Multidimensional auction models in supply contracts

We consider multidimensional auctions for procurement in supply chain settings. A buyer uses a reserves auction to determine which supplier will be awarded the supply contract. Demand distribution are common knowledge, however the buyer only knows the prior distribution of supplier's, cost parameters such as unit. production cost and salvage value. Two types of multidimensional, contracts are considered in this paper. In quantity flexibility contract, each supplier will bid wholesale price and quantity flexibility; in buy-back contract, each supplier will bid wholesale price and buy-back price. The expected utility of the buyer is a function of both terms in a bid. The buyer selects the winner according to the scoring rule. We show that by revealing the buyer's true utility function as the scoring rule, supply chain is always coordinated by the suppliers' bids.