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We consider a general class of finite-player stochastic games with mean-field interaction, in which the linear-quadratic cost functional includes linear operators acting on controls in $L^2$. We propose a novel approach for deriving the…

Optimization and Control · Mathematics 2024-02-16 Eduardo Abi Jaber , Eyal Neuman , Moritz Voß

We study discrete-time mean-field Markov games with infinite numbers of agents where each agent aims to minimize its ergodic cost. We consider the setting where the agents have identical linear state transitions and quadratic cost…

Optimization and Control · Mathematics 2019-10-17 Zuyue Fu , Zhuoran Yang , Yongxin Chen , Zhaoran Wang

Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other…

Trading and Market Microstructure · Quantitative Finance 2025-04-16 Ryan Donnelly , Zi Li

Auctions are modeled as Bayesian games with continuous type and action spaces. Determining equilibria in auction games is computationally hard in general and no exact solution theory is known. We introduce an algorithmic framework in which…

Computer Science and Game Theory · Computer Science 2023-05-10 Martin Bichler , Maximilian Fichtl , Matthias Oberlechner

We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player…

Optimization and Control · Mathematics 2021-12-20 Franco Flandoli , Maddalena Ghio , Giulia Livieri

We consider a symmetric $n$-player nonzero-sum stochastic differential game with controlled jumps and mean-field type interaction among the players. Each player minimizes some expected cost by affecting the drift as well as the jump part of…

Probability · Mathematics 2018-05-14 Chiara Benazzoli , Luciano Campi , Luca Di Persio

We study the traffic routing game among a large number of selfish drivers over a traffic network. We consider a specific scenario where the strategic drivers can be classified into teams, where drivers in the same team have identical payoff…

Optimization and Control · Mathematics 2019-10-03 Ali Reza Pedram , Takashi Tanaka

We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Optimization and Control · Mathematics 2026-01-21 Zongxia Liang , Zhou Zhou , Yaqi Zhuang , Bin Zou

We consider $n$ risk-averse agents who compete for liquidity in an Almgren--Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear-quadratic differential game with state…

Optimization and Control · Mathematics 2015-07-08 Alexander Schied , Tao Zhang

In this paper, we study a class of discrete-time mean-field games under the infinite-horizon risk-sensitive discounted-cost optimality criterion. Risk-sensitivity is introduced for each agent (player) via an exponential utility function. In…

Optimization and Control · Mathematics 2018-10-08 Naci Saldi , Tamer Basar , Maxim Raginsky

We study the high-frequency limits of strategies and costs in a Nash equilibrium for two agents that are competing to minimize liquidation costs in a discrete-time market impact model with exponentially decaying price impact and quadratic…

Trading and Market Microstructure · Quantitative Finance 2018-10-23 Alexander Schied , Elias Strehle , Tao Zhang

We analyze the behavior of a large number of strategic drivers traveling over an urban traffic network using the mean-field game framework. We assume an incentive mechanism for congestion mitigation under which each driver selecting a…

Optimization and Control · Mathematics 2018-08-17 Takashi Tanaka , Ehsan Nekouei , Karl Henrik Johansson

This paper studies relative arbitrage opportunities in a market with competitive investors through stochastic differential games in the limit as the number of players tends to infinity. With common noises introduced by the stock…

Mathematical Finance · Quantitative Finance 2025-11-24 Nicole Tianjiao Yang , Tomoyuki Ichiba

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

Probability · Mathematics 2020-11-03 Masaaki Fujii

In this study, we investigate $N$-player stochastic differential games with regime switching, where the player dynamics are modulated by a finite-state Markov chain. We analyze the associated Nash system, which consists of a system of…

Probability · Mathematics 2025-02-26 Mingrui Wang , Prakash Chakraborty

This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…

Probability · Mathematics 2022-03-24 Mathieu Laurière , Ludovic Tangpi

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…

Probability · Mathematics 2014-09-26 Rene Carmona , Xiuneng Zhu

We consider both $N$-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initially short position of stocks are only allowed to buy while…

Mathematical Finance · Quantitative Finance 2025-07-31 Guanxing Fu , Paul P. Hager , Ulrich Horst

This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…

Optimization and Control · Mathematics 2019-07-03 Athanasios Vasiliadis

For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then,…

Optimization and Control · Mathematics 2018-11-08 Pierre Cardaliaguet , Marco Cirant , Alessio Porretta