In the following entry game, the challenger knows if she is strong (CS) or weak (CW), but the incumbent does not. The challenger decides whether or not to prepare herself for entry (R or U). A challenger who does not prepare herself receives a payoff of 5 if the incumbent accommodates (A) and 3 if the latter fights (F). Preparations cost a strong challenger 1 unit of payoff and a weak challenger 4 units of payoff. The incumbent receives a payoff of 2 if he accommodates a strong challenger and a payoff of -1 if he fights. The incumbent receives a payoff of 0 if he accommodates a weak challenger and a payoff of 2 if he fights. The resulting signaling game played between the challenger and the incumbent is illustrated below. In the signaling game, Nature chooses the challenger to be strong with a probability of 1/3.

a. List out all of the strategies for the challenger and the incumbent. [4 points]

b. Is there a separating perfect Bayesian equilibrium? If so, find all the separating perfect Bayesian equilibria. If not, briefly demonstrate why. [8 points]

c. Is there a pooling perfect Bayesian equilibrium? If so, find all the pooling perfect Bayesian equilibria. If not, briefly demonstrate why. [8 points]