Operations Research20825 marksNumerical: Game theory optimal strategyOptimal strategies for players
Game Theory Problem Considering this information, answer the question given below. | Player A's strategy/Player B's strategy | B1 | B2 | B3 | B4 | B5 | |---|---|---|---|---|---| | A1 | 20 | 20 | 20 | 120 | 80 | | A2 | 80 | -20 | -40 | 60 | 60 | | A3 | -60 | -40 | 20 | 20 | 140 | | A4 | 120 | 80 | -6
Game Theory Problem
Considering this information, answer the question given below.
| Player A's strategy/Player B's strategy | $B_1$ | $B_2$ | $B_3$ | $B_4$ | $B_5$ |
|---|---|---|---|---|---|
| $A_1$ | 20 | 20 | 20 | 120 | 80 |
| $A_2$ | 80 | -20 | -40 | 60 | 60 |
| $A_3$ | -60 | -40 | 20 | 20 | 140 |
| $A_4$ | 120 | 80 | -60 | 60 | 140 |
(a) What would be the optimal strategy for each player?
(b) What is the value of the game?
[5]
Payoff matrix (Player A rows, Player B columns), entries are payoffs to Player A: A\B $B1$ $B2$ $B3$ $B4$ $B5$ ------------------------------ $A1$ 20 20 20 120 80 $A2$ 80 -20 -40 60 60 $A3$ -60 -40 20 20 140 $A4$ 120 80 -60 60 140 This is a $4 \times 5$ two-person zero-sum game. Player A (maximiz...