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The choice of the number of varieties: Justifying simple mechanisms

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  • Wong, Adam Chi Leung

Abstract

We study a mechanism designer’s trade-off between the complexity level and optimality level of a mechanism. While our techniques apply to a much larger class of mechanism design problems, we focus on the quality differentiation model of Mussa and Rosen (1978), restricting the monopolist to menus with at most a finite number n of varieties. We prove that (i) the marginal benefit of adding one more variety is diminishing in n; (ii) the loss from restricting the number of varieties is of order no more than 1/n2; (iii) the marginal benefit of adding one more variety is of order no more than 1/n3; and (iv) offering only two varieties can lead to more than two-thirds of the potential profit from the second best offering. Our analysis suggests that the monopolist would probably offer only a small number of varieties in the menu.

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  • Wong, Adam Chi Leung, 2014. "The choice of the number of varieties: Justifying simple mechanisms," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 7-21.
    • Handle: RePEc:eee:mateco:v:54:y:2014:i:c:p:7-21
    DOI: 10.1016/j.jmateco.2014.08.002
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    1. Kerkkamp, R.B.O. & van den Heuvel, W. & Wagelmans, A.P.M., 2019. "Robust pooling for contracting models with asymmetric information," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1036-1051.
    2. Kerkkamp, R.B.O. & van den Heuvel, W. & Wagelmans, A.P.M., 2018. "Balancing Expected and Worst-Case Utility in Contracting Models with Asymmetric Information and Pooling," Econometric Institute Research Papers EI 2018-01, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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