In the mathematics of

social science Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of soc ...

, and especially game theory, a moving-knife procedure is a type of solution to the

fair division Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. That problem arises in various real-world settings such as division of i ...

problem. The canonical example is the division of a

cake Cake is a flour confection made from flour, sugar, and other ingredients, and is usually baked. In their oldest forms, cakes were modifications of bread, but cakes now cover a wide range of preparations that can be simple or elaborate, ...

using a

knife A knife ( : knives; from Old Norse 'knife, dirk') is a tool or weapon with a cutting edge or blade, usually attached to a handle or hilt. One of the earliest tools used by humanity, knives appeared at least 2.5 million years ago, as evide ...

. 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: * 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. (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-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 Webb most often refers to James Webb Space Telescope which is named after James E. Webb, second Administrator of NASA. It may also refer to: Places Antarctica *Webb Glacier (South Georgia) * Webb Glacier (Victoria Land) *Webb Névé, Victoria L ...

References

{{game theory Cake-cutting