Who’s Afraid of Strategic Behavior? Mechanisms for Group Purchasing

Abstract

We study mechanisms to manage group purchasing among a set of buyers of a given product with a concave purchase cost function. The buyers are cost‐sensitive and willing to buy a range of product quantities at different prices. We investigate two types of mechanisms that can be used by a group purchasing organization (GPO): (a) ordering mechanisms where the buyers, without divulging private information, choose their order quantities and pay for them according to a given cost‐sharing rule or a fixed price; and (b) bidding mechanisms where the buyers announce their valuations for different quantities and the GPO determines their purchase quantities and cost‐shares according to pre‐announced schemes. Under the choice of appropriate cost‐sharing rules, we introduce a sequential joint ordering mechanism and a family of ordering strategies under which some buyers’ strategic deviations never worsen other buyers. We propose a class of bidding mechanisms with some desirable properties and show that a Nash equilibrium bid schedule always exists wherein all buyers’ profits are at least as high as those under truthful bidding. In our proposed mechanisms, some buyers’ strategic deviation from truthful bidding can only make the others better off. Thus, buyers need not worry about strategic behavior of their counterparts. We compare the performances of the system under different mechanisms and show the superiority of our proposed bidding mechanism. We show that the profits generated by our proposed bidding mechanisms under the proportional cost‐sharing rule are never dominated by the maximum profits of the first‐best fixed price.