Electronic Proceedings of the Twenty-second Annual International Conference on Technology in Collegiate Mathematics
Chicago, Illinois, March 11-14, 2010
|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
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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