Multi-dimensional auctions under information asymmetry for costs and qualities

Papakonstantinou, A. and Bogetoft, P. (2012): Multi-dimensional auctions under information asymmetry for costs and qualities.

Abstract

This paper discusses the design of a novel multi-dimensional mechanism which allows a principal to procure a single project or an item from multiple suppliers through a two-step payment. The suppliers are capable of producing different qualities at costs which cannot exceed a certain value and the mechanism balances between the costs faced by the suppliers and the benefit the principal achieves from higher qualities. Iniatially, the principal implements a standard second score auction and allocates the project to a single supplier based its reported cost and quality, while then it elicits truthful reporting of the quality by issuing a symmetric secondary payment after observing the winner’s production. We then provide an alternate mechanism in which the principal issues an asymmetric secondary payment which rewards agents for producing higher qualities, while it penalises them for producing lower qualities than they reported. We prove that for both mechanisms truthful revelation of costs and qualities is a dominant strategy (weakly for costs) and that they are immune to combined misreporting of both qualities and costs. We also show that the mechanisms are individually rational, and that the optimal payments received by the winners of the auctions are equal to the payment issued by the standard second score auction.

• Item Type: MPRA Paper
• Language: English
• Keywords: multi-dimensional auctions, procurement, contract theory, auction theory
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D86 - Economics of Contract: Theory; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design

References

1. Che, Y-K.: Design competition through multidimensional auctions. RAND Journal of Economics 244 (1993) pp. 668–680.

2. Branco, F.: The design of multidimensional auctions. RAND Journal of Economics 281 (1997) pp. 63–81.

3. Beil, D. R. and Wein, L.: An inverse-optimization-based auction mechanism to support a multiattribute RFQ process. Management Science 4911 (2003) pp. 1529–1545.

4. Parkes, D. and Kalagnanam, J.: Models for Iterative Multiattribute Procurement Auctions. Management Science 513 (2005) pp. 435–451.

5. Bogetoft, P. and Nielsen, K.: DEA based auctions. European Journal of Operational Research 1842 (2008) pp. 685–700.

6. Charnes, A., Cooper, W. W. and Rhodes, E.: Measuring the efficiency of decision making units. European Journal of Operational Research 26 (1978) pp. 429–444.

7. Charnes, A., Cooper, W. W. and Rhodes, E.: Short Communication: Measuring the efficiency of decision making units. European Journal of Operational Research 3 (1979) pp. 339.

8. He, M., Jennings, N. R. and Leung, H.-F.: On Agent-Mediated Electronic Commerce IEEE Transactions on knowledge and data engineering154 (2003) pp. 985–1002.

9. Bichler, M.: An experimental analysis of multi-attribute auctions. Decision Support Systems 29 (2000) pp. 249–268.

10. Bichler, M. and Kalagnanam, J.: Configurable Offers andWinner Determination in Multi- Attribute Auctions European Journal of Operational Research 160 (2003) pp. 380–394.

11. Asker, J. and Cantillon, E.: Properties of scoring auctions. RAND Journal of Economics 391 (2008) pp. 69–85.