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.
[1] 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:[2] (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