# Multi dimensional Auction in economics

I am following this paper . They have different suppliers and one buyer and They are using auction to select best suppliers Suppliers will submit. suppliers offer a multidimensional bidding on quality Q and price p. The “quality” Q includes not only the quality of the product or service but also all its nonmonetary characteristics. The buyer derives utility from a contract U(Q,p)= V(Q)− p where V(.) is the buyer's valuation function of quality Q The best suppliers will be selected using a scoring rule S(Q,p)= V(Q)− p

I am confused there . Is this scoring rule is any standard in economics to calculate bet suppliers? Or this concept comes from? any one here to help

https://onlinelibrary.wiley.com/doi/epdf/10.1002/mde.3237

From the buyer's point of view, the "best" supplier is the one who offers them the highest utility. Using the utility function for scoring suppliers seems quite natural then. (In this paper the utility function is assumed to be quasilinear in money, which is just for simplicity.)

• the question here is that scoring function is of any standard why we use this scoring function there? why we didn't use any other method like simply assigning score using Likert scale to product quality? we have quality Q of product and price p and for economics point of view we can say that its a utility function and we can write it as S(Q,p)= V(Q)− p to calculate best suppliers. ?? Apr 19 at 16:08
• I'm not sure I understand your problem. The buyer has preferences over $(Q,p)$ bundles. These induce preferences over offers, and therefore over suppliers. The utility function $U(Q,p)$ of the buyer represents these preferences. For comparing suppliers, the buyer needs a scoring function that gives preferred suppliers a higher score. By definition, the buyer's utility function does the job. Apr 20 at 6:04

There are two parts to this question: practical and theoretical.

On the practical side, scoring auctions are common in procurement. For example, here is the relevant section of procurement guidelines for the U.S. government:

(a) Proposal evaluation is an assessment of the proposal and the offeror’s ability to perform the prospective contract successfully. An agency shall evaluate competitive proposals and then assess their relative qualities solely on the factors and subfactors specified in the solicitation. Evaluations may be conducted using any rating method or combination of methods, including color or adjectival ratings, numerical weights, and ordinal rankings. The relative strengths, deficiencies, significant weaknesses, and risks supporting proposal evaluation shall be documented in the contract file.

Here is the relevant section of procurement guidelines for the state of Colorado:

(3) The invitation for competitive sealed best value bids must identify the evaluation factors upon which the award will be made. When making the award determination, the responsible officer shall evaluate the factors specified in the invitation for bids and shall not evaluate any other factors other than those specified in the invitation for bids. The factors that must be included in the invitation for bids and that the responsible officer shall consider include, but need not be limited to:

(a) The project price stated in the bid;

(b) The bidder’s design and technical approach to the public project;

...

Since multidimensional bid evaluation occurs in practice, it follows that bid scoring occurs in practice (whether or not an explicit scoring rule is given).

On the theoretical side, the question is, "Why is the scoring rule the same as the procurer's utility?" Che (1993) addresses this nicely. A procurer with commitment can credibly claim to evaluate bids in a way which does not ex post maximize its payoff. However, a procurer without commitment cannot do this: bidders know that after bids are submitted, the procurer will simply evaluate bids according to its true utility function.

It follows that the unique scoring rule without commitment is [a monotone transformation of] the procurer's utility function. Arguably, the paper you cite is implicitly making this no-commitment assumption.