Application Of Global Minimizers Based On QPSO Algorithm In Nash Equilibria

With the fast development and globalization of economy, the circumstance of investment becomes more complex and challenging, and demand proposed by the investors becomes higher and higher, so the Nash Equilibrium model turns to be more complex. To solve the problem modeled by Nash Equilibrium, the traditional method may be with low efficiency and thus many heuristics, such as GA and Artificial Neural Network have been employed to solve the Nash Equilibrium problem while traditional methods.The purpose of this paper is to discuss a novel class of evolutionary computation technique-Swarm Intelligence Algorithm,among which the Quantum-behaved Particle Swarm Optimization (QPSO) algorithm is a recently proposed approach and is a variant of original Particle Swarm Optimization (PSO).QPSO is global convergent and will be a promising solver for complex optimization problem, which is shown by some previous work. Thus, the research of this paper will be of somewhat significance in evolutionary computation area.Because Nash equilibrium's defines itself had not certainly explained how to solves Nash equilibrium in Games ,In this thesis, firstly, we study the Particle Swarm Optimization algorithm (PSO)and Quantum-Behaved Particle Swarm Optimization (QPSO).Secondly, we study the"Stretching"technique, and combine respectively with Particle Swarm Optimization algorithm (PSO), called STQPSO, and Quantum-Behaved Particle Swarm Optimization (QPSO), called STPSO, to solve the Nash Equilibrium problems and compare their results. We find that the performances (namely the result of search, speed of convergence, stability, and so on) of QPSO are more efficiently in the field of the Nash Equilibrium than traditional PSO by emulating algorithm.At last in order to solve"Mexican hat",we used"Stretching"technique and"Repulsion"technique bind respectively with Quantum-Behaved Particle Swarm Optimization (QPSO) and compare their results. We find that the performances (namely the result of search, speed of convergence, stability, and so on) of Improved QPSO are more efficiently than traditional QPSO and single technique in the field of the Nash Equilibrium by emulate algorithm. Algorithmic simulate having testified the "Repulsion" technology being able to avoid appearing effectively "Mexican hat " phenomenon.