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Related papers: Discrete-time Risk-sensitive Mean-field Games

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The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. This paper proposes a game where agents' strategic sets consist of all possible sharing…

Risk Management · Quantitative Finance 2016-07-11 Michail Anthropelos , Constantinos Kardaras

This paper proposes and studies a class of discrete-time finite-time-horizon Stackelberg mean-field games, with one leader and an infinite number of identical and indistinguishable followers. In this game, the objective of the leader is to…

Optimization and Control · Mathematics 2022-10-11 Xin Guo , Anran Hu , Jiacheng Zhang

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

Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…

Optimization and Control · Mathematics 2019-10-31 Martin Frank , Michael Herty , Torsten Trimborn

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…

Computer Science and Game Theory · Computer Science 2022-07-26 Yue Guan , Mi Zhou , Ali Pakniyat , Panagiotis Tsiotras

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

Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…

Optimization and Control · Mathematics 2025-05-09 Julian Barreiro-Gomez , Tyrone E. Duncan , Bozenna Pasik-Duncan , Hamidou Tembine

This paper studies mean field games for multi-agent systems with control-dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal…

Optimization and Control · Mathematics 2019-06-10 Bing-Chang Wang , Yuan-Hua Ni , Huanshui Zhang

We investigate an infinite-horizon time-inconsistent mean-field game (MFG) in a discrete time setting. We first present a classic equilibrium for the MFG and its associated existence result. This classic equilibrium aligns with the…

Optimization and Control · Mathematics 2024-09-13 Erhan Bayraktar , Zhenhua Wang

We investigate stochastic utility maximization games under relative performance concerns in both finite-agent and infinite-agent (graphon) settings. An incomplete market model is considered where agents with power (CRRA) utility functions…

Optimization and Control · Mathematics 2024-12-05 Zongxia Liang , Keyu Zhang , Yaqi Zhuang

We consider an $N$-player game where the states of the players evolve with time as Stochastic Differential Equations (SDEs) with interaction only in the drift terms. Each player controls the drift of the SDE satisfied by her state process,…

Probability · Mathematics 2026-03-24 Erhan Bayraktar , Nikolaos Kolliopoulos

This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of…

Optimization and Control · Mathematics 2022-06-14 Bing-Chang Wang , Huanshui Zhang , Minyue Fu , Yong Liang

We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…

Probability · Mathematics 2018-08-24 Rene Carmona , Peiqi Wang

In this paper, we study the infinite-time mean field games with discounting, establishing an equilibrium where individual optimal strategies collectively regenerate the mean-field distribution. To solve this problem, we partition all agents…

Optimization and Control · Mathematics 2026-03-17 Yongsheng Song , Zeyu Yang

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

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

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…

Machine Learning · Computer Science 2021-12-20 Kai Cui , Anam Tahir , Mark Sinzger , Heinz Koeppl

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…

Trading and Market Microstructure · Quantitative Finance 2023-03-24 Eyal Neuman , Moritz Voß

Recent advances at the intersection of dense large graph limits and mean field games have begun to enable the scalable analysis of a broad class of dynamical sequential games with large numbers of agents. So far, results have been largely…

Computer Science and Game Theory · Computer Science 2022-02-21 Kai Cui , Heinz Koeppl

We study how risk-sensitive players act in situations where the outcome is influenced not only by the state-action profile but also by the distribution of it. In such interactive decision-making problems, the classical mean-field game…

Optimization and Control · Mathematics 2015-05-26 Hamidou Tembine