An Alternative Approach to the Lottery Method in Utility Theory for Game Theory

William P. Fox

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

DOI: 10.4236/ajor.2015.53016                

Abstract

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

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