Consider the following Bertrand Duopoly game between Firm A and Firm B.

Bertrand Duopoly	Firm B
Low Price	High Price
Firm A	Low Price	0, 0	5, -1
High Price	-1, 5	4, 4

a. Is there a dominant strategy equilibrium for a one-shot, simultaneous-move game? If so, what is it? If not, explain why.

b. Identify any and all Nash equilibria for a one-shot, simultaneous-move game. (1 point)

c. What is Firm A's secure strategy for a one-shot, simultaneous-move game? What is Firm B's secure strategy for a one-shot, simultaneous-move game?

d. Assume that Firm A and Firm B agree to collude and both charge high prices as long as neither of them cheats by charging low prices. If one of the firms cheats, trigger strategies take hold whereby the "victim" punishes the "cheater" by charging low prices forever after. If this game is infinitely repeated, calculate the interest rate (i) necessary to sustain collusion.

e. Assume that Firm A and Firm B agree to collude and both charge high prices as long as neither of them cheats by charging low prices. If one of the firms cheats, trigger strategies take hold whereby the "victim" punishes the "cheater" by charging low prices thereafter. If this game is finitely repeated with an unknown final period, assuming that the interest rate is 0%, calculate the probability that the game will end after a given play () necessary to sustain collusion.