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

Feng He | Zendy; Wei Zhang | Zendy; Guoqiang Zhang | Zendy

Open Access

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

Author(s) -

Feng He,

Wei Zhang,

Guoqiang Zhang

Publication year - 2016

Publication title -

plos one

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.99

H-Index - 332

ISSN - 1932-6203

DOI - 10.1371/journal.pone.0161634

Subject(s) - nash equilibrium , mathematical optimization , best response , nonlinear system , stochastic game , mathematical economics , function (biology) , differential (mechanical device) , differential evolution , mathematics , computer science , physics , quantum mechanics , evolutionary biology , biology , thermodynamics

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.

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