Monotonicity and Competitive Equilibrium in Cake-cutting

Understand

We study the monotonicity properties of solutions in 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 problem and examine whether they are satisfied by various common division rules.