Mechanism design and bounded rationality: The case of type misreporting

• Study the effects of bounded rationality in mechanism design problems.
• Players behave as if their types were in a neighborhood of their true types.
• The designer wants to know how such perturbations affect outcomes.
• In quasi-linear utilitarian environments the designer’s loss is of square order.
• Only constant social choice functions are completely immune to the perturbations.

In this paper we study the effects of bounded rationality in mechanism design problems. We model bounded rationality by assuming that in the presence of an incentive compatible mechanism, players behave as if their types were in a δδ-neighborhood of their true types. In our results, we explore what are the effects of such bounded rationality in the outcomes of the mechanism design problem. To such end, we characterize the social choice functions that are robust to the δδ-perturbations in the sense that the designers’ loss is at most of order δkδk for a certain kk. A notable finding is that in quasi-linear utilitarian environments the designer’s loss is of order of δ2δ2. We illustrate the applicability of our results by means of examples.