Reinforcement Learning Algorithm for Mixed Mean Field Control Games
Reinforcement Learning Algorithm for Mixed Mean Field Control Games
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DOI：
10.4208/jml.220915
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
Andrea Angiuli;Nils Detering;J. Fouque;M. Laurière;Jimin Lin
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文献类型：
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作者：
Andrea Angiuli;Nils Detering;J. Fouque;M. Laurière;Jimin Lin
我们提出了一个新的组合平均场控制博弈（MFCG）问题，它可以被解释为合作群体之间的竞争博弈，其解是群体之间的纳什均衡.玩家在每个小组内协调他们的策略。一个例子是对经典交易者问题的修改。交易者群体最大化他们的财富。他们面临着交易成本，他们自己的终端位置，以及他们集团内的平均持有量。资产价格受到所有代理人交易的影响。我们提出了一个三时间尺度的强化学习算法来近似解决这样的MFCG问题。我们测试的基准线性二次规格，我们提供解析解的算法。
We present a new combined \textit{mean field control game} (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between groups. Players coordinate their strategies within each group. An example is a modification of the classical trader's problem. Groups of traders maximize their wealth. They face cost for their transactions, for their own terminal positions, and for the average holding within their group. The asset price is impacted by the trades of all agents. We propose a three-timescale reinforcement learning algorithm to approximate the solution of such MFCG problems. We test the algorithm on benchmark linear-quadratic specifications for which we provide analytic solutions.