Aversion to Uncertainty and Its Implications for Revenue Maximization

Most work in mechanism design assumes that buyers are risk neutral; some considers risk aversion arising due to a non-linear utility for money. Yet behavioral studies have established that real agents exhibit risk attitudes which cannot be captured by any expected utility model. We initiate the study of revenue-optimal mechanisms under buyer behavioral models beyond expected utility theory. We adopt a model from prospect theory which arose to explain these discrepancies and incorporates agents under-weighting uncertain outcomes. In our model, an event occurring with probability x < 1 is worth strictly less to the agent than x times the value of the event when it occurs with certainty. In contrast to the risk-neutral setting, the optimal mechanism may be randomized and appears challenging to find, even for a single buyer and a single item for sale. Nevertheless, we give a characterization of the optimal mechanism which enables positive approximation results. In particular, we show that under a reasonable bounded-risk-aversion assumption, posted pricing obtains a constant approximation. Notably, this result is risk-robust in that it does not depend on the details of the buyer’s risk attitude. Finally, we examine a dynamic setting in which the buyer is uncertain about his future value. In contrast to positive results for a risk-neutral buyer, we show that the buyer’s risk aversion may prevent the seller from approximating the optimal revenue in a risk-robust manner. University of Wisconsin-Madison. [email protected]. Supported in part by NSF awards CCF-1320854 and CCF-1617505. University of Washington, [email protected]. Supported in part by NSF award CCF-1420381 and by a Microsoft Research PhD Fellowship. University of Wisconsin-Madison, [email protected]. Supported by a Cisco graduate fellowship. University of Texas at Austin, [email protected]. Supported in part by NSF awards CCF-1733832, CCF1350823, CCF-1216103, and CCF-1331863.