The price of anarchy in supply chains: quantifying the efficiency of price-only contracts

In this paper, we quantify the efficiency of decentralized supply chains that use price-only contracts. With a price-only contract, a buyer and a seller agree only on a constant transaction price, without specifying the amount that will be transferred. It is well known that these contracts do not provide incentives to the parties to coordinate their inventory/capacity decisions. We measure efficiency with the price of anarchy (PoA), defined as the largest ratio of profits between the integrated supply chain (that is, fully coordinated) and the decentralized supply chain. We characterize the efficiency of various supply chain configurations: push or pull inventory positioning, two or more stages, serial or assembly systems, single or multiple competing suppliers, and single or multiple competing retailers.