Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/144693
Authors: 
Sziklai, Balázs
Segal-Halevi, Erel
Year of Publication: 
2015
Series/Report no.: 
IEHAS Discussion Papers MT-DP - 2015/52
Abstract: 
We study the monotonicity properties of solutions in the classic problem of fair cake-cutting - dividing a single heterogeneous resource among agents with subjective utilities. 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 all are worse-off (if there is less to share). We formally introduce these concepts to the cakecutting setting and present a meticulous axiomatic analysis. We show that classical cakecutting protocols, like the Cut and Choose, Banach-Knaster, Dubins-Spanier and many other fail to be monotonic. We also show that, when the allotted pieces must be contiguous, proportionality and Pareto-optimality are incompatible with each of the monotonicity axioms. We provide a resource-monotonic protocol for two players and show the existence of rules that satisfy various combinations of contiguousness, proportionality, Pareto-optimality and the two monotonicity axioms.
Subjects: 
resource-monotonicity
population-monotonicity
cake-cutting
leximin divisions
equitable divisions
JEL: 
D63
ISBN: 
978-615-5594-18-2
Document Type: 
Working Paper

Files in This Item:
File
Size
719.99 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.