Related papers: A Mean Field Competition
This paper studies competitions with rank-based reward among a large number of teams. Within each sizable team, we consider a mean-field contribution game in which each team member contributes to the jump intensity of a common Poisson…
In this paper, we consider the problem of a Principal aiming at designing a reward function for a population of heterogeneous agents. We construct an incentive based on the ranking of the agents, so that a competition among the latter is…
We discuss a natural game of competition and solve the corresponding mean field game with \emph{common noise} when agents' rewards are \emph{rank dependent}. We use this solution to provide an approximate Nash equilibrium for the finite…
We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…
We formulate a mean field game where each player stops a privately observed Brownian motion with absorption. Players are ranked according to their level of stopping and rewarded as a function of their relative rank. There is a unique mean…
We consider a class of optimal control problems that arise in connection with optimal advertising under uncertainty. Two main features appear in the model: a delay in the control variable driving the state dynamics; a mean-field term both…
We study a setting in which a principal selects an agent to execute a collection of tasks according to a specified priority sequence. Agents, however, have their own individual priority sequences according to which they wish to execute the…
We analyze a mean field tournament: a mean field game in which the agents receive rewards according to the ranking of the terminal value of their projects and are subject to cost of effort. Using Schr\"{o}dinger bridges we are able to…
We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…
We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…
Multi-agent reinforcement learning methods have shown remarkable potential in solving complex multi-agent problems but mostly lack theoretical guarantees. Recently, mean field control and mean field games have been established as a…
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…
We study the design of optimal incentives in sequential processes. To do so, we consider a basic and fundamental model in which an agent initiates a value-creating sequential process through costly investment with random success. If…
Mean-Field Games are games with a continuum of players that incorporate the time-dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best Reply Strategy have been proposed. They assume that the agents…
We consider a deterministic mean field games problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect…
The goal of the paper is to introduce a set of problems which we call mean field games of timing. We motivate the formulation by a dynamic model of bank run in a continuous-time setting. We briefly review the economic and game theoretic…
We introduce a class of robust control problems formulated in min-max form, in which the principal agent is viewed as a central planner facing Nature. The agent's cost is a nonlinear function of all its possible realizations, encompassing…
This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an…
A principal uses payments conditioned on stochastic outcomes of a team project to elicit costly effort from the team members. We develop a multi-agent generalization of a classic first-order approach to contract optimization by leveraging…
This paper studies the connections between mean-field games and the social welfare optimization problems. We consider a mean field game in functional spaces with a large population of agents, each of which seeks to minimize an individual…