Operations Research20795 marksNumerical: game theory optimal strategyOptimal strategies for players
Game Theory Problem: Finding Optimal Strategies Determine the best strategy for each player A and B and the value of the game. | Player A / Player B | B1 | B2 | B3 | B4 | |---|---|---|---|---| | A1 | 40 | 40 | 40 | 40 | | A2 | 30 | 30 | 20 | 50 | | A3 | 10 | 30 | 90 | 20 |
Game Theory Problem: Finding Optimal Strategies
Determine the best strategy for each player A and B and the value of the game.
| Player A / Player B | $B_1$ | $B_2$ | $B_3$ | $B_4$ |
|---|---|---|---|---|
| $A_1$ | 40 | 40 | 40 | 40 |
| $A_2$ | 30 | 30 | 20 | 50 |
| $A_3$ | 10 | 30 | 90 | 20 |
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Payoff matrix (Player A gains): A\B B₁ B₂ B₃ B₄ --------------------- A₁ 40 40 40 40 A₂ 30 30 20 50 A₃ 10 30 90 20 This is a 2-person zero-sum game. Strategy Row values Row Min ------------------------------ A₁ 40, 40, 40, 40 40 A₂ 30, 30, 20, 50 20 A₃ 10, 30, 90, 20 10 Maximin