Abstract
This paper defines models of cooperation among players partitioning a completely divisible good (such as a cake or a piece of land). The novelty of our approach lies in the players’ ability to form coalitions before the actual division of the good with the aim to maximize the average utility of the coalition. A social welfare function which takes into account coalitions drives the division. In addition, we derive a cooperative game which measures the performance of each coalition. This game is compared with the game in which players start cooperating only after the good has been portioned and has been allocated among the players. We show that a modified version of the game played before the division outperforms the game played after the division.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Berliant M (1985) Equilibrium models with land: a criticism and an alternative. Reg Sci Urban Econ 15:325–340
Berliant M, Dunz K (2004) A foundation of location theory: existence of equilibrium, the welfare theorems, and core. J Math Econ 40:593–618
Berliant M, Thomson W, Dunz K (1992) On the fair division of a heterogeneous commodity. J Math Econ 21:201–216
Brams SJ (2008) Mathematics and democracy—designing better voting and fair division procedures. Princeton University Press, Princeton
Brams SJ, Taylor AD (1996) Fair division: from cake-cutting to dispute resolution. Cambridge University Press, Cambridge
Dubins L, Spanier H (1961) How to cut a cake fairly. Am Math Mon 68(1):1–17
Hill TP (1993) Partitioning inequalities in probability and statistics. In: Stochastic inequalities. IMS lecture notes, vol 22. IMS, Hayward, pp 116–132
Legut J (1990) On totally balanced games arising from cooperation in fair division. Games Econ Behav 2:47–60
Legut J, Potters JAM, Tijs S (1994) Economies with land—A game theoretical approach. Games Econ Behav 6:416–430
Legut J, Potters JAM, Tijs S (1995) A transfer property of equilibrium payoffs in economies with land. Games Econ Behav 10:355–367
Lyapunov A (1940) Sur les fonctions-vecteurs complétement additives. Bull Acad Sci USSR 4:465–478
Sprumont Y (1990) Population monotonic allocation schemes for cooperative games with transferable utility. Games Econ Behav 2:378–394
Tadenuma K, Thomson W (1995) Games of fair division. Games Econ Behav 9:191–204
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dall’Aglio, M., Branzei, R. & Tijs, S. Cooperation in dividing the cake. TOP 17, 417–432 (2009). https://doi.org/10.1007/s11750-009-0075-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-009-0075-6