The following Table summarizes the profits of two firms as a function of their capacity investments levels (you can also interpret these levels as the quantities they produce):
qB = 0 qB = 1 qB = 2 qB = 3
qA =0 0; 0 0;12 0; 20 0; 18
qA =1 12; 0 10;10 6; 13 4; 12
qA =2 20; 0 13;6 8; 8 3; 4
qA =3 19; 0 12;4 4; 3 0; 0
(a) Suppose that both firms invest simultaneously. How much would they produce if they could credibly commit by signing a binding contract?
(b) How much would they produce if, because of antitrust laws, such contract is not legally enforceable? Explain briefly.
(c) Suppose instead that firm A is an incumbent, who invests first, and firm B is a potential new entrant, which knows the level of A's investment when it selects its own level. Provide the extensive form representation of this game and obtain the corresponding perfect equilibrium strategies of both firms. Which are their corresponding equilibrium payoffs? Is this outcome one of blockaded, deterred or accommodated entry?
(d) Consider the scenario described in (c) but now suppose that .rm B has to incur an entry cost which reduces its profit in 5, a cost that can only be avoided by not entering the market (i.e.: when B's production level is 0). Everything else remains as above. Answer question (c) in this new scenario.