Introducing Game Theory and its ApplicationsCRC Press, 2016 M02 3 - 272 páginas The mathematical study of games is an intriguing endeavor with implications and applications that reach far beyond tic-tac-toe, chess, and poker to economics, business, and even biology and politics. Most texts on the subject, however, are written at the graduate level for those with strong mathematics, economics, or business backgrounds. |
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Página 11
... strategy, (A2 ). When A removes 2 sticks, B must if the last stick and B loses. Observe that (A 1 ) is not a winning ... (X's) player, in the game of Tic-Tac-Toe. First move: Move into the center. X Case 1. The Chapter one: 11 Combinatorial ...
... strategy, (A2 ). When A removes 2 sticks, B must if the last stick and B loses. Observe that (A 1 ) is not a winning ... (X's) player, in the game of Tic-Tac-Toe. First move: Move into the center. X Case 1. The Chapter one: 11 Combinatorial ...
Página 16
... X has a non-losing strategy, but has no winning strategy, then the other player Y must have a non-losing strategy. Consequently, in a combinatorial game, either one player has a winning strategy or both players have non-losing strategies ...
... X has a non-losing strategy, but has no winning strategy, then the other player Y must have a non-losing strategy. Consequently, in a combinatorial game, either one player has a winning strategy or both players have non-losing strategies ...
Página 19
... strategy is less obvious.) 4. David and Jill play regular Tic-Tac-Toe ... (X) or a nought (O) in any unoccupied square. The winner is the first player ... strategy.) 8. Ancient Tic-Tac-Toe. In this game, played in ancient China, Greece ...
... strategy is less obvious.) 4. David and Jill play regular Tic-Tac-Toe ... (X) or a nought (O) in any unoccupied square. The winner is the first player ... strategy.) 8. Ancient Tic-Tac-Toe. In this game, played in ancient China, Greece ...
Página 24
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Contenido
1 | |
9 | |
Twoperson Zerosum Games | 53 |
The Simplex Method The Fundamental Theorem of Duality Solution of Twoperson Zerosum Games | 109 |
Nonzerosum Games and kPerson Games | 143 |
Finite Probability Theory | 207 |
Utility Theory | 219 |
Nashs Theorem | 223 |
Answers to Selected Exercises | 227 |
Bibliography | 247 |
Back Cover | 256 |
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alternately apply assigned assume basic point Black called canonical lpp choose collection column condition Consider consists constants constraints contains corresponding defined definition determined dominates draw entry equal equation equilibrium pair event Example Exercise expected fact fair Figure Find game matrix given graph Heads Hence imputation integer k-tuple least linear look loses matrix matrix games maximin Maximize maximum mean method Minimize mixed move Nash equilibrium non-losing strategy Note objective function obtain occurs optimal original outcomes pay-offs perfect pile pivot play player position possible prefers probability procedure proof pure random receive remove respect result saddle point segment Shapley value side Similarly simplex simplex method solution solve square standard sticks strategy for player tableau Theorem third two-person variables White winning strategy yields