Stromquist moving-knife procedure

In problems of fair division, the Stromquist moving-knife procedure is a moving-knife procedure for three players. It is named for Walter Stromquist who presented it in 1980.

In the procedure, the referee begins with his knife at the left hand side of the cake; the referee then draws the knife across the cake, from left to right. Each of the three players holds a knife, parallel to the referee's, at a position which he thinks halves the portion of the cake to the right of the referee's knife.

Any player may call "cut" at any time: the player who calls receives the part of the cake to the left of the referee's knife. The cake is then cut by the "middle" player's knife (that is, the knife that is second in order from the referee's). Of the two other (ie, non-calling) players, the one whose knife is closest to the referee's gets the middle piece, and the other player gets the rightmost piece.

The procedure is envy-free but not necessarily efficient. There is no natural generalization to more than three players.