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The Design of Ambiguous Mechanisms

  • Alfredo Di Tillio
  • Nenad Kos
  • Matthias Messner

This paper considers the optimal mechanism design problem of an expected revenue maximizing principal who wants to sell a single unit of a good to an agent who is ambiguity averse in the sense of Gilboa and Schmeidler (1989). We show that the optimal static mechanism is an ambiguous mechanism. An ambiguous mechanism specifies a message space and a set of outcome functions. After showing that (a version of) the Revelation Principle holds in our environment, we give an exact characterization of the (smallest) optimal ambiguous mechanism. If the type set is composed of N (finite) types, then the (smallest) optimal ambiguous mechanism contains N - 1 outcome functions. We show that the share of the surplus that the designer can extract from the agent increases as the type set becomes larger and the probability of each single type decreases. In the limiting case where the agent’s type is drawn from a non-atomic distribution on an interval, the optimal ambiguous mechanism extracts all the rent from the agent.

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Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 446.

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Date of creation: 2012
Date of revision:
Handle: RePEc:igi:igierp:446
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  1. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
  2. Jeffrey C. Ely & Kim-Sau Chung, 2004. "Foundations of Dominant Strategy Mechanisms," Econometric Society 2004 North American Summer Meetings 169, Econometric Society.
  3. Andreas Pape & Subir Bose & Emre Ozdenoren, 2004. "Optimal auctions with ambiguity," Econometric Society 2004 North American Summer Meetings 609, Econometric Society.
  4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  5. Garrett, Daniel F., 2014. "Robustness of simple menus of contracts in cost-based procurement," Games and Economic Behavior, Elsevier, vol. 87(C), pages 631-641.
  6. Bergemann, Dirk & Schlag, Karl, 2011. "Robust monopoly pricing," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2527-2543.
  7. Lang, Matthias & Wambach, Achim, 2013. "The fog of fraud – Mitigating fraud by strategic ambiguity," Games and Economic Behavior, Elsevier, vol. 81(C), pages 255-275.
  8. Azrieli, Yaron & Teper, Roee, 2011. "Uncertainty aversion and equilibrium existence in games with incomplete information," Games and Economic Behavior, Elsevier, vol. 73(2), pages 310-317.
  9. Turocy, Theodore L., 2008. "Auction choice for ambiguity-averse sellers facing strategic uncertainty," Games and Economic Behavior, Elsevier, vol. 62(1), pages 155-179, January.
  10. Kos, Nenad & Messner, Matthias, 2013. "Extremal incentive compatible transfers," Journal of Economic Theory, Elsevier, vol. 148(1), pages 134-164.
  11. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521741231, October.
  12. Subir Bose & Arup Daripa, 2007. "A Dynamic Mechanism and Surplus Extraction Under Ambiguity," Birkbeck Working Papers in Economics and Finance 0716, Birkbeck, Department of Economics, Mathematics & Statistics.
  13. Elyakime, Bernard & Laffont, Jean-Jacques & Loisel, Patrice & Vuong, Quang, 1993. "First-Price Sealed-Bid Auctions with Secret Reservation Prices," IDEI Working Papers 27, Institut d'Économie Industrielle (IDEI), Toulouse.
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