Suppose That There Are Only Two Vehicle Dealerships (A and B)in

Essay

Suppose that there are only two vehicle dealerships (A and B)in a small city.Each dealership is considering three strategies that are designed to take sales of new vehicles from the other dealership over a period of four months.The strategies,assumed to be the same for both dealerships,are:
Strategy 1: Offer a cash rebate on a new vehicle.
Strategy 2: Offer free optional equipment on a new vehicle.
Strategy 3: Offer a 0% loan on a new vehicle.
The payoff table (in number of new vehicle sales gained per week by Dealership A (or lost by Dealership B)is shown below. $$\begin{array}{l}\begin{array} { | l c | c c c | } &&&\text { Dealership B }\\\\&& \text { Cash Rebate } & \text { Free Options } & 0 \% \text { Loan } \\{ \text { Dealership } A } &&b _ { 1 } & b _ { 2 } & b _ { 3 } \\\hline \text { Cash Rebate } a _ { 1 }& & 2 & 2 & 1 \\\text { Free Options }a _ { 2 } & & - 3 & 3 & - 1 \\0 \% \text { Loan } a _ { 3 }& & 3 & - 2 & 0 \\\hline\end{array}\end{array}$$ Identify the pure strategy for this two-person zero-sum game.What is the value of the game?