2. Two identical firms ( same product, same cost structure ) compete by choosing quantities. For simplicity, assume their three possible choices are to produce 7.5 , 10 , or 15 units of output each. The payoff matrix below summarizes all possible combinations and the resulting profits for each firm ( firm 1' s profits are shown in the bottom left of each cell ) .
a . Assume the firms play this competition game by choosing quantities simultaneously. What is the Nash equilibrium? Does either of the firms have a dominant strategy?
b . Assume the firms now play this competition game by choosing quantities sequentially and that Firm 1 chooses first. What is the equilibrium? Is there a first or second - mover advantage? Explain.
c . Imagine Firm 2 could pay x dollars to change the rules of the game. How much would it be willing to pay to move first in the sequential game? And how much would Firm 2 be willing to pay to make the game simultaneous again?
d . Consider the simultaneous version of the game again. Identify the dominated strategy for each firm and eliminate it , thus reducing the game. What is the Nash equilibrium in this reduced game?
e . What is the equilibrium in the reduced game from part ( d ) if it is played sequentially? student submitted image, transcription available