Consider the Following Two-Person Zero-Sum Game Is There an Optimal Pure Strategy for This Game? If

question 23

Essay

Consider the following two-person zero-sum game.Assume the two players have the same three strategy options.The payoff table below shows the gains for Player A. $$\begin{array}{l}\begin{array} { | c | c c c c | } &&\text { Player B }\\{ \text { Plaver } \mathrm { A } } & \text { Strategy } b _ { 1 } & \text { Strategy } b _ { 2 } & \text { Strategy } b _ { 3 } \\\hline \text { Strategy }a _ { 1 } & 3 & 5 & - 2 \\\text { Strategy }a _ { 2 } & - 2 & - 1 & 2 \\\text { Strategy } a _ { 3 } & 2 & 1 & - 5 \\\hline\end{array}\end{array}$$ Is there an optimal pure strategy for this game? If so,what is it? If not,can the mixed-strategy probabilities be found algebraically? What is the value of the game?

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