Author(s)

William P. Fox

Department of Defense Analysis, Naval Postgraduate School, Monterey, USA.

In game theory, in order to properly use mixed strategies, equalizing strategies or the Nash arbitration method, we require cardinal payoffs. We present an alternative method to the possible tedious lottery method of von Neumann and Morgenstern to change ordinal values into cardinal values using the analytical hierarchy process. We suggest using Saaty’s pairwise comparison with combined strategies as criteria for players involved in a repetitive game. We present and illustrate a methodology for moving from ordinal payoffs to cardinal payoffs. We summarize the impact on how the solutions are achieved.

Analytical Hierarchy Process, Cardinal Utility, Game Theory, Payoff Matrix

Fox, W. (2015) An Alternative Approach to the Lottery Method in Utility Theory for Game Theory. American Journal of Operations Research, 5, 199-208. doi: 10.4236/ajor.2015.53016.