Screening with an approximate type space

Consider a standard single-agent quasilinear mechanism design problem with a potentially large type space. We wish to provide an upper bound to the principal’s payoff loss if she operates on the basis of a discrete approximation rather than the true type space. We show that, if the principal simply uses the mechanism that is optimal for the approximate type space, the loss cannot be bound even as the approximate type space converges to the true one. We propose instead the Profit-Participation algorithm, whereby the principal first computes the optimal mechanism for the approximate type but then she discounts the resulting prices in a way that is proportional to her payoff under the approximate type space for each possible allocation. We bound the principal’s payoff loss and show that it vanishes as approximate type space converges to the true one. We apply our results to situations where the principal faces: (i) computation costs; (ii) search costs; or (iii) model uncertainty.