Welfare and Revenue Guarantees for Competitive Bundling Equilibrium
Competitive equilibrium, the central equilibrium notion in markets with indivisible goods, is based on pricing each good such that the demand for goods equals their supply and the market clears. This equilibrium notion is not guaranteed to exist beyond the narrow case of substitute goods, might result in zero revenue even when consumers value the goods highly, and overlooks the widespread practice of pricing bundles rather than individual goods. Alternative equilibrium notions proposed to address these shortcomings have either made a strong assumption on the ability to withhold supply in equilibrium, or have allowed an exponential number of prices.
In this paper we study the notion of competitive bundling equilibrium – a competitive equilibrium over the market induced by partitioning the goods into bundles. Such an equilibrium is guaranteed to exist, is succinct, and satisfies the fundamental economic condition of market clearance. We establish positive welfare and revenue guarantees for this solution concept: For welfare we show that in markets with homogeneous goods, there always exists a competitive bundling equilibrium that achieves a logarithmic fraction of the optimal welfare. We also extend this result to establish nontrivial welfare guarantees for markets with heterogeneous goods. For revenue we show that in a natural class of markets for which competitive equilibrium does not guarantee positive revenue, there always exists a competitive bundling equilibrium that extracts as revenue a logarithmic fraction of the optimal welfare. Both results are tight.
- 4.Borgs, C., Chayes, J., Immorlica, N., Mahdian, M., Saberi, A.: Multi-unit auctions with budget-constrained bidders. In: Proceedings of 7th ACM Conference on Electronic Commerce (EC) (2005)Google Scholar
- 6.Dobzinski, S., Feldman, M., Talgam-Cohen, I., Weinstein, O.: Welfare and revenue guarantees for competitive bundling equilibrium. CoRR abs/1406.0576 (2014). http://arxiv.org/abs/1406.0576
- 8.Feldman, M., Gravin, N., Lucier, B.: Combinatorial walrasian equilibrium. In: Proceedings of 44th ACM Symposium on Theory of Computing (STOC), pp. 61–70 (2013)Google Scholar
- 9.Feldman, M., Lucier, B.: Clearing markets via bundles. In: Lavi, R. (ed.) SAGT 2014. LNCS, vol. 8768, pp. 158–169. Springer, Heidelberg (2014) Google Scholar
- 15.Maskin, E., Riley, J.: Optimal multi-unit auctions. In: Hahn, F. (ed.) The Economics of Missing Markets, Information, and Games, pp. 312–335. Oxford University Press, Oxford (1989) Google Scholar
- 17.Nisan, N.: Survey: algorithmic mechanism design (through the lens of multi-unit auctions). In: Young, P., Zamir, S. (eds.) Handbook of Game Theory, vol. 4, chap. 9. Elsevier, Amsterdam (2014)Google Scholar
- 18.Parkes, D.: Iterative combinatorial auctions. In: Cramton, P., Shoham, Y., Steinberg, R. (eds.) Combinatorial Auctions, chap. 2. MIT Press, Cambridge (2006) Google Scholar
- 19.Parkes, D.C.: iBundle: an efficient ascending price bundle auction. In: Proceedings of 1st ACM Conference on Electronic Commerce (EC), pp. 148–157 (1999)Google Scholar
- 20.Parkes, D.C., Ungar, L.H.: Iterative combinatorial auctions: theory and practice. In: Proceedings of the 17th National Conference on Artificial Intelligence, AAAI 2000, pp. 74–81 (2000)Google Scholar
- 21.Parkes, D.C., Ungar, L.H.: An ascending-price generalized Vickrey auction. In: Proceedings of Stanford Institute for Theoretical Economics Workshop on The Economics of the Internet, Stanford, CA (2002)Google Scholar
- 22.Sun, N., Yang, Z.: An efficient and incentive compatible dynamic auction for multiple complements. J. Polit. Econ. (2014, to appear)Google Scholar
Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.