An idustry is monopolized by a single firm (the incumbent). A second firm (the challenger) is considering entry. The challenger can be strong or weak by equal probability. If the challenger enters, the incumbent chooses either accommodate or fight. The incumbent cannot observe the type of the challenger. the game payoff is;

QUESTION;

check if the challengers strategies are part of a perfect bayesian equilibrium and prove it;

1)challenger plays out, independently if weak or strong

2)challenger plays in, independently if weak or strong

3)challenger plays out when he is weak and in when he is strong

4)challenger plays in when he is weak and out

Nature Strong Weak Challenger Challenger 5 ino Out Incumbent Fight Accomodate Fight Accomodate Top number is challenger's payoff Bottom number is incumbent's payoff NW NW