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 9
... square. The X player moves first. The first player to completely fill a row, column, or either diagonal with that player's symbol wins. Figure 1.1 shows some examples of Tic-Tac-Toe results. OX XOX XXO OX OOX OOX OX OXX XOX WinforO's.
... square. The X player moves first. The first player to completely fill a row, column, or either diagonal with that player's symbol wins. Figure 1.1 shows some examples of Tic-Tac-Toe results. OX XOX XXO OX OOX OOX OX OXX XOX WinforO's.
Página 12
... square. By the symmetry of the Tic-Tac-Toe board, we may assume that it is the upper left-hand corner. O X O Player A should now counter with: X X Player B's next move is forced: O O X X (When we say that a move is forced , we mean that ...
... square. By the symmetry of the Tic-Tac-Toe board, we may assume that it is the upper left-hand corner. O X O Player A should now counter with: X X Player B's next move is forced: O O X X (When we say that a move is forced , we mean that ...
Página 13
... square: OXO XXO XOX and the result is a draw. Thus, in Case 1, either player A wins (if B fails to make the indicated forced moves) or there is a draw. Case 2. Player B follows A's first move by moving into a non-corner square. By ...
... square: OXO XXO XOX and the result is a draw. Thus, in Case 1, either player A wins (if B fails to make the indicated forced moves) or there is a draw. Case 2. Player B follows A's first move by moving into a non-corner square. By ...
Página 18
... square: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Players alternately take any number of sticks from a single row or column. At least one stick must be taken. There is an additional restriction that a group of sticks cannot be ...
... square: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Players alternately take any number of sticks from a single row or column. At least one stick must be taken. There is an additional restriction that a group of sticks cannot be ...
Página 19
... square: 2 7 6 9 51 4 3 8 Note that, in a magic square, the rows, column, and diagonals all add up to the same number, in this case, fifteen. 2. (Leo Moser) Two players alternately choose a word from the following list of nine words ...
... square: 2 7 6 9 51 4 3 8 Note that, in a magic square, the rows, column, and diagonals all add up to the same number, in this case, fifteen. 2. (Leo Moser) Two players alternately choose a word from the following list of nine words ...
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