"Screening with an Approximate Type Space"
Publication type: Working paper
When designing institutions, we sometimes operate on the basis of approximate models of the underlying environment. Can we still achieve near-optimal solutions? We explore this issue for single-agent mechanism design problem with quasilinear preferences, where the principal knowingly uses a discrete model of the true type space. 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 model converges to the true type space. Instead, we show that solving the problem as if the model was correct is not a valid approximation.
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