Variational Mean Field Games for Market Competition
Variational Mean Field Games for Market Competition
复制标题
市场竞争的变分平均场博弈
DOI：
10.1007/978-3-030-01947-1_5
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Charafeddine Mouzouni
中科院分区：
文献类型：
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作者：
P. J. Graber;Charafeddine Mouzouni
本文研究了具有反射边界条件的Bertrand和Cournot平均场博弈模型。我们证明了方程组解的存在性、唯一性和正则性，并证明了该方程组可以写成凸极小化问题的最优性条件。我们还为Graber和Bensoussan（Appl Math Optim 77：47-71，2018）中提到的系统提供了一个简短的唯一性证明，其中唯一性仅针对小参数证明。最后，我们证明了相应的一阶系统在确定性极限下弱解的存在唯一性。
In this paper, we explore Bertrand and Cournot Mean Field Games models for market competition with reflection boundary conditions. We prove existence, uniqueness and regularity of solutions to the system of equations, and show that this system can be written as an optimality condition of a convex minimization problem. We also provide a short proof of uniqueness to the system addressed in Graber and Bensoussan (Appl Math Optim 77:47–71, 2018), where uniqueness was only proved for small parameters ?. Finally, we prove existence and uniqueness of weak solutions to the corresponding first order system at the deterministic limit.