局部纳什均衡驱动下的非保守经济财富演化
Evolution of wealth in a nonconservative economy driven by local Nash equilibria
摘要：
我们开发了一个模型，在非保守的经济环境中的财富的演变，扩展了作者早期开发的理论。该模型考虑了一个系统的理性代理人在博弈论框架中进行交互。这种演变驱动了财富和经济配置变量中代理人的动态。选择成本函数来表示每个代理的风险规避策略。也就是说，代理人更有可能与市场互动，市场越可预测，因此其个体风险越小。这产生了一个动力学方程的一个有效的单粒子剂密度与纳什均衡作为当地的热力学平衡。我们考虑一个制度的规模分离的大尺度动力学是由一个流体动力学封闭与此局部平衡。针对财富分布演化大尺度动力学中流体动力学封闭性的非保守性问题，提出了一类广义碰撞不变量（GCI）.其结果是一个系统的气体动力学型方程的密度和平均财富的代理商在大规模上。我们恢复的逆伽马分布，这在文献中已经被认为是一个局部平衡的成本函数的特定选择。
英文摘要：
We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed earlier by the authors. The model considers a system of rational agents interacting in a game theoretical framework. This evolution drives the dynamic of the agents in both wealth and economic configuration variables. The cost function is chosen to represent a risk averse strategy of each agent. That is, the agent is more likely to interact with the market, the more predictable the market, and therefore the smaller its individual risk. This yields a kinetic equation for an effective single particle agent density with a Nash equilibrium serving as the local thermodynamic equilibrium. We consider a regime of scale separation where the large scale dynamics is given by a hydrodynamic closure with this local equilibrium. A class of generalized collision invariants (GCIs) is developed to overcome the difficulty of the non-conservative property in the hydrodynamic closure derivation of the large scale dynamics for the evolution of wealth distribution. The result is a system of gas dynamics-type equations for the density and average wealth of the agents on large scales. We recover the inverse Gamma distribution, which has been previously considered in the literature, as a local equilibrium for particular choices of the cost function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
