AJOR  Vol.5 No.3 , May 2015
An Alternative Approach to the Lottery Method in Utility Theory for Game Theory
Author(s) William P. Fox
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.

Cite this paper
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.
References
[1]   Straffin, P. (2004) Game Theory and Strategy. The Mathematical Association of America: New Mathematics Library, Washington DC.

[2]   Fox, W. and Everton, S. (2013) Mathematical Modeling in Social Network Analysis: Using TOPSIS to Find Node Influences in a Social Network. Journal of Mathematics and Systems Science, 3, 531-541.

[3]   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.

[4]   Fox, W. and Everton, S.F. (2014) Using Mathematical Models in Decision Making Methodologies to Find Key Nodes in the Noordin Dark Network. American Journal of Operations Research, 1-13 (Online).

[5]   Fox, W. and Thompson, M.N. (2014) Phase Targeting of Terrorist Attacks: Simplifying Complexity with Analytical Hierarchy Process. International Journal of Decision Sciences, 5, 57-64.

[6]   Fox, W.P. (2014) Phase Targeting of Terrorist Attacks: Simplifying Complexity with TOPSIS. Journal of Defense Management, 4, 116.
http://dx.doi.org/10.4172/2167-0374.1000116

[7]   Fox, W.P. (2014) Using Multi-Attribute Decision Methods in Mathematical Modeling to Produce an Order of Merit List of High Valued Terrorists. American Journal of Operation Research, 4, 365-374.
http://dx.doi.org/10.4236/ajor.2014.46035

[8]   Saaty, T. (1980) The Analytical Hierarchy Process. McGraw Hill, New York.

[9]   Alinezhad, A. and Amini, A. (2011) Sensitivity Analysis of TOPSIS Technique: The Results of Change in the Weight of One Attribute on the Final Ranking of Alternatives. Journal of Optimization in Industrial Engineering, 7, 23-28.

[10]   Fox, W.P. (2012) Mathematical Modeling of the Analytical Hierarchy Process Using Discrete Dynamical Systems in Decision Analysis. Computers in Education Journal, 3, 27-34.

[11]   Fox, W. (2014) Chapter 221, TOPSIS in Business Analytics. Encyclopedia of Business Analytics and Optimization, V, 281-291.

[12]   Feix, M. (2007) Game Theory: Toolkit and Workbook for Defense Analysis Students. MS Thesis, Naval Postgraduate School, Monterey.

 
 
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