Suppose that there are only two vehicle dealerships (A and B) in a small city. E
ID: 2644438 • Letter: S
Question
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.
Dealership B
Dealership A Cash Rebate Free Options 0% Loan
Cash Rebate 2,?2 2,?2 1,?1
Free Options ?3,3 3,?3 ?1,1
0% Loan 3,?3 ?2,2 0,0
Identify the pure strategy for this two?person zero?sum game.
Explanation / Answer
SOLUTION:
Identifying maxi-min and Suitable strategy,
DEALERSHIP B
Cash Rebate
Free Options
0% Loan
B1
B2
B3
Row Minimum
DEALERSHIP A
Cash Rebate
A1
2
2
1
1
Free Options
A2
3
3
1
1
0% Loan
A3
3
2
0
0
Suitable Strategy for Dealer A = A1, A2
Max-min = 1
DEALERSHIP B
Cash Rebate
Free Options
0% Loan
B1
B2
B3
DEALERSHIP A
Cash Rebate
A1
2
2
1
Free Options
A2
3
3
1
0% Loan
A3
3
2
0
Column Maximum
3
3
1
Suitable Strategy for Dealer B = B3
Max-min = 1
Value of the Game and Saddle Point,
DEALERSHIP B
Cash Rebate
Free Options
0% Loan
B1
B2
B3
Row Minimum
DEALERSHIP A
Cash Rebate
A1
2
2
1
1
Free Options
A2
3
3
1
1
0% Loan
A3
3
2
0
0
Column Maximum
3
3
1
Value of the Game is = 1
Saddle Point = 1
Note:
Cash Rebate
Free Options
0% Loan
B1
B2
B3
Row Minimum
DEALERSHIP A
Cash Rebate
A1
2
2
1
1
Free Options
A2
3
3
1
1
0% Loan
A3
3
2
0
0
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