Two-stage Minimum Cost Spanning Tree Game under Fuzzy Optimistic Coalition

Abstract

This paper discusses the problem of cost allocation when players have different levels of optimism based on the two-stage minimum spanning tree game, and uses Choquet integral to calculate the characteristic function of fuzzy optimistic coalition and fuzzy pessimistic coalition. It is proved that the subgame of the two-stage clear optimistic coalition minimum cost spanning tree game is also a convex game. Finally, an example is used to prove that the two-stage fuzzy pessimistic coalition minimum cost spanning tree game has a dynamical instability solution.