稳定匹配问题中的纳什均衡

Nash Equilibrium in Stable Matching Problems

摘要:

从纳什、均衡的角度出发，考虑图论中的稳定匹配问题，发现稳定匹配可以用纳什均衡理论进行直观解释.对GS算法进行编程和运用，并且列举一个匹配问题，运用Matlab编程求解最优稳定匹配.最后考虑的着色和最短路径问题也都蕴含纳什均衡的思想.

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.