Sharp Equilibria for Time-Inconsistent Mean-Field Stopping Games

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-08-08 DOI:10.1137/23m1625512

Ziyuan Wang, Zhou Zhou

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 2319-2345, August 2024.
Abstract. We investigate time-inconsistent mean-field stopping games under nonexponential discounting in discrete time. At the intrapersonal level, each player plays against her future selves as a result of the time inconsistency caused by nonexponential discounting. At the interpersonal level, she plays against other players due to players’ interaction via the proportion of players that have stopped. We look for sharp mean-field equilibria (MFEs), such that given other players’ stopping policies, the representative player’s strategy not only is an intrapersonal equilibrium, but also an optimal one among all such intrapersonal equilibria. We analyze two classes of examples. The first one is on time-inconsistent bank-run models, and we construct an (optimal) sharp MFE by a monotone iteration scheme. The second one has a Markovian setup and no common noise, and we show the existence of a sharp MFE based on the Tikhonov fixed-point theorem.

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时间不一致均值场停止博弈的尖锐均衡点

SIAM 控制与优化期刊》第 62 卷第 4 期第 2319-2345 页，2024 年 8 月。摘要。我们研究了离散时间非指数贴现下的时间不一致均值场停止博弈。在个人层面上，由于非指数贴现导致的时间不一致，每个博弈者都在与未来的自己博弈。在人际层面上，由于玩家之间的互动，玩家会通过已停止游戏的玩家比例与其他玩家进行博弈。我们寻找尖锐的均场均衡（MFEs），即给定其他玩家的停止策略，代表玩家的策略不仅是一个人际均衡，而且是所有此类人际均衡中的最优策略。我们分析了两类例子。第一类是时间不一致的银行运行模型，我们通过单调迭代方案构建了一个（最优）尖锐的 MFE。第二个例子是马尔可夫模型，没有普通噪声，我们根据提霍诺夫定点定理证明了尖锐 MFE 的存在。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.