Auction-based Discovery of Walrasian Equilibrium Pricing for Minimum Spanning Supply Trees

In this paper we consider a distribution network model where each edge is owned by a selfish owner agent and a customer agent wants to supply a product or service to each of the nodes in the network using the edges that result in lowest possible distribution cost, i.e., a minimum spanning supply tree. We characterize the Walrasian Equilibrium price space of such an economy and propose a descending-price auction mechanism, which discovers one of these prices following certain conditions. Finally, we study the strategic behavior of the owner agents in such an auction and show that following a greedy strategy is a Nash Equilibrium for the owner agents.