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Nonmonotone Mechanism Design

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  • Levent Ulku

    () (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM))

Abstract

I characterize the set of implementable allocation functions in the standard one dimensional mechanism design environment where the relationship between private information and payoffs is possibly non-monotone. The characterization is useful in two aspects. First it leads to a rather mild condition under which individual rationality follows directly from incentive compatibility. Second, it can be conveniently used to determine the implementability of allocation functions in certain novel applications. In particular I show that neither monotonicity of allocations, nor the monotone differences property on values is necessary for implementation. In an application, I study a buyer-seller relationship where the buyer’s value displays habit formation, which enters into his payoff through a commonly known parameter. Habit implies that the agent’s value is a nonmonotone function of his type and that monotone diferences condition can not be satisfied for all parameters. For a set of parameters, the seller-optimal mechanism is nonmonotone: the seller screens out low and high types.

Suggested Citation

  • Levent Ulku, 2012. "Nonmonotone Mechanism Design," Working Papers 1202, Centro de Investigacion Economica, ITAM.
  • Handle: RePEc:cie:wpaper:1202
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    File URL: http://ftp.itam.mx/pub/academico/inves/ulku/12-02.pdf
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    References listed on IDEAS

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    1. Matthews, Steven & Moore, John, 1987. "Monopoly Provision of Quality and Warranties: An Exploration in the Theory of Multidimensional Screening," Econometrica, Econometric Society, vol. 55(2), pages 441-467, March.
    2. Fernando Branco, 1996. "Multiple unit auctions of an indivisible good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 77-101.
    3. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-1259, September.
    4. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9781107004368, May.
    5. Garcia, Diego, 2005. "Monotonicity in direct revelation mechanisms," Economics Letters, Elsevier, vol. 88(1), pages 21-26, July.
    6. Sushil Bikhchandani & Shurojit Chatterji & Ron Lavi & Ahuva Mu'alem & Noam Nisan & Arunava Sen, 2006. "Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation," Econometrica, Econometric Society, vol. 74(4), pages 1109-1132, July.
    7. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-361, March.
    8. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-1119, July.
    9. Vohra,Rakesh V., 2011. "Mechanism Design," Cambridge Books, Cambridge University Press, number 9780521179461, May.
    10. Mookherjee, Dilip & Reichelstein, Stefan, 1992. "Dominant strategy implementation of Bayesian incentive compatible allocation rules," Journal of Economic Theory, Elsevier, vol. 56(2), pages 378-399, April.
    11. Dirk Bergemann & Juuso Valimaki, 2002. "Information Acquisition and Efficient Mechanism Design," Econometrica, Econometric Society, vol. 70(3), pages 1007-1033, May.
    12. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
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    More about this item

    Keywords

    Implementation; Monotonicity; Monotone differences; Habits;

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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