Graphon games have been introduced to study games with many players who
interact through a weighted graph of interaction. By passing to the limit, a
game with a continuum of players is obtained, in which the interactions are
through a graphon. In this paper, we focus on a graphon game for optimal
investment under relative performance criteria, and we propose a deep learning
method. The method builds upon two key ingredients: first, a characterization
of Nash equilibria by forward-backward stochastic differential equations and,
second, recent advances of machine learning algorithms for stochastic
differential games. We provide numerical experiments on two different financial
models. In each model, we compare the effect of several graphons, which
correspond to different structures of interactions.

通过前向 - 后向随机微分方程的纳什均衡特性和随机微分博弈的机器学习算法的最新进展，本文针对相对绩效准则下的最优投资提出了一种基于图上游戏的深度学习方法，并对两个不同的金融模型进行了数值实验，比较了几个不同的图上结构对结果的影响。

基于深度学习方法的异质代理人相对绩效优化投资

A Deep Learning Method for Optimal Investment Under Relative Performance  Criteria Among Heterogeneous Agents

We study an optimal investment problem that arises in the context of the
vehicle-sharing system. Given a set of locations to build stations, we need to
determine i) the sequence of stations to be built and the number of vehicles to
acquire in order to obtain the target state where all stations are built, and
ii) the number of vehicles to acquire and their allocation in order to maximize
the total profit returned by operating the system when some or all stations are
open. The profitability associated with operating open stations, measured over
a specific time period, is represented as a linear optimization problem applied
to a collection of open stations. With operating capital, the owner of the
system can open new stations. This property introduces a set-dependent aspect
to the duration required for opening a new station, and the optimal investment
problem can be viewed as a variant of the Traveling Salesman Problem (TSP) with
set-dependent cost. We propose an A* search algorithm to address this
particular variant of the TSP. Computational experiments highlight the benefits
of the proposed algorithm in comparison to the widely recognized Dijkstra
algorithm and propose future research to explore new possibilities and
applications for both exact and approximate A* algorithms.

在车辆共享系统中，我们研究了一个最优投资问题，其中包括确定建立站点的顺序、车辆数量以及获得目标状态的策略，以及通过经营系统来最大化总利润的车辆数量和分配策略。该问题可以视为具有集合相关成本的旅行推销员问题的变体，并使用 A * 搜索算法进行解决。