Cooperative games, replicator dynamics, and stability

合作博弈、复制动力学和稳定性

• 批准号: 388390901
• 负责人: Professor Dr. André Casajus
• 金额: --
• 依托单位: Lehrstuhl VWL (Mikroökonomie)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/388390901?language=en
• 关键词: Cooperative; games; replicator; dynamics; stability

Evolutionary models have been part and parcel of economics for a long time. A specific class of such models has been developed within game theory. In usual parlance, "evolutionary game theory" means the combination of evolutionary approaches with non-cooperative games. Particularly close to the theory of evolution in biology are replicator dynamics.So far, only few efforts have been taken to combine evolutionary approaches with cooperative game theory. This is what this projects aims at. We develop and analyze replicator dynamics that are based on cooperative games, particularly with respect to stable populations.In the first part of the project, we continue the study of the Lovász-Shapley replicator dynamics initiated by Casajus, Kramm, and Wiese (2020, JET). These dynamics are derived from cooperative games with transferable utility (TU games) by help of the Lovász-Shapley solution (Casajus and Wiese, 2017, IJGT). Players are regarded as types of agents and their weights as the sizes of the populations of agents of these types. In order to handle them, we have to apply the theory of differential equations with discontinuous right-hand side (Filippov, 1988). Whereas the relation between the stable populations in these dynamics and the underlying TU games already has been clarified, remains the question of the existence and stability of cycles, for example.The Lovász-Shapley solution is based on a Leontief type technology, i.e., the types are complements. Alternatively, one could consider a technology, where the types are perfect substitutes, or, more generally, technologies that can be described by CES production functions. In the second part of the project, we generalize the Lovász-Shapley solution for these production functions using the construction introduced by Casajus and Wiese (2017, IJGT). We analyze these CES solutions and compare their properties with those of the Lovász-Shapley solution.In the third part of the project, we extend the analysis of the first part to the CES solutions.

进化模型长期以来一直是经济学的重要组成部分。博弈论中已经开发出了一类特定的模型。用通常的说法，“进化博弈论”意味着进化方法与非合作博弈的结合。与生物学中的进化论特别接近的是复制动力学。到目前为止，只有很少的努力将进化方法与合作博弈论结合起来。这就是该项目的目的。我们开发和分析基于合作博弈的复制动态，特别是在稳定群体方面。在该项目的第一部分，我们继续研究由 Casajus、Kramm 和 Wiese 发起的 Lovász-Shapley 复制动态（2020，JET）。这些动态源自具有可转移效用的合作博弈（TU 博弈），借助 Lovász-Shapley 解决方案（Casajus 和 Wiese，2017，IJGT）。玩家被视为代理的类型，他们的权重被视为这些类型代理的群体规模。为了处理它们，我们必须应用右手边不连续的微分方程理论（Filippov，1988）。尽管这些动态中的稳定群体与潜在的 TU 博弈之间的关系已经得到澄清，但仍然存在循环的存在性和稳定性问题。Lovász-Shapley 解决方案基于 Leontief 类型技术，即类型是互补的。或者，人们可以考虑一种技术，其中类型是完美的替代品，或者更一般地说，可以通过 CES 生产函数来描述的技术。在该项目的第二部分中，我们使用 Casajus 和 Wiese (2017, IJGT) 引入的结构概括了这些生产函数的 Lovász-Shapley 解决方案。我们分析了这些 CES 解决方案，并将它们的属性与 Lovász-Shapley 解决方案的属性进行了比较。在该项目的第三部分，我们将第一部分的分析扩展到 CES 解决方案。