Related papers: Mean Field Equilibrium in Dynamic Games with Compl…
A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…
Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…
We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and…
We propose a reinforcement learning algorithm for stationary mean-field games, where the goal is to learn a pair of mean-field state and stationary policy that constitutes the Nash equilibrium. When viewing the mean-field state and the…
This paper studies the relation between equilibria in single-period, discrete-time and continuous-time mean field game models. First, for single-period mean field games, we establish the existence of equilibria and then prove the…
We investigate a time-inconsistent, non-Markovian finite-player game in continuous time, where each player's objective functional depends non-linearly on the expected value of the state process. As a result, the classical Bellman optimality…
We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game…
This paper aims to solve two fundamental problems on finite or infinite horizon dynamic games with perfect or almost perfect information. Under some mild conditions, we prove (1) the existence of subgame-perfect equilibria in general…
In this paper, we consider the social optimal problem of discrete time finite state space mean field games (referred to as finite mean field games [1]). Unlike the individual optimization of their own cost function in competitive models, in…
We introduce and study an evolutionary complementarity game where in each round a player of population 1 is paired with a member of population 2. The game is symmetric, and each player tries to obtain an advantageous deal, but when one of…
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…
In this paper, we present a new development of inspection games in a mean field setting. In our dynamic version of an inspection game, there is one inspector and a large number N interacting inspectees with a finite state space. By applying…
We study a class of dynamic decision problems of mean field type with time inconsistent cost functionals, and derive a stochastic maximum principle to characterize subgame perfect Nash equilibrium points. Subsequently, this approach is…
This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as…
In this paper we formulate and solve a mean-field game described by a linear stochastic dynamics and a quadratic or exponential-quadratic cost functional for each generic player. The optimal strategies for the players are given explicitly…
We investigate the convergence of symmetric stochastic differential games with interactions via control, where the volatility terms of both idiosyncratic and common noises are controlled. We apply the stochastic maximum principle, following…
Mean field type models describing the limiting behavior, as the number of players tends to $+\infty$, of stochastic differential game problems, have been recently introduced by J-M. Lasry and P-L. Lions. Numerical methods for the…
Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…
Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…
We find closed-form solutions to the stochastic game between a broker and a mean-field of informed traders. In the finite player game, the informed traders observe a common signal and a private signal. The broker, on the other hand,…