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Efficiency and Revenue in Asymmetric Auctions

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We study the efficiency and revenue properties of first- and second-price auctions in an environment where bidders’ values are drawn from different binary distributions. We identify a necessary and sufficient condition for a first-price auction to induce an efficient allocation. The condition reveals the source of allocative inefficiencies in asymmetric firstprice auctions. We further show that the seller’s revenue is higher in a second-price auction than it is in a first-price auction whenever allocations in the two auction formats are efficient. We highlight how the difference in different bidder types’ beliefs induces the results.

Abstract

We study the efficiency and revenue properties of first- and second-price auctions in an environment where bidders’ values are drawn from different binary distributions. We identify a necessary and sufficient condition for a first-price auction to induce an efficient allocation. The condition reveals the source of allocative inefficiencies in asymmetric firstprice auctions. We further show that the seller’s revenue is higher in a second-price auction than it is in a first-price auction whenever allocations in the two auction formats are efficient. We highlight how the difference in different bidder types’ beliefs induces the results.

참고문헌 (13)

  1. Cheng, H, "Ranking Sealed High-Bid and Open Asymmetric Auctions", Journal of Mathematical Economics, 42, pp.471~498 (2006)
  2. Doni, N, "Revenue Comparison in Asymmetric Auctions with Discrete Valuations", BE Journal of Theoretical Economics, 13, pp.429~461 (2013)
  3. Fibich, G, "Revenue Equivalence in Asymmetric Auctions", Journal of Economic Theory, 115, pp.309~321 (2004)
  4. Gavious, A, "Ranking Asymmetric Auctions", International Journal of Game Theory, 43, pp.369~393 (2014)
  5. Hubbard, T. P, "Asymmetric Auctions with More than Two Bidders", ~ (2015)
  6. Kaplan, T. R, "Asymmetric First-Price Auctions with Uniform Distributions : Analytical Solutions to the General Case", Economic Theory, 50, pp.269~302 (2012)
  7. Kirkegaard, R, "A Mechanism Design Approach to Ranking Asymmetric Auctions", Econometrica, 80, pp.2349~2364 (2012)
  8. Kirkegaard, R, "Ranking Asymmetric Auctions with Two Groups of Bidders", ~ (2016)
  9. Lebru, B, "First Price Auctions in the Asymmetric N Bidder Case", International Economic Review, 40, pp.125~142 (1999)
  10. Lebrun, B, "Uniqueness of the Equilibrium in First-price Auctions", Games and Economic Behavior, 55, pp.131~151 (2006)
  11. Maskin, E, "Auction Theory with Private Values", American Economic Review, 72, pp.150~155 (1985)
  12. Maskin, E, "Asymmetric Auctions", Review of Economic Studies, 67, pp.413~438 (2000)
  13. Plum, M, "Characterization and Computation of Nash-Equilibria for Auctions with Incomplete Information", International Journal of Game Theory, 20, pp.393~418 (1992)

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