2009/09/02 by John Cloutier, Cloutier, John, Kathryn Nyman +3 · 1 citation
Computer Science · Economics, Econometrics and Finance · #52B05 #91B32 #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Game Theory and Voting Systems #History and Overview (math.HO)
paper · pdf · doi:10.48550/arxiv.0909.0301
openalex publication_date 2009/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a generalized cake-cutting problem in which we seek to divide multiple cakes so that two players may get their most-preferred piece selections: a choice of one piece from each cake, allowing for the possibility of linked preferences over the cakes. For two players, we show that disjoint envy-free piece selections may not exist for two cakes cut into two pieces each, and they may not exist for three cakes cut into three pieces each. However, there do exist such divisions for two cakes cut into three pieces each, and for three cakes cut into four pieces each. The resulting allocations of pieces to players are Pareto-optimal with respect to the division. We use a generalization of Sperner's lemma on the polytope of divisions to locate solutions to our generalized cake-cutting problem.