Nash Equilibrium in Stable Matching Problems

Abstract:

We consider the stable matching problem in graph theory，and find the stable matching actually follows the principal of Nash equilibrium. In addition， a program of GS algorithm for solutions is conducted. A matching problem is also given and the solution is obtained with the Matlab program. Finally, the study results are extended to the coloring problem and shortest path problem.

Key words:stable matching; Nash equilibrium; GS algorithm