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A Differential Evolution Algorithm Based on Nikaido-Isoda Function for Solving Nash Equilibrium in Nonlinear Continuous Games

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  • Feng He
  • Wei Zhang
  • Guoqiang Zhang

Abstract

A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful.

Suggested Citation

  • Feng He & Wei Zhang & Guoqiang Zhang, 2016. "A Differential Evolution Algorithm Based on Nikaido-Isoda Function for Solving Nash Equilibrium in Nonlinear Continuous Games," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-17, September.
    • Handle: RePEc:plo:pone00:0161634
    DOI: 10.1371/journal.pone.0161634
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    Cited by:

    1. Napat Harnpornchai & Wiriyaporn Wonggattaleekam, 2021. "A Nikaido Isoda-Based Hybrid Genetic Algorithm and Relaxation Method for Finding Nash Equilibrium," Mathematics, MDPI, vol. 10(1), pages 1-17, December.
    2. Faranak Emtehani & Nasim Nahavandi & Farimah Mokhatab Rafiei, 2023. "Trade credit financing for supply chain coordination under financial challenges: a multi-leader–follower game approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-39, December.

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