Answers
a)the game in matrix form when two firms have two decisions to make 1)exit and 2)not exit
| FIRM1,FIRM2 | EXIT(q) | NOT EXIT(1-q) |
| EXIT(r) | 0,0 | 0,2 |
| NOT EXIT(1-r) | 2,0 | -1,-1 |
b)the nash equillibria will be (2,0) or (0,2) because both of these are best strategy by the firm.
when firm 2 is fixed at choosing to EXIT the best payoff for firm1 is 2(not exiting) when firm2 is fixed at choosing to not exit the best payoff for firm1 is 0(exit).Now when firm1 is fixed to exit the best payoff for firm2 is 2(not exit) and when firm1 is fixed to not exiting the best payoff for firm2 is 0(exit) so there are two equilibrium points.
c)to determine mixed strategy nash equilibrium,
STRATEGY1 : 0q+0(1-q) STRATEGY2 : 2q+(-1)(1-q)
0q+0(1-q) = 2q+(-1)(1-q)
by solving we get, q=1/3 (There is no pure strategy nash equilibrium)
similarly r=1/3
(r,q)=(1/3,1/3)
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