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.)
 * One player moves the knife across the cake, conventionally from left to right.
 * The cake is cut when either player calls "stop".
 * If each player calls stop when he or she perceives the knife to be at the 50-50 point, then the first player to call stop will produce an envy-free division if the caller gets the left piece and the other player gets the right piece.

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


 * The Stromquist moving-knives procedure
 * The Austin moving-knife procedures
 * The Levmore–Cook moving-knives procedure
 * The Robertson–Webb rotating-knife procedure
 * The Dubins–Spanier moving-knife procedure
 * The Webb moving-knife procedure