Generalized Nash games concepts: existence, tractability and applications to population models

广义纳什博弈概念：存在性、易处理性及其在人口模型中的应用

• 批准号: RGPIN-2017-04530
• 负责人: Cojocaru, MonicaGabriela
• 金额: $ 1.75万
• 依托单位: University of Guelph
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=647893
• 关键词: Generalized; Nash; games; concepts; existence

This proposal focuses on the notion of generalized Nash games (GNG), tackling questions of existence of solutions, computational methods for finding these solutions, and the role this modelling concept can play in applied problems in populations.*GNG were introduced in the 50's, and represent models of noncooperative behaviour among players whose strategy sets, together with their payoff functions, depend on the strategy choices of other players. The popularity of GNG as a modelling framework is not by far as wide as that of usual Nash games. This is due to the fact that solving GNG poses very complex mathematical difficulties and both existence theory for solutions and computational methods vary depending on the subclasses of GNG under investigation. My research plans include both a theoretical component and a modelling one. ***1) In the theoretical direction, I plan to extend recently developed personal results and computational methods to provide answers to the question of existence of generalized Nash equilibria (GNE) for GNG without shared constraints. One of the most intriguing features of a GNG is the fact that their solution sets are generally very large. My own work on this topic plans to fully explore variational inequality-based and evolutionary algorithmic approaches for describing entire solution sets of GNG.*Further, I plan to relate the concept of evolutionary stable state (ESS) to a GNG, and investigate whether this concept can be linked to a (slightly modified) replicator dynamics. If so, I want to investigate the counterparts, in the generalized setting, of classic relations/results between ESS states and Nash games.***2) In the modelling direction, I will concentrate on developing meaningful models of population behaviour where the rise of constraints on players' choices takes place organically. The models I am interested in developing fall into two categories: health and socio-economic. I want to study single-payer budget constraints across producers of medical treatments, and its impact on the allocation of publicly covered treatments for specific age groups in a population (such as prophylactic vaccines for shingles, influenza, or HIV). In the socio-economic realm, constraints such as resource sharing or norm establishment can be incorporated in population groups' or individuals' decision making, leading to a GNG framework. Such classes of models are the cap-and-trade environmental accords between economies or regions, or resource pooling constraints on producers who want to defend against cyber attacks on their markets. *** I am interested to investigate the importance of looking at the particular applied problem at hand in the GNG framework, the benefits of knowing/computing GNE states and their particular significance in the given model. I plan to disseminate the results in the respective applied communities (population health, operations research, economics).

该提案重点关注广义纳什博弈 (GNG) 的概念、解决解的存在性问题、寻找这些解的计算方法以及该建模概念在群体应用问题中可以发挥的作用。*GNG 于 20 世纪 50 年代引入，并代表参与者之间的非合作行为模型，其策略集及其收益函数取决于其他参与者的策略选择。 GNG 作为建模框架的受欢迎程度还没有普通纳什博弈那么广泛。这是因为求解 GNG 会带来非常复杂的数学困难，并且解的存在理论和计算方法都会根据所研究的 GNG 子类的不同而有所不同。我的研究计划包括理论部分和建模部分。 ***1）在理论方向上，我计划扩展最近开发的个人结果和计算方法，为没有共享约束的 GNG 的广义纳什均衡（GNE）的存在问题提供答案。 GNG 最有趣的特征之一是它们的解决方案集通常非常大。我自己在这个主题上的工作计划充分探索基于变分不等式和进化算法的方法来描述 GNG 的整个解决方案集。*此外，我计划将进化稳定状态 (ESS) 的概念与 GNG 联系起来，并研究这是否概念可以与（稍作修改的）复制器动力学联系起来。如果是这样，我想在广义环境中研究 ESS 状态和纳什博弈之间的经典关系/结果的对应部分。***2）在建模方向上，我将专注于开发有意义的人口行为模型，其中人口增长对玩家选择的限制是有机发生的。我有兴趣开发的模型分为两类：健康和社会经济。我想研究医疗治疗生产商的单一支付者预算限制，及其对特定年龄组的公共承保治疗分配的影响（例如带状疱疹、流感或艾滋病毒的预防性疫苗）。在社会经济领域，资源共享或规范建立等约束可以纳入人口群体或个人的决策中，从而形成GNG框架。此类模型包括经济体或地区之间的限额与交易环境协议，或者对想要防御市场网络攻击的生产者的资源池限制。 *** 我有兴趣研究在 GNG 框架中查看当前特定应用问题的重要性、了解/计算 GNE 状态的好处以及它们在给定模型中的特殊意义。我计划在各自的应用社区（人口健康、运筹学、经济学）传播研究结果。