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 5
... strategy . The original meaning of the word was "the art of directing the larger military movements and operations ... winning strategy if the player following that strategy always receives a positive pay-off, no matter what the player's ...
... strategy . The original meaning of the word was "the art of directing the larger military movements and operations ... winning strategy if the player following that strategy always receives a positive pay-off, no matter what the player's ...
Página 6
... wins.) Player B has the following winning strategy in this game. If A starts by taking one stick, then B should remove two, forcing A to remove the last stick. If A starts by removing two sticks, then B should take away one stick, again ...
... wins.) Player B has the following winning strategy in this game. If A starts by taking one stick, then B should remove two, forcing A to remove the last stick. If A starts by removing two sticks, then B should take away one stick, again ...
Página 10
... winning strategy, that is, that player can always ensure a win, or both players have non-losing strategies, that is, they can make sure that they never lose. Even in as simple a game as Tic-Tac-Toe, the description of a strategy can be ...
... winning strategy, that is, that player can always ensure a win, or both players have non-losing strategies, that is, they can make sure that they never lose. Even in as simple a game as Tic-Tac-Toe, the description of a strategy can be ...
Página 11
... winning strategy, (A2 ). When A removes 2 sticks, B must if the last stick and B loses. Observe that (A 1 ) is not a winning strategy; is B left responds with one with stick strategy to remove (B1 ), and that loses. is, if B removes a ...
... winning strategy, (A2 ). When A removes 2 sticks, B must if the last stick and B loses. Observe that (A 1 ) is not a winning strategy; is B left responds with one with stick strategy to remove (B1 ), and that loses. is, if B removes a ...
Página 14
... winning strategies in the following games. 1. Player A names a positive integer n and player B then names a positive integer k . A wins $1 from B if ... winning strategy for the first player. 14 Introducing Game Theory and Its Applications.
... winning strategies in the following games. 1. Player A names a positive integer n and player B then names a positive integer k . A wins $1 from B if ... winning strategy for the first player. 14 Introducing Game Theory and Its Applications.
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