Relationships Between Bankruptcy Games and Minimum Cost Spanning Tree Games

Abstract

The cost allocation problem of setting charges to the users in a given network is considered with the aid of minimum cost spanning trees in the network. In addition, the bankruptcy problem of dividing the estate of the bankrupt concern among the various creditors according to their claims is treated. The paper aims to establish that, under certain circumstances, the bankruptcy problem can be seen as a minimum cost spanning tree allocation problem. In the game theoretic setting, the paper provides the conditions on the estate and the claims which are sufficient and necessary for the representation of bankruptcy games as minimum cost spanning tree games. Finally, it is shown that a particular cost allocation rule for the minimum cost spanning tree allocation problem agrees with a certain division rule for the bankruptcy problem.