Teaching the applications of optimisation in game theory's zero sum and non-zero sum games

William P. Fox

International Journal of Data Analysis Techniques and Strategies, 2010, vol. 2, issue 3, 258-284

Abstract: We apply linear and non-linear programming to find the solutions for Nash equilibriums and Nash arbitration in game theory problems. Linear programming was shown as a viable method for solving mixed strategy zero-sum games. We review this methodology and suggest a class of zero-sum game theory problems that are well suited for linear programming. We applied this theory of linear programming to non-zero sum games. We suggest and apply a separate formulation for a maximising linear programming problem for each player. We move on the Nash arbitration method and remodel this problem as a non-linear optimisation problem. We take the game's payoff matrix and we form a convex polygon. Having found the status quo point (x*, y*), we maximise the product (x-x*)(y-y*) over the convex polygon using KTC non-linear optimisation techniques. The results give additional insights into game theory analysis.

Keywords: nonlinear optimisation; game theory; linear programming; Nash equilibrium; Nash arbitration; non-zero sum games; zero sum games. (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.inderscience.com/link.php?id=34059 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ids:injdan:v:2:y:2010:i:3:p:258-284

Access Statistics for this article

More articles in International Journal of Data Analysis Techniques and Strategies from Inderscience Enterprises Ltd
Bibliographic data for series maintained by Sarah Parker ().