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.^[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]

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

References

↑ Elisha Peterson, Francis Edward Su. "Four-Person Envy-Free Chore Division". JSTOR: Mathematics Magazine: Vol. 75, No. 2 (Apr., 2002), pp. 117-122. Retrieved 2008-03-19.
↑ Austin, A. K. (1982). "Sharing a Cake". The Mathematical Gazette. 66 (437): 212. doi:10.2307/3616548. JSTOR 3616548.

Topics in game theory

Definitions	Normal-form game Extensive-form game Escalation of commitment Graphical game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

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Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key figures	Albert W. Tucker Amos Tversky Ariel Rubinstein Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin Jean Tirole Jean-François Mertens John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Thomas Schelling William Vickrey

See also	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons Tyranny of small decisions

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