Realizing fair outcomes in minimum cost spanning tree problems through non-cooperative mechanisms

In the context of minimum cost spanning tree problems, we present a bargaining mechanism for connecting all agents to the source and dividing the cost amongst them. The basic idea is very simple: we ask each agent the part of the cost he is willing to pay for an arc to be constructed. We prove that there exists a unique payoff allocation associated with the subgame perfect Nash equilibria of this bargaining mechanism. Moreover, this payoff allocation coincides with the rule defined in Bergantiños and Vidal-Puga