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

General Mills 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

a. Use Excel to create a spreadsheet showing only the payoff to Kellogg’s arising from each strategy combination. For each possible strategy for General Mills (that is, for each column), determine the best response for Kellogg’s. (Hint: Use the MAX function to find the maximum value for each column.) Does Kellogg’s have a dominant strategy?

b. In the same spreadsheet, create a new block of entries showing the payoff to General Mills for each strategy combination. For each possible strategy of Kellogg’s, identify General Mills’

highest possible payoff and corresponding best strategy.

c. Determine the Nash equilibrium for this game.

Is it a dominant-strategy equilibrium?