Mechanisms for division problems with single-dipped preferences

A mechanism allocates one unit of an infinitely divisible commodity among agents reporting a number between zero and one. Nash, Pareto optimal Nash, and strong equilibria are analyzed for the case where the agents have single-dipped preferences. One of the main results is that when the mechanism is anonymous, monotonic, standard, and order-preserving, then the Pareto optimal Nash and strong equilibria coincide and assign Pareto optimal allocations that are egalitarian in the sense that the difference between minimal and maximal shares is minimized. This is compared to the case of single-peaked preferences, as considered in Bochet, Sakai, and Thomson (2021).

This presentation is based on joint work with Bas Dietzenbacher and Doudou Gong.

Links to the the seminar recording and the slides.