Abstract
Inspired by Internet ad auction applications, we study the problem of allocating a single item via an auction when bidders place very different values on the item. We formulate this as the problem of prior-free auction and focus on designing a simple mechanism that always allocates the item. Rather than designing sophisticated pricing methods like prior literature, we design better allocation methods. In particular, we propose quasi-proportional allocation methods in which the probability that an item is allocated to a bidder depends (quasi-proportionally) on the bids.
We prove that corresponding games for both all-pay and winners-pay quasi-proportional mechanisms admit pure Nash equilibria and this equilibrium is unique. We also give an algorithm to compute this equilibrium in polynomial time. Further, we show that the revenue of the auctioneer is promisingly high compared to the ultimate, i.e., the highest value of any of the bidders, and show bounds on the revenue of equilibria both analytically, as well as using experiments for specific quasi-proportional functions. This is the first known revenue analysis for these natural mechanisms (including the special case of proportional mechanism which is common in network resource allocation problems).
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References
Abernethy, J., Hazan, E., Rakhlin, A.: Competing in the Dark: An Efficient Algorithm for Bandit Linear Optimization. In: COLT 2008 (2008)
Baliga, S., Vohra, R.: Market Research and Market Design (2003)
Baye, M., Kovenock, D., de Vried, C.: The all-pay auction with Complete Information. Economic Theory 8, 291–305
Che, Y., Gale, I.: Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints. Economic Letters, 373–379 (1996)
Clarke, E.: Multipart pricing of public goods. Public Choice 11, 17–33 (1971)
Even Dar, E., Mansour, Y., Nadav, U.: On the convergence of regret minimization dynamics in concave games. In: STOC 2009 (2009)
Fiat, A., Goldberg, A.V., Hartline, J.D., Karlin, A.R.: Competitive generalized auctions. In: STOC 2002, pp. 72–81 (2002)
Groves, T.: Incentives in teams. Econometrica 41(4), 617–631 (1973)
Hajek, B., Gopalakrishnan, G.: Do greedy autonomous systems make for a sensible internet? Presented at the Conference on Stochastic Networks, Stanford University (2002)
Hartline, J., Karline, A.: Profit Maximization in Mechanism Design. In: Algorithmic Game Theory (October 2007)
Johari, R., Tsitsiklis, J.N.: Efficiency loss in a network resource allocation game. Mathematics of Operations Research 29(3), 407–435 (2004)
Kalai, A., Vempala, S.: Efficient algorithms for online decision problems. J. Comput. Syst. Sci. 71(3), 291–307 (2005)
Kelly, F.: Charging and rate control for elastic traffic. European Transactions on Telecommunications 8, 33–37 (1997)
Liu, D., Chen, J.: Designing online auctions with past performance information. Decision Support Systems 42, 1307–1320 (2006)
Lu, P., Teng, S.-H., Yu, C.: Truthful Auctions with Optimal Profit. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, pp. 27–36. Springer, Heidelberg (2006)
Myerson, R.: Optimal auction design. Mathematics of Operations Research 6, 58–73 (1981)
Rosen, J.: Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 520–534 (1965)
Segal, I.: Optimal Pricing Mechanisms with Unknown Demand. American Economic Review 93(3), 509–529 (2003)
Vickrey, W.: Counterspeculation, auctions and competitive-sealed tenders. Finance 16(1), 8–37 (1961)
Zinkevich, M.: Online convex programming and generalized infinitesimal gradient ascent. In: Twentieth International Conference on Machine Learning (2003)
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Mirrokni, V., Muthukrishnan, S., Nadav, U. (2010). Quasi-Proportional Mechanisms: Prior-Free Revenue Maximization. In: López-Ortiz, A. (eds) LATIN 2010: Theoretical Informatics. LATIN 2010. Lecture Notes in Computer Science, vol 6034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12200-2_49
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DOI: https://doi.org/10.1007/978-3-642-12200-2_49
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