{"title":"Linear-quadratic-singular stochastic differential games and applications","authors":"","doi":"10.1007/s10203-023-00422-0","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We consider a class of non-cooperative <em>N</em>-player nonzero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is quadratic in the state and linear in the control. We call these games <em>linear-quadratic-singular stochastic differential games</em>. Under natural assumptions, we show the existence of open-loop Nash equilibria, which are characterized through a linear system of forward-backward stochastic differential equations. The proof is based on an approximation via a sequence of games in which players are restricted to play Lipschitz continuous strategies. We then discuss an application of these results to a model of capacity expansion in oligopoly markets.</p>","PeriodicalId":43711,"journal":{"name":"Decisions in Economics and Finance","volume":"29 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Decisions in Economics and Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s10203-023-00422-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"SOCIAL SCIENCES, MATHEMATICAL METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a class of non-cooperative N-player nonzero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is quadratic in the state and linear in the control. We call these games linear-quadratic-singular stochastic differential games. Under natural assumptions, we show the existence of open-loop Nash equilibria, which are characterized through a linear system of forward-backward stochastic differential equations. The proof is based on an approximation via a sequence of games in which players are restricted to play Lipschitz continuous strategies. We then discuss an application of these results to a model of capacity expansion in oligopoly markets.
摘要 我们考虑了一类具有奇异控制的非合作 N 人非零和随机微分博弈，在这类博弈中，每个博弈者都可以影响一个线性随机微分方程，以最小化一个成本函数，该成本函数在状态中为二次方，在控制中为线性。我们称这些博弈为线性-二次-奇异随机微分博弈。在自然假设条件下，我们证明了开环纳什均衡的存在，并通过一个线性的前向-后向随机微分方程系对其进行了表征。证明是基于通过博弈序列的近似方法，在这个博弈序列中，博弈者被限制使用利普希茨连续策略。然后，我们讨论了这些结果在寡头市场产能扩张模型中的应用。
期刊介绍：
Decisions in Economics and Finance: A Journal of Applied Mathematics is the official publication of the Association for Mathematics Applied to Social and Economic Sciences (AMASES). It provides a specialised forum for the publication of research in all areas of mathematics as applied to economics, finance, insurance, management and social sciences. Primary emphasis is placed on original research concerning topics in mathematics or computational techniques which are explicitly motivated by or contribute to the analysis of economic or financial problems.
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