5,0 N 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 fights, and 1 if it accom- modates. The Incumbent's profits are 5 if the incumbent doesnt enter; if the Entrant enters the Incumbent's profits are 1 if it Accommodates and -1 if it Fights. A firm may be rational in which case its payoff is its profits or tough in which case it receives an additional disutility of 4 if it accommodates. The payoff matrix is then I\E F -1,-1 5,0 1,1 if the Incumbent is rational and, if it's tough, I E E F -1,-1 5,0 -3,1 5,0. 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 different entrant, and the Incum- bent competes 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 1 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 fights after entry in the first market? 5,0 N 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 fights, and 1 if it accom- modates. The Incumbent's profits are 5 if the incumbent doesnt enter; if the Entrant enters the Incumbent's profits are 1 if it Accommodates and -1 if it Fights. A firm may be rational in which case its payoff is its profits or tough in which case it receives an additional disutility of 4 if it accommodates. The payoff matrix is then I\E F -1,-1 5,0 1,1 if the Incumbent is rational and, if it's tough, I E E F -1,-1 5,0 -3,1 5,0. 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 different entrant, and the Incum- bent competes 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 1 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 fights after entry in the first market
