The Price of Anarchy in the Retailer's Dual-channel Supply Chain: Dominant Structure and Efficiency Loss

To quantify the efficiency of decentralized retailer's dual-channel supply chain, we characterize the worst-case efficiency loss with the price of anarchy (PoA). Two Stackelberg game frameworks respectively in manufacturer and retailer dominant structures are discussed. In equilibrium, players gain more expected profits from occupying dominant position in the retailer's dual-channel supply chain. However, the retailer's dual-channel supply chain gets the same total expected profit in the manufacturer and retailer dominant structures. That is, the PoA in two dominant structures are the same. And, some executable policies to increase total expected profit and decrease efficiency loss in the retailer's dual-channel supply chain are obtained. Numerical study displays that efficiency loss in decentralized retailer's dual-channel supply chain is at least 20% and at most 33.3%.