Envy-Free Cake-Cutting in Two Dimensions


  • Erel Segal-Halevi Bar-Ilan University
  • Avinatan Hassidim Bar-Ilan University
  • Yonatan Aumann Bar Ilan University




cake-cutting, envy-free, two-dimensional, square, quarter-plane, fair-division, moving-knife


We consider the problem of fair division of a two dimensional heterogeneous good among several agents. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols either consider a one-dimensional resource, or allocate each agent several disconnected pieces. In practice, however, the two dimensional shape of the allotted piece is of crucial importance in many applications, e.g., squares or bounded aspect-ratio rectangles are most useful for building houses as well as advertisements. We thus introduce and study the problem of envy-free two-dimensional division wherein the utility of the agents depends on the geometric shape of the allocated pieces (as well as the location and size). In addition to envy-freeness, we require that the fraction allocated to each agent be at least a certain constant that depends only on the shape of the cake and the number of agents. We focus on the case where the allotted pieces must be square and the cakes are either squares or the unbounded plane. We provide algorithms for the problem for settings with two and three agents.




How to Cite

Segal-Halevi, E., Hassidim, A., & Aumann, Y. (2015). Envy-Free Cake-Cutting in Two Dimensions. Proceedings of the AAAI Conference on Artificial Intelligence, 29(1). https://doi.org/10.1609/aaai.v29i1.9309



AAAI Technical Track: Game Theory and Economic Paradigms