Question

ACB Co. and SCG Co. are competitors in soft drink products market. They consider investing some money in advertising campaigns. If ACB Co. invests $30000 in advertising campaign, it will gain 5% market share if SCG Co. does nothing, it will gain 3% market share if SCG Co. invests $15000 in advertisement, and gain 2% market share if SCG Co. invests $22000 in advertisement. If ACB Co. invests $25000 in advertising campaign, it will gain 4% market share if SCG Co. does nothing, it will gain 1% market share if SCG Co. invests $15000 in advertisement, and loss 1% market share if SCG Co. invests $22000 in advertisement. If ACB Co. does nothing, it will not loss its market share if SCG Co. does nothing, it will loss 3% market share if SCG Co. invests $15000 in advertisement, and loss 4% market share if SCG Co. invests $22000 in advertisement.

(a)Develop a payoff table for this problem.

(b) What are the best strategies for each company using?

(c) What is the value of the game? Which company has more advantages?

Answer 1

Payoff Table:

	SCG Co.
Do nothing	Invest $15,000	Invest $22,000
ACB Co.	Invest $30,000	5	3	2
Invest $25,000	4	1	‒ 1
Do nothing	0	‒ 3	‒ 4

METHOD 1: DOMINANCE METHOD

	SCG Co.
Do nothing	Invest $15,000	Invest $22,000
ACB Co.	Invest $30,000	5	3	2
Invest $25,000	4	1	‒ 1
Do nothing	0	‒ 3	‒ 4

For ACB Co., strategy of investing $30,000 will always be BETTER than strategy of investing $25,000 and doing nothing;

	SCG Co.
Do nothing	Invest $15,000	Invest $22,000
ACB Co.	Invest $30,000	5	3	2

For SCG Co., strategy of investing $22,000 will always be BETTER than strategy of investing $15,000 and doing nothing.

	SCG Co.
Invest $22,000
ACB Co.	Invest $30,000	2

Conclusion:

• For ACB Co., strategy of investing $30,000 is always the best strategy;

• For SCG Co., strategy of investing $22,000 is always the best strategy;

• The value of the game is 2.

• Since the value of the game is positive, ACB Co. (player in rows – positive player) has more advantages. METHOD 2: PURE STRATEGY

	SCG Co.	Minimum in Rows
Do nothing	Invest $15,000	Invest $22,000
ACB Co.	Invest $30,000	5	3	2	2
Invest $25,000	4	1	‒ 1	‒ 1
Do nothing	0	‒ 3	‒ 4	‒ 4
Maximums in Columns	5	3	2

Conclusion:

• For ACB Co., strategy of investing $30,000 is always the best strategy;

• For SCG Co., strategy of investing $22,000 is always the best strategy;

• The value of the game is 2. Since the value of the game is positive, ACB Co. (player in rows – positive player) has more advantages.