Question

General Mills and Kellogg’s, major rivals in the cereal market, decide simultaneously on their advertising strategies. Each firm has five advertising options, A through E. The following table shows their net profits ($millions) for various advertising strategy combinations. In each cell, the first entry is the profit for Kellogg’s, and the second is for General Mills.

		General Mills
		A	B	C	D	E
Kellogg’s	A	23, 22	37, 18	42, 11	21, 20	25, 15
	B	11, 24	30, 20	27, 29	25, 22	27, 27
	C	32, 18	28, 22	30, 20	37, 18	34, 16
	D	19, 20	41, 26	38, 24	32, 25	28, 23
	E	21, 31	33, 17	25, 22	30, 19	23, 28

1.Use Excel to create a spreadsheet showing the payoff to Kellogg’s for each strategy combination. For each possible strategy for General Mills (for each column), determine the best response for Kellogg’s.Then do the same for General Mills, with each possible strategy for Kellogg’s.

2. Does Kellogg’s have a dominant strategy? Explain. Does General Mills? Explain.

3. Comment on the Nash equilibrium, if any, for this game

Answer 1

a. For each strategy of one firm, the best response for the other one has been marked with an asterisk. For eg, for Kellogg’s strategy A, the best response of General Mills is A, as A is giving it the highest payoff corresponding to Kellogg’s A.

	A	B	C	D	E
A	23,22*	37,18	42*,11	21,20	25,15
B	11,24	30,20	27,29*	25,22	27,27
C	32*,18	28,22*	30,20	37*,18	34*,16
D	19,20	41*,26*	38,24	32,25	28,23
E	21,31*	33,17	25,22	30,19	23,28

b. None of the firms have a dominant strategy. A dominant strategy is one where the payoff to a player is the highest for all the possible strategies of another player. For eg, if Kellogg has a dominant strategy, let's say A, then the payoff from A would be higher for all the strategies of General Mills as compared to the corresponding payoffs from strategies B to E of Kellogg.

c. The game has (D, B) as the Nash equilibrium, where the D is the strategy of Kellogg and B of General Mills. This is the Nash equilibrium as corresponding to D, it is the best response for General Mills, similarly, D is the best repose of Kellogg corresponding to General Mills' B.