Erel Segal-Halevi, Balázs R. Sziklai (2018): Monotonicity and competitive equilibrium in cake-cutting, Economic Theory, pp 1–39 link
We study monotonicity properties of solutions to the classic problem of fair cake-cutting—dividing a heterogeneous resource among agents with different preferences. Resource- and population-monotonicity relate to scenarios where the cake, or the number of participants who divide the cake, changes. It is required that the utility of all participants change in the same direction: either all of them are better-off (if there is more to share or fewer to share among) or all are worse-off (if there is less to share or more to share among). We formally introduce these concepts to the cake-cutting setting and show that they are violated by common division rules. In contrast, we prove that the Nash-optimal rule—maximizing the product of utilities—is resource-monotonic and population-monotonic, in addition to being Pareto-optimal, envy-free and satisfying a strong competitive-equilibrium condition. Moreover, we prove that it is the only rule among a natural family of welfare-maximizing rules that is both proportional and resource-monotonic.
Challenging Science and Innovation Policy Utrecht, 1-3 June 2022, hosted by Copernicus Institute of Sustainable Development, Utrecht University The “European Forum for Studies ... Read More »
Published in ‘Does EU Membership Facilitate Convergence? The Expierience of the EU’s Eastern Enlargement – Volume II’ Edited by Landesmann, Michael, Székely, Istvan P. ... Read More »
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