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An Approach for Reducing the Graphical Model and Genetic Algorithm for Computing Approximate Nash Equilibrium in Static Games

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Abstract

In this paper, an approach for reducing the graphical model and a genetic algorithm for computing the approximate Nash equilibrium in a static multi-agent game is studied. In order to describe the relationship between strategies of various agents, the concepts of the influence degree and the strategy dependency are presented. Based on these concepts, an approach for reducing a graphical model is given. For discretized mixed strategies, the relationship between the discrete degree and the approximate degree is developed. Based on the regret degree, a genetic algorithm for computing the approximate Nash equilibrium is given. Experimental results indicate the genetic algorithm has high efficiency and few equilibrium errors.

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Authors and Affiliations

  1. School of Information Science and Engineering, Yunnan University, Kunming, 650091, People’s Republic of China

    Wei-Yi Liu, Kun Yue, Jin Li & Li Ding

  2. School of Software, Yunnan University, Kunming, 650091, People’s Republic of China

    Jin Li

  3. Faculty of Materials and Metallurgical Engineering, Kunming University of Science and Technology, Kunming, 650093, People’s Republic of China

    Ning Song

Authors
  1. Wei-Yi Liu
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  2. Kun Yue
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  3. Jin Li
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  4. Ning Song
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  5. Li Ding
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Corresponding author

Correspondence to Kun Yue.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 60763007, 60933001), the Natural Science Foundation of Yunnan Province No. 2007F009M, 2008CD083), the Research Foundation of the Educational Department of Yunnan Province (08Y0023), the Research Foundation of Yunnan University (No. 2009F32Q).

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Liu, WY., Yue, K., Li, J. et al. An Approach for Reducing the Graphical Model and Genetic Algorithm for Computing Approximate Nash Equilibrium in Static Games. J Intell Robot Syst 60, 241–261 (2010). https://doi.org/10.1007/s10846-010-9419-6

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  • DOI: https://doi.org/10.1007/s10846-010-9419-6

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