Smith is a potential entrant who moves ?rst, and Jones is an incumbent monopolist who moves second. Smith can either Enter or Stay out. If Smith stays out, the game ends, Jones earns a monopoly pro?t of 300, and Smith gets zero. If Smith enters, then Jones can either accommodate or ?ght.1 If Jones accommodates entry, each earns the duopoly pro?t 50. If Jones ?ghts entry, each earns a negative pro?t of minus ten.
(a) In rollback equilbrium, what is each player?s ?final pay?
(b) Suppose Jones operates in two markets. Smith can decide to enter in one market, both, or neither. Speci?cally, on the ?rst day, the above entry-deterrence game is played in market A. After the dust has settled in market A, on the next day the entry-deterrence game is repeated in market B. (Each is free to behave di¤erently in the two markets.) Final payo¤s are simply added together across the two markets. (For example, if there is a ?ght in market A, but no entry in B, then Jones earns -10+300=290, and Smith earns -10.) This must be considered as one big game played over two days (not two separate games which can be analyzed independently). In rollback equilbrium, what is each player?s total pay over the two days?
(c) Suppose the game from part (b) is modi?ed as follows. Smith does not have ?deep pockets?: if there is a ?ght in market A, so he loses 10, he is bankrupt and cannot enter in market B. In rollback equilbrium, what is each player?s total pay over the two days?