Consider two firms, A and B, that produce super computers. Each can produce the next generation super computer for math (M) or for chip research (C). However, only one can successfully produce for both markets simultaneously. Also, if one produces one type, the other might not be able to successfully produce the same type, because of the limited market. The following payoff matrix illustrates the problem.

Scenario AA
Firm B
M C
Firm A M 2, 1 2, 2
C 1, 1 3, 2

Does a Nash equilibrium exist ? (Answer yes or No). If a nash equilibrium exists, give the payoffs.