Differential evolution as a new method of computing nash equilibria

  • Authors:

  • Urszula Boryczka;Przemyslaw Juszczuk

  • Affiliations:

  • Institute of Computer Science, University of Silesia, Sosnowiec, Poland;Institute of Computer Science, University of Silesia, Sosnowiec, Poland

  • Venue:
  • Transactions on Computational Collective Intelligence IX
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

Abstract

The Nash equilibrium is one of the central concepts in game theory. Recently it was shown, that problems of finding Nash equilibrium and an approximate Nash equilibrium are PPAD-complete. In this article we present the Differential Evolution algorithm adapted to that problem, and we compare it with two well-known algorithms: the Simplicial Subdivision and the Lemke-Howson. The problem of finding the Nash equilibrium for two players games may be classified as a continuous problem, where two probability distributions over the set of pure strategies of both players should be found. Each deviation from the global optimum is interpreted as the Nash approximation and called the ε-Nash equilibrium. We show that the Differential Evolution approach can be determined as a method, which in successive iterations is capable of obtaining ε value close to the global optimum. We show, that the Differential Evolution may be succesfully used to obtain satisfactory results and it may be easily expanded into n-person games. Moreover, we present results for the problem of computing Nash equilibrium, when some arbitrary set strategies have a non-zero probability of being chosen.