Question 4 Consider the following dynamic game of incomplete information. This game starts with a nature move in which the type of player 1 is chosen. There are two types of Player 1 - strong and weak. Player 1's type is revealed only to themselves, and they then choose whether to consume "beer" or "quiche." Player 2 (a "bully") observes only what player 1 consumes, not their type, and decides whether to fight player 2 or not. For the purposes of solving this game, assume there is an exogenous probability distribution over types where 10% of player 1's are weak types and 90\% of player 1's are strong types. (a) Are there any pooling equilibria of this game? Show why or why not. Check for a pooling equilibrium in which both types of player 1 (weak and strong) drink beer. (b) Are there any separating equilibria of this game? Show why or why not. Check for a separating equilibrium in which strong types of player 1 drink beer and weak types of player 1 eat quiche. Question 4 Consider the following dynamic game of incomplete information. This game starts with a nature move in which the type of player 1 is chosen. There are two types of Player 1 - strong and weak. Player 1's type is revealed only to themselves, and they then choose whether to consume "beer" or "quiche." Player 2 (a "bully") observes only what player 1 consumes, not their type, and decides whether to fight player 2 or not. For the purposes of solving this game, assume there is an exogenous probability distribution over types where 10% of player 1's are weak types and 90\% of player 1's are strong types. (a) Are there any pooling equilibria of this game? Show why or why not. Check for a pooling equilibrium in which both types of player 1 (weak and strong) drink beer. (b) Are there any separating equilibria of this game? Show why or why not. Check for a separating equilibrium in which strong types of player 1 drink beer and weak types of player 1 eat quiche