George Christodoulou
Abstract
We study the price of anarchy (PoA) of simultaneous first-price auctions (FPAs) for buyers with submodular and subadditive valuations. The current best upper bounds for the Bayesian price of anarchy (BPoA) of these auctions are e/(e − 1) [Syrgkanis and Tardos 2013] and 2 [Feldman et al. 2013], respectively. We provide matching lower bounds for both cases even for the case of full information and for mixed Nash equilibria via an explicit construction. We present an alternative proof of the upper bound of e/(e − 1) for FPAs with fractionally subadditive valuations that reveals the worst-case price distribution, which is used as a building block for the matching lower bound construction.
We generalize our results to a general class of item bidding auctions that we call bid-dependent auctions (including FPAs and all-pay auctions) where the winner is always the highest bidder and each bidder’s payment depends only on his own bid.
Finally, we apply our techniques to discriminatory price multiunit auctions. We complement the results of de Keijzer et al. [2013] for the case of subadditive valuations by providing a matching lower bound of 2. For the case of submodular valuations, we provide a lower bound of 1.109. For the same class of valuations, we were able to reproduce the upper bound of e/(e − 1) using our nonsmooth approach.
- Michael R. Baye, Dan Kovenock, and Casper G. de Vries. 1996. The all-pay auction with complete information. Economic Theory 8, 2, 291--305.Google Scholar
Cross Ref
- Kshipra Bhawalkar and Tim Roughgarden. 2011. Welfare guarantees for combinatorial auctions with item bidding. In Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms. Google ScholarDigital Library
- Kshipra Bhawalkar and Tim Roughgarden. 2012. Simultaneous single-item auctions. In Internet and Network Economics. Lecture Notes in Computer Science, Vol. 7695. Springer, 337--349. Google ScholarDigital Library
- Sushil Bikhchandani. 1999. Auctions of heterogeneous objects. Games and Economic Behavior 26, 193--220.Google ScholarCross Ref
- Michal Bresky. 2008. Pure Equilibrium Strategies in Multi-Unit Auctions with Private Value Bidders. CERGE-EI Working Papers wp376. The Center for Economic Research and Graduate Education, Economic Institute, Prague. http://ideas.repec.org/p/cer/papers/wp376.html.Google Scholar
- Ioannis Caragiannis, Christos Kaklamanis, Panagiotis Kanellopoulos, and Maria Kyropoulou. 2011. On the efficiency of equilibria in generalized second price auctions. In Proceedings of the 12th ACM Conference on Electronic Commerce. ACM, New York, NY, 81--90. Google ScholarDigital Library
- Shuchi Chawla and Jason D. Hartline. 2013. Auctions with unique equilibria. In Proceedings of the ACM Conference on Electronic Commerce. 181--196. Google ScholarDigital Library
- Shuchi Chawla, Jason D. Hartline, David L Malec, and Balasubramanian Sivan. 2010. Multi-parameter mechanism design and sequential posted pricing. In Proceedings of the 42nd ACM Symposium on Theory of Computing (STOC’10). Google ScholarDigital Library
- George Christodoulou, Annamária Kovács, and Michael Schapira. 2008. Bayesian combinatorial auctions. In Proceedings of the 35th International Colloquium on Automata, Languages, and Programming, Part I (ICALP’08). Google ScholarDigital Library
- George Christodoulou, Annamária Kovács, Alkmini Sgouritsa, and Bo Tang. 2013. Tight bounds for the price of anarchy of simultaneous first price auctions. arXiv:1312.2371 Google ScholarDigital Library
- Edward H. Clarke. 1971. Multipart pricing of public goods. Public Choice 11, 1, 17--33.Google ScholarCross Ref
- Bart de Keijzer, Evangelos Markakis, Guido Schäfer, and Orestis Telelis. 2013. Inefficiency of standard multi-unit auctions. In Algorithms—ESA 2013. Lecture Notes in Computer Science, Vol. 8125. Springer, 385--396. DOI:http://dx.doi.org/10.1007/978-3-642-40450-4_33Google Scholar
- Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz. 2007. Internet advertising and the generalized second-price auction: Selling billions of dollars worth of keywords. American Economic Review 97, 1, 242--259. http://ideas.repec.org/a/aea/aecrev/v97y2007i1p242-259.html.Google ScholarCross Ref
- Uriel Feige. 2006. On maximizing welfare when utility functions are subadditive. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing (STOC’06). Google ScholarDigital Library
- Uriel Feige and Jan Vondrák. 2010. The submodular welfare problem with demand queries. Theory of Computing 6, 1, 247--290. DOI:http://dx.doi.org/10.4086/toc.2010.v006a011Google ScholarCross Ref
- Michal Feldman, Hu Fu, Nick Gravin, and Brendan Lucier. 2013. Simultaneous auctions are (almost) efficient. In Proceedings of the 45th Symposium on Theory of Computing (STOC’13). Google ScholarDigital Library
- Hu Fu, Robert D. Kleinberg, and Ron Lavi. 2012. Conditional equilibrium outcomes via ascending price processes with applications to combinatorial auctions with item bidding. In Proceedings of the 13th ACM Conference on Electronic Commerce (EC’12). ACM, New York, NY. Google ScholarDigital Library
- Theodore Groves. 1973. Incentives in teams. Econometrica 41, 4, 617--663.Google ScholarCross Ref
- Jason D. Hartline and Tim Roughgarden. 2009. Simple versus optimal mechanisms. In Proceedings of the 10th ACM Conference on Electronic Commerce (EC’09). Google ScholarDigital Library
- Avinatan Hassidim, Haim Kaplan, Yishay Mansour, and Noam Nisan. 2011. Non-price equilibria in markets of discrete goods. In Proceedings of the 12th ACM Conference on Electronic Commerce (EC’11). ACM, New York, NY. Google ScholarDigital Library
- Elias Koutsoupias and Christos Papadimitriou. 1999. Worst-case equilibria. In Proceeding of 26th International Symposium on Theoretical Aspects of Computer Science (STACS’99). Google ScholarDigital Library
- Vijay Krishna. 2002. Auction Theory. Academic Press.Google Scholar
- Alessandro Lizzeri and Nicola Persico. 2000. Uniqueness and existence of equilibrium in auctions with a reserve price. Games and Economic Behavior 30, 1, 83--114.Google ScholarCross Ref
- Brendan Lucier and Allan Borodin. 2010. Price of anarchy for greedy auctions. In Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms. 537--553. Google ScholarDigital Library
- Brendan Lucier and Renato Paes Leme. 2011. GSP auctions with correlated types. In Proceedings of the 12th ACM Conference on Electronic Commerce (EC’11). Google ScholarDigital Library
- Evangelos Markakis and Orestis Telelis. 2012. Uniform price auctions: Equilibria and efficiency. In Proceedings of the 5th International Conference on Algorithmic Game Theory (SAGT’12). 227--238. Google ScholarDigital Library
- Paul Milgrom. 2000. Putting auction theory to work: The simultaneous ascending auction. Journal of Political Economy 108, 2, 245--272.Google ScholarCross Ref
- Noam Nisan and Amir Ronen. 1999. Algorithmic mechanism design (extended abstract). In Proceedings of the 31st Annual ACM Symposium on Theory of Computing (STOC’99). 129--140. Google ScholarDigital Library
- Noam Nisan and Amir Ronen. 2000. Computationally feasible VCG-based mechanisms. In Proceedings of the ACM Conference on Electronic Commerce. Google ScholarDigital Library
- Noam Nisan and Ilya Segal. 2006. The communication requirements of efficient allocations and supporting prices. Journal of Economic Theory 129, 1, 192--224. DOI:http://dx.doi.org/10.1016/j.jet.2004.10.007Google ScholarCross Ref
- Renato Paes Leme and Éva Tardos. 2010. Pure and Bayes-Nash price of anarchy for generalized second price auction. In Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS’10). 735--744. Google ScholarDigital Library
- Tim Roughgarden. 2012. The price of anarchy in games of incomplete information. In Proceedings of the 13th ACM Conference on Electronic Commerce (EC’12). Google ScholarDigital Library
- Tim Roughgarden. 2014. Barriers to near-optimal equilibria. In Proceedings of the 55th Annual IEEE Symposium on Foundations of Computer Science (FOCS’14). Google ScholarDigital Library
- Vasilis Syrgkanis and Eva Tardos. 2013. Composable and efficient mechanisms. In Proceedings of the 45th Symposium on Theory of Computing (STOC’13). Google ScholarDigital Library
- Hal R. Varian. 2007. Position auctions. International Journal of Industrial Organization 25, 6, 1163--1178.Google ScholarCross Ref
- William Vickrey. 1961. Counterspeculation, auctions, and competitive sealed tenders. Journal of Finance 16, 1, 8--37.Google ScholarCross Ref
Index Terms
- Tight Bounds for the Price of Anarchy of Simultaneous First-Price Auctions
Recommendations
Uniform Price Auctions: Equilibria and Efficiency
We study the Uniform Price Auction, one of the standard sealed-bid multi-unit auction formats in Auction Theory, for selling multiple identical units of a single good to multi-demand bidders. Contrary to the truthful and efficient multi-unit Vickrey ...
On the efficiency of equilibria in generalized second price auctions
EC '11: Proceedings of the 12th ACM conference on Electronic commerceIn sponsored search auctions, advertisers compete for a number of available advertisement slots of different quality. The auctioneer decides the allocation of advertisers to slots using bids provided by them. Since the advertisers may act strategically ...
A dynamic axiomatic approach to first-price auctions
EC '13: Proceedings of the fourteenth ACM conference on Electronic commerceThe first-price auction is popular in practice for its simplicity and transparency. Moreover, its potential virtues grow in complex settings where incentive compatible auctions may generate little or no revenue. Unfortunately, the first-price auction is ...
Comments