On solutions to Cournot–Nash equilibria equations on the sphere
On solutions to Cournot–Nash equilibria equations on the sphere
复制标题
球面上古诺-纳什均衡方程的解
DOI：
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发表时间：
2013
期刊：
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通讯作者：
Micah W. Warren
中科院分区：
文献类型：
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作者：
Micah W. Warren
我们讨论了Blanchet和Carlier最近提出的古诺-纳什均衡方程。这些方程涉及到一个最优的运输问题，其中的源措施是已知的，但目标措施是问题的一部分。所得方程是Monge-Ampere型的，可能有非局部项。如果成本函数是一个特定的形式，方程是容易受到标准的最佳运输PDE技术，与一些修改，以处理新的条款。我们给出了球面上问题的一些充分条件，由此我们可以得出解是光滑的结论。
We discuss equations associated to Cournot‐Nash Equilibria as put forward recently by Blanchet and Carlier. These equations are related to an optimal transport problem in which the source measure is known, but the target measure is part of the problem. The resulting equation is of Monge‐Ampere type with possible nonlocal terms. If the cost function is of a particular form, the equation is vulnerable to standard optimal transportation PDE techniques, with some modifications to deal with the new terms. We give some sufficient conditions for the problem on the sphere from which we can conclude that solutions are smooth.