Moving-knife procedure

In the mathematics of social science, and especially game theory, a moving-knife procedure is a type of solution to the fair division problem. The canonical example is the division of a cake using a knife.

The simplest example is a moving-knife equivalent of the I cut, you choose scheme, first described by A.K.Austin as a prelude to his own procedure:

(This procedure is not necessarily efficient.)

Generalizing this scheme to more than two players cannot be done by a discrete procedure without sacrificing envy-freeness.

Examples of moving-knife procedures include