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

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DOI: 10.4236/ajor.2015.53016    2,464 Downloads   2,947 Views   Citations
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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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

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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.
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