Abstract
We study the following Bayesian setting: m items are sold to n selfish bidders in m independent second-price auctions. Each bidder has a private valuation function that expresses 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 valuation functions, then every Bayesian 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.
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References
Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: FOCS 2004, pp. 295–304 (2004)
Blumrosen, L., Nisan, N.: On the computational power of iterative auctions I: demand queries. Discussion paper no. 381, The Center for the Study of Rationality, The Hebrew University. An extended abstract in EC 2005 contained preliminary results (2005)
Clarke, E.H.: Multipart pricing of public goods. Public Choice, 17–33 (1971)
Dobzinski, S., Nisan, N., Schapira, M.: Approximation algorithms for combinatorial auctionss with complement-free bidders. In: The 37th ACM symposium on theory of computing (STOC) (2005)
Dobzinski, S., Schapira, M.: An improved approximation algorithm for combinatorial auctions with submodular bidders. In: SODA 2006 (2006)
Feige, U.: On maximizing welfare where the utility functions are subadditive. In: STOC 2006 (2006)
Feige, U., Vondrak, J.: The allocation problem with submodular utility functions (manuscript, 2006)
Gairing, M., Monien, B., Tiemann, K.: Selfish routing with incomplete information. In: Proceedings of the 17th Annual ACM Symposium on Parallel Algorithms (SPAA), pp. 203–212 (2005)
Garg, D., Narahari, Y.: Price of anarchy of network routing games with incomplete information. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, pp. 1066–1075. Springer, Heidelberg (2005)
Groves, T.: Incentives in teams. Econometrica, 617–631 (1973)
Harsanyi, J.C.: Games with incomplete information played by ’bayesian’ players, parts i ii and iii. Management science 14 (1967-1968)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, pp. 404–413 (1999)
Lehmann, B., Lehmann, D., Nisan, N.: Combinatorial auctions with decreasing marginal utilities. In: ACM conference on electronic commerce (2001)
Nisan, N.: Bidding and allocation in combinatorial auctions. In: ACM Conference on Electronic Commerce (2000)
Nisan, N., Ronen, A.: Algorithmic mechanism design. In: STOC (1999)
Nisan, N., Ronen, A.: Computationally feasible vcg-based mechanisms. In: ACM Conference on Electronic Commerce (2000)
Roughgarden, T., Tardos, E.: How bad is selfish routing? Journal of the ACM 49(2), 236–259 (2002)
Vetta, A.: Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions. In: FOCS. IEEE Computer Society, Los Alamitos (2002)
Vickrey, W.: Counterspeculation, auctions and competitive sealed tenders. Journal of Finance, 8–37 (1961)
Vondrak, J.: Optimal approximation for the submodular welfare problem in the value oracle model. In: STOC 2008 (2008)
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Christodoulou, G., Kovács, A., Schapira, M. (2008). Bayesian Combinatorial Auctions. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_67
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DOI: https://doi.org/10.1007/978-3-540-70575-8_67
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