CHI TIẾT NGHIÊN CỨU …

Tiêu đề

Connecting fair division and game theory through the optimization of knaster's procedure

Tác giả

Jones M.A.

Năm xuất bản

2003

Source title

PRIMUS

Số trích dẫn

DOI

10.1080/10511970308984066

Liên kết

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85023441007&doi=10.1080%2f10511970308984066&partnerID=40&md5=425991e8cc442fa475d00220d42dba79

Tóm tắt

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. © 2003 Taylor & Francis Group, LLC.

Từ khóa

Fair division; Game theory; Knaster's procedure; Optimization

Tài liệu tham khảo

Brams S.J., Taylor A.D., Fair Division: From Cake-Cutting to Dispute Resolution, (1996); For All Practical Purposes: Introduction to Contemporary Mathematics, (2000); Davis M.D., Game Theory: A Nontechnical Introduction., (1997); Gura K., Liberal Arts Mathematics: Probability and Calculus, PRIMUS, 1, 1, pp. 155-163, (1992); Gura K., Growth and Symmetry - Course for Liberal Arts Students, PRIMUS, 6, 4, pp. 337-350, (1996); Parks H.R., Musser G.L., Burton R., Siebler W., Mathematics in Life, Society, & the World, (2000); Steinhaus H., The Problem of Fair Division, Econometrica, 16, 1, pp. 101-104, (1948); Tannenbaum P., Arnold R., Excursions in Modern Mathematics, (2000)