The simplest example is a moving-knife equivalent of the I cut, you choose scheme, sometimes known as Austin's moving-knife procedure. 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. Note that 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

• The Stromquist moving-knife procedure
• The Levmore-Cook moving knife procedure
• The Dubins-Spanier moving-knife procedure
• The Webb moving-knife procedure

References