4. Entry Deterrence: Consider a simple model of entry in two market. The Entrant can enter a market, and if it does so the Incumbent can decide whether to Fight or Accommodate. The Entrant's payoff is 1 if the incumbent ghts, and 1 if it accom modates. The Incumbent's prots are 5 if the incumbent doeant enter; if the Entrant enters the Incumbent's prots are 1 if it Accommodates and 1 if it Fights. A rm may be rational in which case its payoff is its prots or tough in which case it receives an additional dlSUtlllt)' of 4 if it accommodates. The payoff matrix is then I\\E E N F 1,1 5, l] A 1,1 5, I] if the Incumbent is rational and, if it's tough, HE E N F 1,1 5, 0 A 3, l 5, I]. A potential entrant doesnt know if the incumbent is rational or tough when it decides whether to enter but believes the Incumbent is tough with probability 2/3. Suppose that there are two markets, in each market there is a dierent entrant, and the Incum bent oompetes in both market sequentially. {a} Suppose that the Entrant in market 1 has entered (perhaps by mistake}. If the potential entrant in market 2 could not observe the Incumbent's response, how would the Incumbent respond? (b) If the Entrant in market 2 observes the Incumbents response in market 1, can the Incumbents response in {a} be an equilibrium? {c} Show that there is an equilibrium for the Incumbent to Fight in market I regard less of its type. (d) If the type of the Incumbent was known to the Entrant in market 2, could there be an equilibrium in which a rational Incumbent ghts after entry in the rst market