ERIC Number: EJ940263
Record Type: Journal
Publication Date: 2003
Abstractor: As Provided
Reference Count: 9
Connecting Fair Division and Game Theory through the Optimization of Knaster's Procedure
Jones, Michael A.
PRIMUS, v13 n4 p321-336 2003
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.
Descriptors: Advanced Students, Game Theory, Calculus, Liberal Arts, Problem Solving, College Mathematics, Educational Strategies, Undergraduate Study, Mathematics Instruction, Teaching Methods
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Authoring Institution: N/A