Incentive compatibility in kidney exchange problems

The problem of kidney exchanges shares common features with the classical problem of exchange of indivisible goods studied in the mechanism design literature, while presenting additional constraints on the size of feasible exchanges. The solution of a kidney exchange problem can be summarized in a mapping from the relevant underlying characteristics of the players (patients and their donors) to the set of matchings. The goal is to select only matchings maximizing a chosen welfare function. Since the final outcome heavily depends on the private information in possess of the players, a basic requirement in order to reach efficiency is the truthful revelation of this information. We show that for the kidney exchange problem, a class of (in principle) efficient mechanisms does not enjoy the incentive compatibility property and therefore is subject to possible manipulations made by the players in order to profit of the misrepresentation of their private information.