1. |
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A negative payoff indicates a loss to the row player. |
2. |
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The row [1 1 2] dominates the row [1 0 0]. |
3. |
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The column [1 2 3]T dominates the column [1 1 0]T. |
4. |
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If the payoff matrix of a game reduces to a 11 matrix, then the row and column that are left give each player's optimal pure strategy. |
5. |
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If a game has no saddle points, it may still be possible to reduce the game to a 11 game using dominance. |
6. |
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Some strictly determined games do not have saddle points. |
7. |
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The game |
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is not strictly determined. |
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8. |
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The game |
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is not strictly determined. |
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9. |
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In a strictly determined game, the row and column corresponding to optimal pure strategies always intersect in a saddle point. |
10. |
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When analyzing a game, it pays to first check for saddle points. |
11. |
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Different saddle points in the same payoff matrix may have different payoffs. |
12. |
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If a game is not strictly determined, there is a mixed strategy for the row player that is better for the row player than any pure strategy. |
13. |
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For every mixed row strategy, there is a pure strategy for the column player that maximizes his or her outcome. |
14. |
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If you fail to use an optimal strategy, then there is a counter strategy your opponent can use that is worse for you than anything he or she might do if you use an optimal strategy. |
15. |
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It is necessary to first reduce a game by dominance when solving it by the simplex method. |
16. |
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If you use the simplex method to solve a strictly determined game, then the value of the game may differ from the value of a saddle point. |
17. |
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If both players' optimal mixed strategies for a game happen to be pure strategies, then the game is strictly determined. |
18. |
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If a game is strictly determined, it may still be necessary to use the simplex method to solve it. |
19. |
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Every game can be solved by the simplex method. |
20. |
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If you know your opponent's strategy, it is still always best to use your optimal mixed strategy. |