Related papers: Cluster formation in iterated Mean Field Games
We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…
We study a class of non-cooperative aggregative games -- denoted as \emph{social purpose games} -- in which the payoffs depend separately on a player's own strategy (individual benefits) and on a function of the strategy profile which is…
Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malham\'e, Mean…
Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and…
A new approach for the description of phenomena of social aggregation is suggested. On the basis of psychological concepts (as for instance social norms and cultural coordinates), we deduce a general mechanism for the social aggregation in…
In this paper, we consider a finite horizon, non-stationary, mean field games (MFG) with a large population of homogeneous players, sequentially making strategic decisions, where each player is affected by other players through an aggregate…
We study the fragmentation-coagulation (or merging and splitting) evolutionary control model as introduced recently by one of the authors, where $N$ small players can form coalitions to resist to the pressure exerted by the principal. It is…
We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…
Mean Field Games (MFGs) provide a powerful framework for modeling the collective behavior of large populations of interacting agents. In this paper, we address the problem of Imitation Learning (IL) in MFGs subject to common noise, where…
Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…
The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…
This paper studies an inverse problem for a multipopulation mean field game (MFG) system where the objective is to reconstruct the running and terminal cost functions of the system that couples the dynamics of different populations. We…
Here, we observe that mean-field game (MFG) systems admit a two-player infinite-dimensional general-sum differential game formulation. We show that particular regimes of this game reduce to previously known variational principles.…
This article considers a mean field game model inspired by crowd motion models in which agents aim at reaching a given target set and wish to minimize a cost consisting of an individual running cost, an individual cost depending on the…
The work we present in this paper initiated the formal study of fractional hedonic games, coalition formation games in which the utility of a player is the average value he ascribes to the members of his coalition. Among other settings,…
Inspired by successful biological collective decision mechanisms such as honey bees searching for a new colony or the collective navigation of fish schools, we consider a mean field games (MFG)-like scenario where a large number of agents…
Here, we prove the existence of smooth solutions for mean-field games with a singular mean-field coupling; that is, a coupling in the Hamilton-Jacobi equation of the form $g(m)=-m^{-\alpha}$. We consider stationary and time-dependent…
In repeated games, players choose actions concurrently at each step. We consider a parameterized setting of repeated games in which the players form a population of an arbitrary size. Their utility functions encode a reachability objective.…
A procedure to predict the occurrence of periodic clusters in a system of globally coupled maps displaying a constant mean field is presented. The method employs the analogy between a system of globally coupled maps and a single map driven…
To model complex real-world systems, such as traders in stock markets, or the dissemination of contagious diseases, graphon mean-field games (GMFG) have been proposed to model many agents. Despite the empirical success, our understanding of…