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CONNECTING FAIR DIVISION AND GAME THEORY THROUGH THE OPTIMIZATION OF KNASTER'S PROCEDURE

ABSTRACT In 1945, Bronislaw Knaster proposed a procedure to divide any number of indivisible goods between a finite number of players requiring the players to place monetary values or bids on all of the goods. Often discussed in math for liberal arts courses that concentrate on contemporary applications of mathematics for non-major students, Knaster's procedure provides an opportunity to introduce optimization to students who will never take a course in calculus. A simple analysis of the procedure can lead students to determine optimal monetary bids, given the bids of the other players. More advanced students can explicitly prove these results. The optimization problem naturally leads to pure strategy Nash equilibria of Knaster's procedure when viewed as a game, thereby providing a transition between fair division procedures and game theory that can be used in both math for liberal arts courses and upper level courses.