Suppose that instead of acting sequentially that the companies make decisions at

Question

Suppose that instead of acting sequentially that the companies make decisions at the same time. We can represent this game in the matrix below. Suppose that the game is only going to be played twice, and the executives at Pepsi called up Coke and pledged to never introduce a vanilla flavor as long as Coke does not either. Is it an equilibrium of the two round game for both to stay out of the Vanilla soda market in both years? If so, how do you know? If not, what is the equilibrium? Suppose instead that the game is played forever. Under what conditions of the interest rate could we have never seen a vanilla flavored product if this trigger strategy had been used?

Explanation / Answer

a) using backward induction proposition, one can iterately eliminate OUT as a strategy, implying ENTER strictly dominates OUT . Thus in this contect (Enter, Enter) is the nash equilibruim and same argument holds for stage I.

b) With the interest rate interpretation, we would have = 1/ 1 + r where r is the interest rate.

thus we need to solve the following equation

80/1- =100+ (/1+ )75, solve for  , the value is your required discount rate.

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