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 and : Where: is the piece of cake allocated to partner ; is the value measure of partner . It is a real-valued function that, for every piece of cake, returns a number that represents the utility of partner from that piece. Usually these functions are normalized such that and for every . See the page on equitability for examples and comparison to other fairness criteria. Finding an equitable cake-cutting for two partners One cut - full revelation When there are 2 partners, it is possible to get an EQ division with a single cut, but it requires full knowledge of the partners' valuations. Assume that the cake is the interval [0,1]. For each , calculate and and plot them on the same graph. Note that the first graph is increasing from 0 to 1 and the second graph is decreasing from 1 to 0, so they have an intersection point.