1. Intuitive Limit Pricing: Show that of all the separating equilibria of the limit pricing-entry deterrence game in Section 16.2 only the best separating equilibrium does not fail the intuitive criterion.
2. Beer or Quiche? Cho and Kreps (1987) introduced what is now a famous twoplayer signaling game. First, Nature selects player 1, who knows his type, to be either a wimp (W), with probability p = 0.1, or surly (S), with probability 1- p = 0.9. Player 1 then chooses what to have for breakfast: beer (B) or quiche (Q). A surly type prefers beer while a wimp prefers quiche. Player 1's preferred breakfast gives him a payoff of 1 while his less-preferred choice gives him 0.
After breakfast player 2 observes what player 1 ate but does not know whether he is a wimp or surly. Player 2 then chooses whether to duel (D) with player 1 or not to duel (N). Player 1, regardless of his type, prefers no duel, yielding him an extra payoff of 2, to a duel, which gives him 0. (For example, if player 1 eats his preferred breakfast and avoids a duel then his final payoff is 3, while if he eats his preferred breakfast and is forced into a duel then his final payoff is 1.) Player 2, however, prefers to duel if and only if player 1 is a wimp. If player 1 is surly then player 2's payoff is 0 from D and 1 from N. If player 1 is a wimp then player 2's payoff is 2 from D and 1 from N.
a. Draw the extensive form of this game.
b. What are the Bayesian Nash equilibria of this game?
c. What are the perfect Bayesian equilibria?
d. Of the equilibria you found in (c), which fail the intuitive criterion?