Numerical experiments on Yuan’s Method for Nash equilibrium problems
DOI:
https://doi.org/10.22481/intermaths.v2i2.9819Keywords:
Equilíbrio de Nash, Métodos do tipo Jacobi, Região de Confiança, Implementação numéricaAbstract
In this paper numerical results are present on procedures to identify Nash Equilibrium. These experiments were systemized aiming to compare classical approaches with the algorithm propose by Y. Yuan in 2011. The method introduced by Yuan uses a Jacobi-type algorithm and a trust region globalization, developed specifically for Nash Equilibrium problems. In the original work, a theorical analysis is provide, but no considerations on the algorithm’s practical performance are made. Therefore, this paper goal is to meet the need of a numerical implementation and to discuss the algorithm’s numerical behave. In order to do that, the methods were tested in six different examples involving two-players dynamics. The examples differ from each other by the objective function of each player, concerning to vary the theoretical characteristics of them, which is the focus of this analysis. Finally, the effectiveness of both methods in finding a solution for Nash Equilibrium Problems is compared and important points, that influences the performance of Yuan’s algorithm, are raised.
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