Electronic Proceedings of the Twenty-second Annual International Conference on Technology in Collegiate Mathematics

Chicago, Illinois, March 11-14, 2010

Paper S070

This is an electronic reprint, reproduced by permission of Pearson Education Inc. Originally appeared in the Proceedings of the Twenty-second Annual International Conference on Technology in Collegiate Mathematics, ISBN 978-0-321-74614-6, Copyright (C) 2011 by Pearson Education, Inc.

Game Theory and Optimization via Excel

William P. Fox

Naval Postgraduate School

list of all papers by this author

Click to access this paper: paper.pdf

ABSTRACT

We examine game theory problems that are more easily solved in finding the Nash equilibrium and Nash arbitrations points by applying the Kuhn-Tucker conditions for linear and nonlinear programming. We show that for games of 3 x 3 and larger that LP appears to be the method of choice. We apply Kuhn-Tucker conditions to find the Nash Arbitration point. Having found the status quo point (x*y*) and create the convex polygon, we maximize (x-x*)(y-Y*) over the convex polygon using optimization. We show how this can be used in finance and risk management situations.

Keyword(s): optimization, applications, spreadsheets