标题： 带有异质参与者的约束组合博弈 显示英文标题

标题： Constrained portfolio game with heterogeneous agents

摘要： 我们研究在有限参与者和无限参与者（图论）设置下，基于相对绩效关注的随机效用最大化博弈。 考虑了一个不完全市场模型，其中具有幂次（CRRA）效用函数的参与者在共同无风险债券和由共同噪声和特有噪声驱动的个股中进行交易。 两种情况下的纳什均衡由具有二次增长生成器的前向-后向随机微分方程（FBSDEs）表征，其中图论博弈的解导致了一种新型的无限维McKean-Vlasov FBSDEs。 在温和条件下，我们证明了在没有共同噪声的情况下，图论博弈和$n$-参与者博弈都存在纳什均衡。 此外，我们建立了一个收敛结果，表明在灵敏度矩阵有适度假设的情况下，随着参与者数量的增加，有限参与者博弈的纳什均衡及其相关均衡值将收敛到图论博弈的纳什均衡和相关均衡值。 显示英文摘要

摘要： We investigate stochastic utility maximization games under relative performance concerns in both finite-agent and infinite-agent (graphon) settings. An incomplete market model is considered where agents with power (CRRA) utility functions trade in a common risk-free bond and individual stocks driven by both common and idiosyncratic noise. The Nash equilibrium for both settings is characterized by forward-backward stochastic differential equations (FBSDEs) with a quadratic growth generator, where the solution of the graphon game leads to a novel form of infinite-dimensional McKean-Vlasov FBSDEs. Under mild conditions, we prove the existence of Nash equilibrium for both the graphon game and the $n$-agent game without common noise. Furthermore, we establish a convergence result showing that, with modest assumptions on the sensitivity matrix, as the number of agents increases, the Nash equilibrium and associated equilibrium value of the finite-agent game converge to those of the graphon game.