The choice of the number of varieties: Justifying simple mechanisms

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.