DP7900 Screening with an Approximate Type Space

Author(s): Kristóf Madarász, Andrea Prat
Publication Date: June 2010
Keyword(s): computational complexity, mechanism design, model uncertainty, nonlinear pricing, screening
JEL(s): D82
Programme Areas: Industrial Organization
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=7900

We re-visit the single-agent mechanism design problem with quasilinear preferences, but we assume that the principal knowingly operates on the basis of only an approximate type space rather than the (potentially complex) truth. We propose a two-step scheme, the profit-participation mechanism, whereby: (i) the principal `takes the model seriously' and computes the optimal menu for the approximate type space; (ii) but she discounts the price of each allocation proportionally to the profit that the allocation would yield in the approximate model. We characterize the bound to the profit loss and show that it vanishes smoothly as the distance between the approximate type space and the true type space converges to zero. Instead, we show that it is not a valid approximation to simply act as if the model was correct.