A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems

In this paper we present an axiomatic characterization of the weighted Shapley value of the optimistic TU game associated with a minimum cost spanning tree problem. This characterization is based on two monotonicity properties, population monotonicity (if a new agent joint the society nobody is worse off) and the strong cost monotonicity (if the connection cost between any pair of agents increases nobody is better off), and weighted share of extra costs (the extra costs should be divided proportionally to the weights of the agents).