Operations Research20805 marksNumerical: Game theory payoff matrixOptimal strategies for players
The following is the payoff matrix of a game being played by A and B. Determine the optimal strategies for the players and the value of the game.
The following is the payoff matrix of a game being played by A and B. Determine the optimal strategies for the players and the value of the game.
$$\begin{array}{|c|c|c|c|}\hline \text{A's strategies} & B_1 & B_2 & B_3 \ \hline A_1 & 120 & -80 & -20 \ A_2 & 60 & 70 & 30 \ A_3 & -100 & 70 & 20 \ \hline \end{array}$$
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Payoff matrix (A's gains): A \ B $B1$ $B2$ $B3$ ------------ $A1$ 120 -80 -20 $A2$ 60 70 30 $A3$ -100 70 20 Row minima (A's guaranteed minimum for each strategy): - $A1$: $\min(120, -80, -20) = -80$ - $A2$: $\min(60, 70, 30) = 30$ - $A3$: $\min(-100, 70, 20) = -100$ Maximin