Coarse Correlated Equilibria in Linear Quadratic Mean Field Games and Application to an Emission Abatement Game

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-12-14 DOI:10.1007/s00245-024-10198-3

Luciano Campi, Federico Cannerozzi, Fanny Cartellier

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引用次数: 0

Abstract

Coarse correlated equilibria (CCE) are a good alternative to Nash equilibria (NE), as they arise more naturally as outcomes of learning algorithms and as they may exhibit higher payoffs than NE. CCEs include a device which allows players’ strategies to be correlated without any cooperation, only through information sent by a mediator. We develop a methodology to concretely compute mean field CCEs in a linear-quadratic mean field game (MFG) framework. We compare their performance to mean field control solutions and mean field NE (usually named MFG solutions). Our approach is implemented in the mean field version of an emission abatement game between greenhouse gas emitters. In particular, we exhibit a simple and tractable class of mean field CCEs which allows to outperform very significantly the mean field NE payoff and abatement levels, bridging the gap between the mean field NE and the social optimum obtained by mean field control.

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线性二次均值场博弈中的粗相关均衡及其在减排博弈中的应用

粗相关均衡（CCE）是纳什均衡（NE）的一个很好的替代方案，因为粗相关均衡作为学习算法的结果出现得更自然，而且可能比纳什均衡显示出更高的收益。CCE 包含一种装置，它允许博弈者的策略在没有任何合作的情况下，仅通过中介发送的信息相互关联。我们开发了一种在线性-二次均值场博弈（MFG）框架内具体计算均值场 CCE 的方法。我们将其性能与均值场控制解决方案和均值场 NE（通常称为 MFG 解决方案）进行了比较。我们的方法是在温室气体排放者之间的均值场减排博弈中实现的。特别是，我们展示了一类简单易行的均值场 CCE，它可以大大优于均值场 NE 的报酬和减排水平，弥补了均值场 NE 与均值场控制所获得的社会最优之间的差距。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.