Q5 Romeo-Juliet Game with Incomplete Information Consider the following variation of the coordination game with incomplete information that we considered in class. Juliet has two types. She can be Social (i.e., wants to meet Romeo) or Solitary (i.e., wants to avoid Romeo). Probability of Juliet being Social is given by p E [0, 1]. Juliet always knows her type (whether she is Social or Solitary). Romeo does not know which Juliet he will be meeting, but he knows the odds of Juliet being Social and Solitary. Payoffs are given below: Social Juliet Solitary Juliet Bar Movie Bar Movie Bar 3, 1 0, 0 Bar 3, 0 0, 3 Romeo Romeo Movie 0, 0 1, 3 Movie 0, 1 1, 0 (a) Find all Bayesian Nash equilibria when p = 0.5 (i.e., the odds of Juliet being Social is 50% - 50%). (b) Find all Bayesian Nash equilibria when p = 0.9 (i.e., the odds of Juliet being Social is 90% - 10%)