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Dynamic Mechanism Design: Incentive Compatibility, Profit Maximization and Information Disclosure

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  • Alessandro Pavan
  • Ilya Segal
  • Juuso Toikka

Abstract

We examine the design of incentive-compatible screening mechanisms for dynamic environments in which the agents types follow a (possibly non-Markov) stochastic process, decisions may be made over time and may affect the type process, and payoffs need not be time-separable. We derive a formula for the derivative of an agent’s equilibrium payoff with respect to his current type in an incentive-compatible mechanism, which summarizes all first-order conditions for incentive compatibility and generalizes Mirrlees’s envelope formula of static mechanism design. We provide conditions on the environment under which this formula must hold in any incentive-compatible mechanism. When specialized to quasi-linear environments, this formula yields a dynamic “revenue-equivalence result and an expression for dynamic virtual surplus, which is instrumental for the design of optimal mechanisms. We also provide some sufficient conditions for incentive compatibility, and for its robustness to an agent’s observation of the other agents’ past and future types. We apply these results to a number of novel settings, including the design of profit-maximizing auctions and durable-good selling mechanisms for buyers whose values follow an AR(k) process.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1501.

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Date of creation: 08 May 2009
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Handle: RePEc:nwu:cmsems:1501

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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Keywords: asymmetric information; stochastic processes; incentives JEL Classification Numbers: D82; C73; L1;

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Cited by:
  1. Deb, Rahul, 2008. "Optimal Contracting Of New Experience Goods," MPRA Paper 9880, University Library of Munich, Germany.
  2. Marco LiCalz & Alessandro Pavan, 2002. "Tilting the Supply Schedule to Enhance Competition on Uniform-Price Auctions," Discussion Papers 1495, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Auray, Stéphane & Mariotti, Thomas & Moizeau, Fabien, 2007. "Dynamic Regulation of Quality," IDEI Working Papers 397, Institut d'Économie Industrielle (IDEI), Toulouse.
  4. Said, Maher, 2012. "Auctions with dynamic populations: Efficiency and revenue maximization," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2419-2438.
  5. George-Marios Angeletos & Alessandro Pavan, 2006. "Socially Optimal Coordination: Characterization and Policy Implications," NBER Working Papers 12778, National Bureau of Economic Research, Inc.
  6. Daniel Garrett & Alessandro Pavan, 2009. "Dynamic Managerial Compensation: a Mechanism Design Approach," Carlo Alberto Notebooks 127, Collegio Carlo Alberto.
  7. Daniel F. Garrett & Alessandro Pavan, 2012. "Managerial Turnover in a Changing World," Journal of Political Economy, University of Chicago Press, vol. 120(5), pages 879 - 925.

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