Related papers: Minimal-time mean field games
Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized mean-field games with a finite state-action space in a discrete time…
We consider network aggregative games to model and study multi-agent populations in which each rational agent is influenced by the aggregate behavior of its neighbors, as specified by an underlying network. Specifically, we examine systems…
We formulate and solve a multi-player stochastic differential game between financial agents who seek to cost-efficiently liquidate their position in a risky asset in the presence of jointly aggregated transient price impact, along with…
Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by…
We design and compute a class of optimal control problems for reaction-diffusion systems. They form mean field control problems related to multi-density reaction-diffusion systems. To solve proposed optimal control problems numerically, we…
In a probabilistic mean-field game driven by a linear diffusion an individual player aims to minimize an ergodic long-run cost by controlling the diffusion through a pair of -- increasing and decreasing -- c\`adl\`ag processes, while he is…
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…
This paper studies the existence and approximation of equilibria for general time-inconsistent mean field game (MFG) problems in continuous time. To handle the intricate nonlocal equilibrium Hamilton-Jacobi-Bellman (EHJB) system arising…
This paper proposes an efficient computational framework for longitudinal velocity control of a large number of autonomous vehicles (AVs) and develops a traffic flow theory for AVs. Instead of hypothesizing explicitly how AVs drive, our…
In this paper, we present a framework for solving continuous optimal control problems when the true system dynamics are approximated through an imperfect model. We derive a control strategy by applying Pontryagin's Minimum Principle to the…
We investigate the existence of an optimal policy to monitor a mean field systems of agents managing a risky project under moral hazard with accidents modeled by L\'evy processes magnified by the law of the project. We provide a general…
We consider a jump-diffusion mean field control problem with regime switching in the state dynamics. The corresponding value function is characterized as the unique viscosity solution of a HJB master equation on the space of probability…
In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…
Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…
In this paper, we consider the mean field game with a common noise and allow the state coefficients to vary with the conditional distribution in a nonlinear way. We assume that the cost function satisfies a convexity and a weak monotonicity…
We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…
Mean field games are concerned with the limit of large-population stochastic differential games where the agents interact through their empirical distribution. In the classical setting, the number of players is large but fixed throughout…
We study stochastic Mean Field Games on networks with sticky transition conditions. In this setting, the diffusion process governing the agent's dynamics can spend finite time both in the interior of the edges and at the vertices. The…
We consider interacting agent systems with a large number of stochastic agents (or particles) influenced by a fixed number of external stochastic lead agents. Such examples arise, for example in models of opinion dynamics, where a small…
The synthesis of control laws for interacting agent-based dynamics and their mean-field limit is studied. A linearization-based approach is used for the computation of sub-optimal feedback laws obtained from the solution of differential…