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Saddle Squares in Random Two Person Zero Sum Games with Finitely Many Strategies


Abstract By the von Neumann min-max theorem, a two person zero sum game with finitely many pure strategies has a unique value for each player (summing to zero) and each player has a non-empty set of optimal mixed strategies. If the payoffs are independent, identically distributed (iid) uniform (0,1) random variables, then with probability one, both players have unique optimal mixed strategies utilizing the same number of pure strategies with positive probability (Jonasson 2004). The pure strategies with positive probability in the unique optimal mixed strategies are called saddle squares. In 1957, Goldman evaluated the probability of a saddle point (a 1 by 1 saddle square), which was rediscovered by many authors including Thorp (1979). Thorp gav... (more)
Created Date 2011
Contributor Manley, Michael (Author) / Kadell, Kevin W. J. (Advisor) / Kao, Ming-Hung (Committee member) / Lanchier, Nicolas (Committee member) / Lohr, Sharon (Committee member) / Reiser, Mark (Committee member) / Arizona State University (Publisher)
Subject Mathematics / Statistics
Type Doctoral Dissertation
Extent 109 pages
Language English
Copyright
Reuse Permissions All Rights Reserved
Note Ph.D. Mathematics 2011
Collaborating Institutions Graduate College / ASU Library
Additional Formats MODS / OAI Dublin Core / RIS


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Description Dissertation/Thesis