Bidding in sealed-bid and English multi-attribute auctions

In this paper we consider an extension of the traditional auction mechanism, the multi-attribute auction, which enables negotiation on several attributes in addition to the price of the item. In particular, we consider a procurement auction in which the buyer is the auctioneer and the sellers are the bidders. Such domains include auctions on task allocation, services, etc. We focus on three auction protocols for the case of multi-attribute items; a variation of the first-price sealed-bid protocol termed first-score sealed-bid, a variation of the second-price sealed-bid protocol termed second-score sealed-bid, and a variation of the English auction protocol termed sequential full information revelation. We analyze a specific model for these protocols and we provide optimal and stable strategies for the auctioneer agent and for the bidder agents participating in multi-attribute auctions. In addition, we analyze the auctioneer's/buyer's expected payoff and suggest an optimal scoring rule to be announced according to the protocol. Finally, we reveal that the buyer's expected payoff in all three protocols, the first-score-sealed-bid auction, the second-score sealed-bid auction and the English auction, differ only by a predefined constant. We prove that the optimal scoring rule is equal in all three protocols. This result can be interpreted as the extension of the equivalence theory of the single attribute for the case of multi-attribute items.