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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

This paper examines the problem of how to design incentive-compatible mechanisms in environments in which the agents' private information evolves stochastically over time and in which decisions have to be made in each period. The environments we consider are fairly general in that the agents' types are allowed to evolve in a non-Markov way, decisions are allowed to affect the type distributions and payoffs are not restricted to be separable over time. Our first result is the characterization of a dynamic payoff formula that describes the evolution of the agents' equilibrium payoffs in an incentive-compatible mechanism. The formula summarizes all local first-order conditions taking into account how current information affects the dynamics of expected payoffs. The formula generalizes the familiar envelope condition from static mechanism design: the key difference is that a variation in the current types now impacts payoffs in all subsequent periods both directly and through the effect on the distributions of future types. First, we identify assumptions on the primitive environment that guarantee that our dynamic payoff formula is a necessary condition for incentive compatibility. Next, we specialize this formula to quasi-linear environments and show how it permits one to establish a dynamic "revenue-equivalence" result and to construct a formula for dynamic virtual surplus which is instrumental for the design of optimal mechanisms. We then turn to the characterization of sufficient conditions for incentive compatibility. Lastly, we show how our results can be put to work in a variety of applications that include the design of profit-maximizing dynamic auctions with AR(k) values and the provision of experience goods.

Suggested Citation

  • Alessandro Pavan & Ilya Segal & Juuso Toikka, 2008. "Dynamic Mechanism Design: Incentive Compatibility, Profit Maximization and Information Disclosure," Carlo Alberto Notebooks 84, Collegio Carlo Alberto.
  • Handle: RePEc:cca:wpaper:84
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    Cited by:

    1. Stéphane Auray & Thomas Mariotti & Fabien Moizeau, 2011. "Dynamic regulation of quality," RAND Journal of Economics, RAND Corporation, vol. 42(2), pages 246-265, June.
    2. repec:spr:joptap:v::y::i::d:10.1007_s10957-018-1230-8 is not listed on IDEAS
    3. LiCalzi, Marco & Pavan, Alessandro, 2005. "Tilting the supply schedule to enhance competition in uniform-price auctions," European Economic Review, Elsevier, vol. 49(1), pages 227-250, January.
    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, 2007. "Socially Optimal Coordination: Characterization and Policy Implications," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 585-593, 04-05.
    6. 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.
    7. Zhang, Jun, 2013. "Revenue maximizing with return policy when buyers have uncertain valuations," International Journal of Industrial Organization, Elsevier, vol. 31(5), pages 452-461.
    8. Xiaojun Zhao, 2015. "Optimal Income Taxations with Information Asymmetry: The Lagrange Multiplier Approach," Annals of Economics and Finance, Society for AEF, vol. 16(1), pages 199-229, May.
    9. Daniel Garrett & Alessandro Pavan, 2009. "Dynamic Managerial Compensation: A Mechanism Design Approach," 2009 Meeting Papers 375, Society for Economic Dynamics.
    10. Deb, Rahul, 2008. "Optimal Contracting Of New Experience Goods," MPRA Paper 9880, University Library of Munich, Germany.
    11. Mettral, Thomas, 2018. "Deterministic versus Stochastic Contracts in a Dynamic Principal-Agent Model," Rationality and Competition Discussion Paper Series 93, CRC TRR 190 Rationality and Competition.

    More about this item

    Keywords

    dynamic mechanisms; asymmetric information; stochastic processes; incentives;

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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