Auction-based allocation of routes in capacity-constrained networks

Abstract: We study the route-set allocation problem between end nodes in capacity-constrained flow networks with transfer costs. We introduce an origin--destination (OD) bidding language, in which a participant bids for bounded conic combinations of inlet--outlet--quantity licences and the mechanism performs the routing through a network-flow optimising winner-determination problem. We then study payment rules for the OD mechanism. Under a restricted model with openly and uniformly priced sources and bidders who are indifferent to the source of the gas, the Vickrey--Clarke--Groves (VCG) payment is core-stable; the key structural fact is that in this regime some optimal aggregate flows never use a physical pipe in both directions, so the winner-determination problem reduces to a single-commodity network flow whose value is submodular in the set of active bidders. If source access is allowed to depend on the individual consumer -- a realistic feature, e.g. when gas deals are embedded in bilateral political bargaining -- the reduction fails and VCG payments may lie strictly outside the core. For this general model we propose a dual (nodal) pricing rule derived from the shadow prices of the flow-conservation constraints, and prove it is always core-stable, at the cost of dominant-strategy incentive compatibility. Illustrative examples accompany each result.