Rahul Sharma (Editor)

Moving knife procedure

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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:

  • 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

    Moving-knife procedure Wikipedia
    (Text) CC BY-SA