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Collusive Communication Schemes in a First-Price Auction

We study optimal bidder collusion at first-price auctions when the collusive mechanism only relies on signals about bidders’ valuations. We build on Fang and Morris (2006) when two bidders have low or high private valuation of a single object and additionally each receives a private noisy signal from an incentiveless center about the opponent’s valuation. We derive the unique symmetric equilibrium of the first price auction for any symmetric, possibly correlated, distribution of signals, when these can only take two values. Next, we find the distribution of 2-valued signals, which maximizes the joint payoffs of bidders. We prove that allowing signals to take more than two values will not increase bidders’ payoffs if the signals are restricted to be public. We also investigate the case when the signals are chosen conditionally independently and identically out of n = 2 possible values. We demonstrate that bidders are strictly better off as signals can take on more and more possible values. Finally, we look at another special case of the correlated signals, namely, when these are independent of the bidders’ valuations. We show that in any symmetric 2-valued strategy correlated equilibrium, the bidders bid as if there were no signals at all and, hence, are not able to collude.

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Paper provided by Cardiff University, Cardiff Business School, Economics Section in its series Cardiff Economics Working Papers with number E2012/11.

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Length: 50 pages
Date of creation: May 2012
Date of revision:
Handle: RePEc:cdf:wpaper:2012/11
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  1. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  2. Kaplan, Todd R, 2008. "Communication of Preferences in Contests for Contracts," MPRA Paper 18696, University Library of Munich, Germany, revised 08 Aug 2009.
  3. Vasiliki Skreta, 2007. "On the Informed Seller Problem: Optimal Information Disclosure," Levine's Bibliography 122247000000001789, UCLA Department of Economics.
  4. FORGES, Françoise, . "An approach to communication equilibria," CORE Discussion Papers RP 721, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. McAfee, R Preston & McMillan, John, 1992. "Bidding Rings," American Economic Review, American Economic Association, vol. 82(3), pages 579-99, June.
    • McAfee, R. Preston & McMillan, John., 1990. "Bidding Rings," Working Papers 726, California Institute of Technology, Division of the Humanities and Social Sciences.
  6. Antonio Miralles, 2010. "Self-enforced collusion through comparative cheap talk in simultaneous auctions with entry," Economic Theory, Springer, vol. 42(3), pages 523-538, March.
  7. Fang, Hanming & Morris, Stephen, 2006. "Multidimensional private value auctions," Journal of Economic Theory, Elsevier, vol. 126(1), pages 1-30, January.
  8. Xavier Vives, 1990. "Trade Association Disclosure Rules, Incentives to Share Information, and Welfare," RAND Journal of Economics, The RAND Corporation, vol. 21(3), pages 409-430, Autumn.
  9. Yoon, Kiho, 2011. "Optimal mechanism design when both allocative inefficiency and expenditure inefficiency matter," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 670-676.
  10. Condorelli, Daniele, 2012. "What money canʼt buy: Efficient mechanism design with costly signals," Games and Economic Behavior, Elsevier, vol. 75(2), pages 613-624.
  11. Francoise Forges, 2006. "Correlated equilibrium in games with incomplete information revisited," Post-Print hal-00360743, HAL.
  12. Cotter, Kevin D., 1991. "Correlated equilibrium in games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 48-68, June.
  13. FORGES, Françoise, . "Five legitimate definitions of correlated equilibrium in games with incomplete informations," CORE Discussion Papers RP 1071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Giuseppe Lopomo & Leslie Marx & Peng Sun, 2011. "Bidder collusion at first-price auctions," Review of Economic Design, Springer, vol. 15(3), pages 177-211, September.
  15. Daniel Quint, 2010. "Looking smart versus playing dumb in common-value auctions," Economic Theory, Springer, vol. 44(3), pages 469-490, September.
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