Characterizations of the cycle-complete and folk solutions for minimum cost spanning tree problems

Minimum cost spanning tree problems connect agents e¢ ciently to a source when agents are located at di¤erent points and the cost of using an edge is …xed. The folk and cycle-complete cost sharing solutions always o¤er core allocations. We provide similar characterizations for both. A new property is based on the following observation: when all agents have the same cost to connect to the source, we can connect one of them to the source then connect all other agents to him, as if he was the source. Cost sharing should also be done in these two steps. We also use some common properties: Core Selection, Piecewise Linearity and an independence property. The solutions are di¤erentiated by properties that apply when the cheapest edge to the source gets cheaper. Either the savings are equally distributed among all agents (folk) or the agent on that edge gets all of the savings (cycle-complete). Keywords: Minimum cost spanning tree problems; folk solution; cycle-complete solution; core. JEL Classi…cations: C71, D63