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首页> 外文期刊>Applied Mathematical Modelling >Determination of Stackelberg-Nash equilibria using a sensitivity based approach
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Determination of Stackelberg-Nash equilibria using a sensitivity based approach

机译：基于灵敏度的方法确定Stackelberg-Nash平衡

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摘要

A sensitivity based approach is presented to determine Nash solution(s) in multiobjective problems modeled as a non-cooperative game. The proposed approach provides an approximation to the rational reaction set (RRS) for each player. An intersection of these sets yields the Nash solution for the game. An alternate approach for generating the RRS based on design of experiments (DOE) combined with response surface methodology (RSM) is also explored. The two approaches for generating the RRS are compared on three example problems to find Nash and Stackelberg solutions. For the examples presented, it is seen that the proposed sensitivity based approach (ⅰ) requires less computational effort than a RSM-DOE approach, (ⅱ) is less prone to numerical errors than the RSM-DOE approach, (ⅲ) has the ability to find multiple Nash solutions when the Nash solution is not a singleton, (ⅳ) is able to approximate nonlinear RRS, and (ⅴ) on one example problem, found a Nash solution better than the one reported in the literature.
机译：提出了一种基于敏感性的方法来确定建模为非合作博弈的多目标问题中的纳什解决方案。所提出的方法为每个参与者提供了一个合理的反应集（RRS）的近似值。这些集合的交集产生了游戏的Nash解决方案。还探索了一种基于实验设计（DOE）结合响应面方法（RSM）生成RRS的替代方法。在三个示例问题上比较了两种生成RRS的方法，以找到Nash和Stackelberg解决方案。对于给出的示例，可以看出，与RSM-DOE方法相比，所提出的基于灵敏度的方法（ⅰ）比RSM-DOE方法需要更少的计算工作，（RS）与RSM-DOE方法相比更不容易出现数值误差，（ⅲ）具有以下能力：在Nash解不是单例时找到多个Nash解，（ⅳ）能够近似非线性RRS，并且（ⅴ）在一个示例问题上，找到了一个N​​ash解优于文献报道的解决方案。

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  • 来源
    《Applied Mathematical Modelling》 |2014年第22期|4972-4984|共13页
  • 作者

    Ehsan Ghotbi; Wilkistar A. Otieno; Anoop K. Dhingra;

  • 作者单位

    Department of Mechanical Engineering, Alfred University, Alfred, NY 74802, United States;

    Department of Industrial Engineering, University of Wisconsin, Milwaukee, WI 53201, United States;

    Department of Mechanical Engineering, University of Wisconsin, Milwaukee, WI 53201, United States;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Non-cooperative game; Nash solution; Stackelberg game; RSM;

    机译：非合作博弈;纳什解决方案;Stackelberg游戏;RSM;

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