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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... move at that position. A possible move from a given position to another position is represented by an arrow. These ... wins and the other player loses. Player A has the first move. The directed graph for this game is shown in Figure 0.1 ...
... move at that position. A possible move from a given position to another position is represented by an arrow. These ... wins and the other player loses. Player A has the first move. The directed graph for this game is shown in Figure 0.1 ...
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... move may not know which of several positions that player may be in. 1 When such situations cannot occur, that is ... wins a penny from A. Otherwise, A wins a penny from B. This game is finite, deterministic, and zero-sum. Exercise 0.1 ...
... move may not know which of several positions that player may be in. 1 When such situations cannot occur, that is ... wins a penny from A. Otherwise, A wins a penny from B. This game is finite, deterministic, and zero-sum. Exercise 0.1 ...
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... move. The last person to move loses. (Notice that, in a certain sense, this is the opposite of the game in Example 0.1, where the last person to move wins ... wins. Exercise 0.2 Find a winning strategy for one of the players in games (3), (4) ...
... move. The last person to move loses. (Notice that, in a certain sense, this is the opposite of the game in Example 0.1, where the last person to move wins ... wins. Exercise 0.2 Find a winning strategy for one of the players in games (3), (4) ...
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... moves. 3. It is finite, that is, every play of the game ends after a finite number of moves. 4. It is a game with perfect information, that is, the result of every move ... wins. Figure 1.1 shows some examples of Tic-Tac-Toe results. OX XOX ...
... moves. 3. It is finite, that is, every play of the game ends after a finite number of moves. 4. It is a game with perfect information, that is, the result of every move ... wins. Figure 1.1 shows some examples of Tic-Tac-Toe results. OX XOX ...
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... move loses. b. The same game as in (a), except that the last person to move wins. 3. The first player A chooses one of the numbers 1 and 2, and then the game is over (without player B making any moves at all). A pays B one dollar if A ...
... move loses. b. The same game as in (a), except that the last person to move wins. 3. The first player A chooses one of the numbers 1 and 2, and then the game is over (without player B making any moves at all). A pays B one dollar if A ...
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