Nonlocal Bertrand and Cournot mean field games with general nonlinear demand schedule
Nonlocal Bertrand and Cournot mean field games with general nonlinear demand schedule
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DOI：
10.1016/j.matpur.2021.02.002
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
J. Graber;Vincenzo Ignazio;Ariel Neufeld
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文献类型：
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作者：
J. Graber;Vincenzo Ignazio;Ariel Neufeld
在这篇文章中，我们证明了在市场竞争下的可耗竭资源生产的研究中产生的平均场博弈系统的经典解的存在性。单个轨迹由具有跳跃的受控扩散过程建模，该过程在PDE系统中添加了非局部项。假设的哈密顿量是足够普遍的，以涵盖一个大类的例子提出的文献中的贝特朗和古诺平均场游戏。在对哈密尔顿算子的结构的充分限制下，唯一性也成立，这实际上相当于商品可替代性的一个小的上限。
In this article we prove the existence of classical solutions to a system of mean field games arising in the study of exhaustible resource production under market competition. Individual trajectories are modeled by a controlled diffusion process with jumps, which adds a nonlocal term to the PDE system. The assumptions on the Hamiltonian are sufficiently general to cover a large class of examples proposed in the literature on Bertrand and Cournot mean field games. Uniqueness also holds under a sufficient restriction on the structure of the Hamiltonian, which in practice amounts to a small upper bound on the substitutability of goods.