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Fox, W. and Everton, S. (2014) Mathematical Modeling in Social Network Analysis: Using Data Envelopment Analysis and Analytical Hierarchy Process to Find Node Influences in a Social Network. Journal of Defense Modeling and Simulation, 2014, 1-9.

has been cited by the following article:

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

  AUTHORS: William P. Fox

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

  JOURNAL NAME: American Journal of Operations Research, Vol.5 No.3, May 25, 2015

  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.