A Bridge Between Bilevel Programs and Nash Games
A Bridge Between Bilevel Programs and Nash Games
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双层程序和纳什博弈之间的桥梁
DOI：
10.1007/s10957-017-1109-0
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发表时间：
2015
影响因子：
1.9
通讯作者：
Simone Sagratella
中科院分区：
文献类型：
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作者：
Lorenzo Lampariello;Simone Sagratella
我们研究了乐观二层规划问题和广义纳什均衡问题之间的联系。我们注意到，相对于双层问题，我们认为一般情况下，较低级别的程序不被假设有一个唯一的解决方案。受最优值方法的启发，我们提出了一个纳什博弈，将所谓的隐式值函数约束转化为显式定义的约束函数，结合了一些层次结构的味道，原来是与双层规划问题。我们对垂直两层问题和“不平衡”水平模型之间的关系提供了完整的理论分析：特别是，我们定义了一类问题，可以通过找到我们游戏的均衡来计算两层程序的解。此外，通过引用经济学中的一些应用，我们表明，我们的“不均匀”的水平模型，在某种意义上说，是介于垂直双层模型和一个“纯粹的”水平游戏。
We study connections between optimistic bilevel programming problems and generalized Nash equilibrium problems. We remark that, with respect to bilevel problems, we consider the general case in which the lower level program is not assumed to have a unique solution. Inspired by the optimal value approach, we propose a Nash game that, transforming the so-called implicit value function constraint into an explicitly defined constraint function, incorporates some taste of hierarchy and turns out to be related to the bilevel programming problem. We provide a complete theoretical analysis of the relationship between the vertical bilevel problem and our “uneven” horizontal model: in particular, we define classes of problems for which solutions of the bilevel program can be computed by finding equilibria of our game. Furthermore, by referring to some applications in economics, we show that our “uneven” horizontal model, in some sense, lies between the vertical bilevel model and a “pure” horizontal game.
影响因子：
2.2
作者：
Dempe, S.;Franke, S.
通讯作者：
Franke, S.
DOI：
10.1016/j.cor.2012.09.002
发表时间：
2014
期刊：
Comput. Oper. Res.
影响因子：
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作者：
S. Dempe;S. Franke
通讯作者：
S. Dempe;S. Franke