Consider the Following Two-Person Zero-Sum Game Determine the Optimal Strategy for Each Player

question 28

Essay

Consider the following two-person zero-sum game.Assume the two players have the same two strategy options.The payoff table shows the gains for Player A. $$\begin{array}{l}\begin{array} { | c | c c c | } &&\text { Player B }\\\text { Plaver A } & \text { Strategy } b _ { 1 } && \text { Strategy } b _ { 2 } \\\hline \text { Strategy } a _ { 1 } & 3 && 9 \\\text { Strategy } a _ { 2 } & 6 && 2 \\\hline\end{array}\end{array}$$ Determine the optimal strategy for each player.What is the value of the game?

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Definitions:

Quadrant

One of the four sections of a Cartesian plane, divided by the x-axis and y-axis.

Plotting

The action of graphically representing data points or mathematical functions on a coordinate system.

X-intercepts

The points at which a graph intersects the x-axis, indicating the values of x when the function's output equals zero.

Y-intercepts

The points where a graph intersects the y-axis of a coordinate plane.