A Decentralized Mechanism Implementing in Nash Equilibria the Optimal Centralized Solution of a Supply-Chain Problem

Abstract

We study the coordination of production decisions for multiple products among many manufacturers and many suppliers, each with private information about its own objective and its own production capabilities. Our methodology does not require a probabilistic model of the beliefs of each decision maker (manufacturer or supplier) regarding asymmetric information. We discover a game form (decentralized mechanism) which implements in Nash Equilibria the solution of the corresponding centralized supply chain problem. In our mechanism the buyers and sellers in the supply chain submit bids/oers for the quantities they would like to buy/sell and the prices they would like other buyers/sellers to pay/receive per unit of a product. We provide rules for allocating orders and determining payments based on the bids/oers. We show that, in equilibrium, the unit price for all rms supplying a particular product is equal to the unit price for all rms buying the product. One could interpret this price as the clearing price for the product in the internal market among rms or among divisions of the same rm. Unlike prior work on coordinating rm's production and sales decisions through internal markets, our model does not require a centralized planner to set the prices in the internal markets. Instead, the clearing prices are part of the equilibrium outcome.

Keywords: Supply-chain coordination, asymmetric information, competitive/selfish traders, mechanism design, Nash implementation