J.F. Nash, L.S. Shapley, A simple three-person poker game, Contributions to the Theory of Games 1 (1950) 105--116.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....academic elds. Economists and mathematicians have applied a variety of analytical techniques to poker related problems. For example, the earliest investigations in game theory, by luminaries such as John von Neumann and John Nash, used simpli ed poker to illustrate the fundamental principles [22, 23, 38]. Until recently, the computing science community has largely ignored poker. However, the game has a number of attributes that make it an interesting domain for arti cial intelligence research. These properties include incomplete knowledge, multiple competing agents, risk management, opponent ....

J. F. Nash and L. S. Shapley. A simple three-person poker game. Contributions to the Theory of Games, 1:105-116, 1950.

....A co author of the latter is the Dutch economist Tjalling C. Koopmans [ 43] also a Nobel laureate (1975) Additionally, Scarf has published with Lloyd S. Shapley [ 124] one of the major contributors to the development of game theory and a co author of the American mathematician John F. Nash [[104]] a co recipient of the 1994 Nobel Prize in economics 5 . Nash shared his prize with the Hungarian born economist John C. Harsanyi and the German mathematician Reinhard Selten, for their beneficial use of game theory in economics (more precisely, for their pioneering analysis of equilibria in ....

J. F. Nash & L. S. Shapley, A simple three-person poker game, in Contributions to the Theory of Games , Princeton University Press, 1950, pp. 105--116; MR 12,514d.

....plays) All of these are challenging dimensions to a difficult problem. 1 Certain aspects of poker have been extensively studied by mathematicians and economists. There are two main approaches to poker research. One approach is to use simplified variants that are easier to analyze [10] 11] [12]. For example, one could use only two players or constrain the betting rules. However, one must be careful that the simplification does not remove the challenging components of the problem. The other approach is to pick a real variant, but to combine mathematical analysis, simulation and ad hoc ....

....or making the rules too general would make the program weak and or predictable. Additionally, you need an expert who can define these rules. This knowledge acquisition bottleneck may prove to be a serious problem. 4. 2 Game Theoretic Optimal Strategies Kuhn [11] along with Nash and Shapley [12] have demonstrated that optimal strategies using randomization exist for simplified poker. An optimal strategy always takes the best worst case move, and this means two things: the player cannot do better than this strategy if playing against a good opponent, and furthermore the player does ....

J. F. Nash and L. S. Shapley. A simple three-person poker game. In H. W. Kuhn and A. W. Tucker, editors, Contributions to the Theory of Games I, pages 105--116. Princeton University Press, 1950. 69

....While this was interesting, and useful as an example of the application of game theoretic principles, the games studied were too far removed from real poker to be of much practical value. Other fundamental works into the study of simplified poker were developed by John Nash and Lloyd Shapley [61] and by Samuel Karlin [51, 52] Collections of related papers on the theory of games are also available [2, 3, 4] as well as an excellent treatise on the analysis of all games [23, 24] An attempt to adapt these mathematical models to more realistic versions of poker was made by Newman [62] but ....

J F Nash and L S Shapley, A Simple Three-Person Poker Game, Contributions to the Theory of Games, vol.1 [2], Princeton University Press, (1950), 105-116.

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J.F. Nash, L.S. Shapley, A simple three-person poker game, Contributions to the Theory of Games 1 (1950) 105--116.

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Nash, Jr., J.F., Shapley, L.S.: A simple three-person poker game. In Kuhn, H.W., Tucker, A.W., eds.: Contributions to the Theory of Games. Annals of Mathematics Studies. Princeton University Press, Princeton, NJ (1950) 105--116

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Nash, Jr., J.F., Shapley, L.S.: A simple three-person poker game. In Kuhn, H.W., Tucker, A.W., eds.: Contributions to the Theory of Games. Annals of Mathematics Studies. Princeton University Press, Princeton, NJ (1950) 105--116

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J. F. Nash and L. S. Shapley. A simple three-person poker game. Contributions to the Theory of Games, 1:105-116, 1950.

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|| (with L. S. Shapley), A simple three-person poker game, pp. 105-116 of \Contributions to the Theory of Games", Annals of Math. Studies 24, Princeton U. Press 1950.

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