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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. Daniel Quint, 2010. "Looking smart versus playing dumb in common-value auctions," Economic Theory, Springer, vol. 44(3), pages 469-490, September.
  2. Forges, Françoise, 2006. "Correlated equilibrium in games with incomplete information revisited," Economics Papers from University Paris Dauphine 123456789/157, Paris Dauphine University.
  3. 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.
  4. Forges, F., 1984. "An approach to communication equilibria," CORE Discussion Papers 1984035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
  6. Hanming Fang, 2004. "Multidimensional Private Value Auctions," Theory workshop papers 121473000000000021, UCLA Department of Economics.
  7. Vasiliki Skreta, 2007. "On the Informed Seller Problem: Optimal Information Disclosure," Levine's Bibliography 122247000000001789, UCLA Department of Economics.
  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. 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.
  10. 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).
  11. Todd Kaplan, 2012. "Communication of preferences in contests for contracts," Economic Theory, Springer, vol. 51(2), pages 487-503, October.
  12. Kiho Yoon, 2009. "Mechanism Design with Expenditure Consideration," Discussion Paper Series 0903, Institute of Economic Research, Korea University.
  13. 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.
  14. Condorelli, Daniele, 2012. "What money canʼt buy: Efficient mechanism design with costly signals," Games and Economic Behavior, Elsevier, vol. 75(2), pages 613-624.
  15. Cotter, Kevin D., 1991. "Correlated equilibrium in games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 48-68, June.
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