George Christodoulou
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Abstract
We study the following simple Bayesian auction setting: m items are sold to n selfish bidders in m independent second-price auctions. Each bidder has a private valuation function that specifies his or her complex preferences over all subsets of items. Bidders only have beliefs about the valuation functions of the other bidders, in the form of probability distributions. The objective is to allocate the items to the bidders in a way that provides a good approximation to the optimal social welfare value. We show that if bidders have submodular or, more generally, fractionally subadditive (aka XOS) valuation functions, every Bayes-Nash equilibrium of the resulting game provides a 2-approximation to the optimal social welfare. Moreover, we show that in the full-information game, a pure Nash always exists and can be found in time that is polynomial in both m and n.
- Noga Alon, Yuval Emek, Michal Feldman, and Moshe Tennenholtz. 2012. Bayesian ignorance. Theoretical Computer Science 452 (Sept. 2012), 1--11. DOI:http://dx.doi.org/10.1016/j.tcs.2012.05.017 Google Scholar
Digital Library
- Elliot Anshelevich, Anirban Dasgupta, Jon M. Kleinberg, Éva Tardos, Tom Wexler, and Tim Roughgarden. 2004. The price of stability for network design with fair cost allocation. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS'04). 295--304. Google ScholarDigital Library
- Kshipra Bhawalkar and Tim Roughgarden. 2011. Welfare guarantees for combinatorial auctions with item bidding. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA'11). 700--709. Google ScholarDigital Library
- Kshipra Bhawalkar and Tim Roughgarden. 2012. Simultaneous single-item auctions. In WINE’12. 337--349. Google ScholarDigital Library
- Liad Blumrosen and Noam Nisan. 2005. On the computational power of iterative auctions I: Demand queries. Discussion paper no. 381, The Center for the Study of Rationality, The Hebrew University. (2005). An extended abstract in EC’05 contained preliminary results.Google ScholarDigital Library
- Ioannis Caragiannis, Christos Kaklamanis, Panagiotis Kanellopoulos, and Maria Kyropoulou. 2011. On the efficiency of equilibria in generalized second price auctions. In Proceedings of the ACM Conference on Electronic Commerce (EC’11). 81--90. Google ScholarDigital Library
- Ioannis Caragiannis, Christos Kaklamanis, Panagiotis Kanellopoulos, Maria Kyropoulou, Brendan Lucier, Renato Paes Leme, and Éva Tardos. 2012. On the efficiency of equilibria in generalized second price auctions. CoRR abs/1201.6429 (2012). Google ScholarDigital Library
- George Christodoulou, Annamária Kovács, and Michael Schapira. 2008. Bayesian combinatorial auctions. In Proceedings of the 35th International Colloquium Automata, Languages and Programming, (ICALP’08). 820--832. 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 (2013). Google ScholarDigital Library
- Edward H. Clarke. 1971. Multipart pricing of public goods. Public Choice 11, 1 (1971), 17--33.Google ScholarCross Ref
- Bart de Keijzer, Evangelos Markakis, Guido Schäfer, and Orestis Telelis. 2013. Inefficiency of standard multi-unit auctions. In ESA(Lecture Notes in Computer Science), Hans L. Bodlaender and Giuseppe F. Italiano (Eds.), Vol. 8125. Springer, 385--396.Google Scholar
- Shahar Dobzinski. 2011. An impossibility result for truthful combinatorial auctions with submodular valuations. In Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC’11). 139--148. Google ScholarDigital Library
- Shahar Dobzinski, Noam Nisan, and Michael Schapira. 2005. Approximation algorithms for combinatorial auctionss with complement-free bidders. In Proceedings of the 37th ACM Symposium on Theory of Computing (STOC’05). Google ScholarDigital Library
- Shahar Dobzinski and Michael Schapira. 2006. An improved approximation algorithm for combinatorial auctions with submodular bidders. (2006). In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA'06). Google ScholarDigital Library
- Uriel Feige. 2006. On maximizing welfare where the utility functions are subadditive. In Proceedings of the Symposium on Theory of Computing (STOC’06). Google ScholarDigital Library
- Uriel Feige and Jan Vondrak. 2006. The Allocation Problem with Submodular Utility Functions. Manuscript.Google Scholar
- Michal Feldman, Hu Fu, Nick Gravin, and Brendan Lucier. 2013. Simultaneous auctions are (almost) efficient. In Proceedings of the Symposium on Theory of Computing Conference (STOC’13). 201--210. Google ScholarDigital Library
- Hu Fu, Robert Kleinberg, and Ron Lavi. 2012. Conditional equilibrium outcomes via ascending price processes with applications to combinatorial auctions with item bidding. In Proceedings of the ACM Conference on Electronic Commerce. 586. Google ScholarDigital Library
- Martin Gairing, Burkhard Monien, and Karsten Tiemann. 2005. Selfish routing with incomplete information. In Proceedings of the 17th Annual ACM Symposium on Parallel Algorithms (SPAA’05). 203--212. Google ScholarDigital Library
- Dinesh Garg and Yadati Narahari. 2005. Price of anarchy of network routing games with incomplete information. In Proceedings of the 1st International Workshop on Internet and Network Economics (WINE’05). 1066--1075. Google ScholarDigital Library
- Theodore Groves. 1973. Incentives in teams. Econometrica 41, 4 (1973), 617--631.Google ScholarCross Ref
- John C. Harsanyi. 1967. Games with incomplete information played by “bayesian” players, parts i ii and iii. Management Science 14 (1967), 159--182.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 ACM Conference on Electronic Commerce. 295--296. Google ScholarDigital Library
- Elias Koutsoupias and Christos Papadimitriou. 1999. Worst-case equilibria. In Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science. 404--413. Google ScholarDigital Library
- Benny Lehmann, Daniel Lehmann, and Noam Nisan. 2001. Combinatorial auctions with decreasing marginal utilities. In Proceedings of the ACM Conference on Electronic Commerce. Google ScholarDigital Library
- 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
- Brendan Lucier and Allan Borodin. 2010. Price of anarchy for greedy auctions. In Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’10). 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). San Jose, CA, USA, 71--80. Google ScholarDigital Library
- Evangelos Markakis and Orestis Telelis. 2012. Uniform price auctions: Equilibria and efficiency. In Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT’12). 227--238.Google ScholarCross Ref
- Noam Nisan. 2000. Bidding and allocation in combinatorial auctions. In Proceedings of the ACM Conference on Electronic Commerce. Google ScholarDigital Library
- Noam Nisan and Amir Ronen. 1999. Algorithmic mechanism design. In Proceedings of the Symposium on Theory of Computing Conference (STOC’99). 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
- Tim Roughgarden. 2012a. Intrinsic robustness of the price of anarchy. Communications of the ACM 55, 7 (2012), 116--123. Google ScholarDigital Library
- Tim Roughgarden. 2012b. The price of anarchy in games of incomplete information. In Proceedings of the ACM Conference on Electronic Commerce. 862--879. Google ScholarDigital Library
- Tim Roughgarden and Éva Tardos. 2002. How bad is selfish routing? Journal of the ACM 49, 2 (2002), 236--259. Google ScholarDigital Library
- Vasilis Syrgkanis and Éva Tardos. 2013. Composable and efficient mechanisms. In Proceedings of the Symposium on Theory of Computing Conference (STOC’13). 211--220. Google ScholarDigital Library
- Adrian Vetta. 2002. Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions. In FOCS. IEEE Computer Society. Google ScholarDigital Library
- William Vickrey. 1961. Counterspeculation, auctions and competitive sealed tenders. Journal of Finance 16, 1 (1961), 8--37.Google ScholarCross Ref
- Jan Vondrak. 2008. Optimal approximation for the Submodular Welfare Problem in the value oracle model. (2008). In Proceedings of the Symposium on Theory of Computing Conference (STOC’08). Google ScholarDigital Library
Index Terms
- Bayesian Combinatorial Auctions
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