A cake is a metaphor for a heterogeneous, divisible good. When two players divide such a good, there is always a perfect division—one that is efficient (Pareto-optimal), envy-free, and equitable—which can be effected with a finite number of cuts under certain mild conditions; this is not...

Barbanel, Brams, and Stromquist (2009) asked whether there exists a two-person moving-knife procedure that yields an envy-free, undominated, and equitable allocation of a pie. We present two procedures: One yields an envy-free, almost undominated, and almost equitable allocation, whereas the...

Cutting a cake -- or any heterogeneous, divisible good -- fairly has received much attention in recent years, but fair division of a pie into wedge-shaped sectors has received far less. Whereas cake-cutting is applicable to land division, pie-cutting is more applicable to the division of an...

A cake is a metaphor for a heterogeneous, divisible good. When two players divide such a good, there is always a perfect division — one that is efficient (Pareto-optimal), envy-free, and equitable — which can be effected with a finite number of cuts under certain mild conditions; this is not...

Barbanel, Brams, and Stromquist (2009) asked whether there exists a two-person moving-knife procedure that yields an envy-free, undominated, and equitable allocation of a pie. We present two procedures: One yields an envy-free, almost undominated, and almost equitable allocation, whereas the...

Is there a division among n players of a cake using n-1 parallel vertical cuts, or of a pie using n radial cuts, that is envy-free (each player thinks he or she receives a largest piece and so does not envy another player) and undominated (there is no other allocation as good for all players and...