Markovian strategies with continuous and impulse controls for a differential game model of revolution

IF 1.3 4区社会学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Sociology Pub Date : 2020-02-16 DOI:10.1080/0022250X.2020.1726344

W. Ruan

引用次数: 1

Abstract

ABSTRACT This paper is concerned with a piecewise-deterministic differential game model of political regime changes. We modify and study the model proposed by Boucekkine et al. in [7]. The original model does not allow all players to take full controls as the situation progresses. Hence, it does not lead to closed-loop strategies. We fix the problem by deriving and using a system of quasi-variational inequalities associated with the differential game, and proving a criterion for the regime change. As a result, we find Markovian strategies for all players. A numerical example for illustration of the method is given. Implications of the results to political changes in a society are discussed. Some results are extended to more general models that incorporate gradual and abrupt changes, as well as continuous and impulse controls.

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具有连续和脉冲控制的微分革命博弈模型的马尔可夫策略

摘要本文研究了一个政治体制变迁的分段确定性微分博弈模型。我们对Boucekkine等人在[7]中提出的模型进行了修改和研究。最初的模式不允许所有玩家在局势发展时完全控制局面。因此，它不会导致闭环策略。我们通过推导和使用与微分对策相关的拟变分不等式系统来解决这个问题，并证明了制度变化的一个标准。因此，我们发现了适用于所有玩家的马尔可夫策略。给出了该方法的一个数值例子。讨论了结果对社会政治变革的影响。一些结果被扩展到更通用的模型，包括渐进和突变，以及连续和脉冲控制。

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

Journal of Mathematical Sociology 数学-数学跨学科应用

CiteScore

2.90

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The goal of the Journal of Mathematical Sociology is to publish models and mathematical techniques that would likely be useful to professional sociologists. The Journal also welcomes papers of mutual interest to social scientists and other social and behavioral scientists, as well as papers by non-social scientists that may encourage fruitful connections between sociology and other disciplines. Reviews of new or developing areas of mathematics and mathematical modeling that may have significant applications in sociology will also be considered. The Journal of Mathematical Sociology is published in association with the International Network for Social Network Analysis, the Japanese Association for Mathematical Sociology, the Mathematical Sociology Section of the American Sociological Association, and the Methodology Section of the American Sociological Association.