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Goods Revenue Monotonicity in Combinatorial Auctions

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  • Muto, Nozomu
  • Yasuhiro, Shirata

Abstract

We study a new monotonicity problem in combinatorial auctions called goods revenue monotonicity, which requires that the auctioneer earn no more revenue by dropping goods from the endowments. Although no mechanism satisfies goods revenue monotonicity together with strategy-proofness, efficiency, and participation even in the domain of substitute valuations, we find a restricted domain called per-capita goodsbidder submodular domain in which there exists a goods revenue monotone mechanism satisfying the above three conditions. The restriction is likely to be met when bidders’ valuations are similar. Finally, we provide a relation to the monopoly theory, and argue that per-capita goods-bidder submodularily is independent of the standard elasticity argument.

Suggested Citation

  • Muto, Nozomu & Yasuhiro, Shirata, 2013. "Goods Revenue Monotonicity in Combinatorial Auctions," Discussion Papers 2013-13, Graduate School of Economics, Hitotsubashi University.
  • Handle: RePEc:hit:econdp:2013-13
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    File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/25908/1/070econDP13-13.pdf
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    References listed on IDEAS

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    1. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, December.
    2. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    3. Holmstrom, Bengt, 1979. "Groves' Scheme on Restricted Domains," Econometrica, Econometric Society, vol. 47(5), pages 1137-1144, September.
    4. Laurent Lamy, 2010. "Core-selecting package auctions: a comment on revenue-monotonicity," International Journal of Game Theory, Springer;Game Theory Society, pages 503-510.
    5. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    6. Olszewski, Wojciech & Chung, Kim-Sau, 2007. "A non-differentiable approach to revenue equivalence," Theoretical Economics, Econometric Society, vol. 2(4), December.
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