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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... stick or two sticks. The last player to move wins and the other player loses. Player A has the first move. The directed graph for this game is shown in Figure 0.1. (Each segment is assumed to be an arrow directed downward.) If you are ...
... stick or two sticks. The last player to move wins and the other player loses. Player A has the first move. The directed graph for this game is shown in Figure 0.1. (Each segment is assumed to be an arrow directed downward.) If you are ...
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... sticks at each move. The last person to move loses. (Notice that, in a certain sense, this is the opposite of the ... sticks, then B should take away one stick, again forcing A to remove the last stick. In either case, B wins. Exercise ...
... sticks at each move. The last person to move loses. (Notice that, in a certain sense, this is the opposite of the ... sticks, then B should take away one stick, again forcing A to remove the last stick. In either case, B wins. Exercise ...
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... sticks. Each of the two players alternately removes one or two sticks. The game continues until there are no sticks left. The last person to move loses. b. The same game as in (a), except that the last person to move wins. 3. The first ...
... sticks. Each of the two players alternately removes one or two sticks. The game continues until there are no sticks left. The last person to move loses. b. The same game as in (a), except that the last person to move wins. 3. The first ...
Página 11
... stick, player A must remove the last stick. If player B removes two sticks, the game is over.) (A2 ) Remove two sticks. (Player B must then remove the last stick.) Player B also has two strategies (B 1 ) and (B2 ). (B1 ) If player A took 1 ...
... stick, player A must remove the last stick. If player B removes two sticks, the game is over.) (A2 ) Remove two sticks. (Player B must then remove the last stick.) Player B also has two strategies (B 1 ) and (B2 ). (B1 ) If player A took 1 ...
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... sticks. (Remember that 1 or 2 sticks are removed each time, and the last person to move loses.) 4. The same game as Example 1.1 except that the initial pile contains 5 sticks. 5. Consider the general case of the game in Example 1.1 ...
... sticks. (Remember that 1 or 2 sticks are removed each time, and the last person to move loses.) 4. The same game as Example 1.1 except that the initial pile contains 5 sticks. 5. Consider the general case of the game in Example 1.1 ...
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