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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... games that are not zero-sum and/or involve more than two players. Here it is often natural to consider cases where the players must no longer act as isolated individuals but are permitted to form coalitions with other players. Games in ...
... games that are not zero-sum and/or involve more than two players. Here it is often natural to consider cases where the players must no longer act as isolated individuals but are permitted to form coalitions with other players. Games in ...
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... game in question ends only in a win (W) or a loss (L) for each player, then the triple (L,L,W) would indicate that A and B have lost and C has won.) Example 0.1 Consider the following game for two players A and B. Start with a pile of ...
... game in question ends only in a win (W) or a loss (L) for each player, then the triple (L,L,W) would indicate that A and B have lost and C has won.) Example 0.1 Consider the following game for two players A and B. Start with a pile of ...
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... Consider the same game as in Example 1.1, except that the last person to move wins the game. The possible strategies are unchanged. However, player B now has a winning strategy, (B2 ). Example 1.3 Consider a game like that of Example ...
... Consider the same game as in Example 1.1, except that the last person to move wins the game. The possible strategies are unchanged. However, player B now has a winning strategy, (B2 ). Example 1.3 Consider a game like that of Example ...
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... Consider the general case of the game in Example 1.2, where the initial pile contains n sticks. Recall that the players remove 1 or 2 sticks at a time and the last person to move wins. Describe those values of n for which the second ...
... Consider the general case of the game in Example 1.2, where the initial pile contains n sticks. Recall that the players remove 1 or 2 sticks at a time and the last person to move wins. Describe those values of n for which the second ...
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... game G. □ Now consider any combinatorial game. By the Fundamental Theorem, at least one of the players X has a non-losing strategy. If X does not have a winning strategy, then the Corollary tells us that the other player Y also has a ...
... game G. □ Now consider any combinatorial game. By the Fundamental Theorem, at least one of the players X has a non-losing strategy. If X does not have a winning strategy, then the Corollary tells us that the other player Y also has 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