied to system…
Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating…
We consider a class of dynamic collective choice models with social interactions, whereby a large number of non-uniform agents have to individually settle on one of multiple discrete alternative choices, with the relevance of their would-be…
We provide an in-depth study of Nash equilibria in multi-objective normal form games (MONFGs), i.e., normal form games with vectorial payoffs. Taking a utility-based approach, we assume that each player's utility can be modelled with a…
This paper studies a new class of dynamic optimization problems of large-population (LP) system which consists of a large number of negligible and coupled agents. The most significant feature in our setup is the dynamics of individual…
We study stationary mean field games with singular controls in which the representative player interacts with a long-time weighted average of the population through a discounted and an ergodic performance criterion. This class of games…
This paper studies the competition among multiple fund managers with relative performance over the excess logarithmic return. Fund managers compete with each other and have expected utility or mean-variance criteria for excess logarithmic…
The mean field games (MFG) theory has broad application in mathematical modeling of social phenomena. The Mean Field Games System (MFGS) is the key to the MFG theory. This is a system of two nonlinear parabolic partial differential…
We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…
We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. the control. Existence, uniqueness, and stability of solutions are studied from the point…
Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…
Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…
In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens…
Mean field games (MFGs) offer a versatile framework for modeling large-scale interactive systems across multiple domains. This paper builds upon a previous work, by developing a state-of-the-art unified approach to decode or design the…
This paper studies mean field game (MFG) of controls by featuring the joint distribution of the state and the control with the reflected state process along an exogenous stochastic reflection boundary. We contribute to the literature with a…