Problem set 6 - Q2 - Solution to (c) Requirement 3 These beliefs must be reasonable given any information that has been revealed (so are determined by and consistent with Bayes' Rule) and the equilibrium strategies whenever possible. It must be g = 1 (Why?). MNow we have (E;. 5.9 = 1) Exercise 2 |This game has some similarity with one of the unmarked BNE exercises posted under week 9] Boeing is the sole supplier of aircrafis to all Asian airlines. Airbus is deciding whether to enter the Asian market and compete with Boeing. + Airbus can take an (a) aggressive entry strategy which we refer to as E,. Airbus can also take a (b) soft entry strategy which we refer to as Ez. Finally, Airbus can completely (c) stay out of the market which we refer to as O{ut). e Boeing can decide to engage in price war (P) or share (S) the market with Airbus. Airbus chooses first between Ei, Ez, and O, after which Boeing chooses between P and S. (1) If Airbus stays out of the market, Boeing gets 4, Airbus gets (. (1) If Airbus chooses E or Ez but Boeing chooses P, each gets (- 1) (ii1) If Airbus chooses E; and Boeing chooses S, Airbus gets 3, Boeing gets 1. {(iv)If Airbus chooses E; and Boeing chooses 5, Airbus gets 2, Boeing gets 2. Moving second. Boeing knows whether Airbus has chosen to stay out or enter, but it does not know whether Airbus has chosen E; or Ez. [Hint: think of information set] (a) (1 mark) Draw the relevant game tree associated the sequential game described above. Clearly label nodes/information sets, who moves at each node/information sets, actions, payotfs (at terminal nodes) [No explanation needed] (b) (1 mark) Draw the payoff matrix for the normal form game associated with the sequential move game described above. State the two Nash equilibria in pure strategies. [MNo explanation needed] (c) (3 marks) Consider the two Nash equilibria found in 2b. Is any one of them a Perfect Bayesian Equilibrium (PBE)? Explain. In particular, consider each NE and argue why they are or are not part of a PBE. [Note: A complete description of PBE must specify beliefs as a part of description of the equilibrium. ]