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

  • Authors:

  • William P. Fox

  • Affiliations:

  • Department of Defense Analysis, Naval Postgraduate School, 589 Dyer Road, Room 103F, Monterey, CA 93943 USA

  • Venue:
  • International Journal of Data Analysis Techniques and Strategies
  • Year:
  • 2010

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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.