Equitable cake-cutting

Equitable (EQ) cake-cutting is a kind of a fair cake-cutting problem, in which the fairness criterion is equitability. It is a cake-allocation in which the subjective value of all partners is the same, i.e., each partner is equally happy with his/her share. Mathematically, that means that for all partners i and j:

${\displaystyle V_{i}(X_{i})=V_{j}(X_{j})}$

Where:

• ${\displaystyle X_{i}}$ is the piece of cake allocated to partner i;
• ${\displaystyle V_{i}}$ is the value measure of partner i. It is a real-valued function that, for every piece of cake, returns a number that represents the utility of partner i from that piece. Usually these functions are normalized such that ${\displaystyle V_{i}(\emptyset )=0}$ and ${\displaystyle V_{i}(EntireCake)=1}$ for every i.

See the page on equitability for examples and comparison to other fairness criteria.