Exercise 1. Question 1 (Fight or Cave) There are two players, A and B. Each player i

Exercise I. Question I (Fight or Cave) There are two players, A and B. Each player i E {A, B} can be Of one Of two types: {1,2). The probability that a player is Of type 2 equals p. When A and B meet, each can decide to fight or cave. If both players fight, then player i gets payoff tj where j i and c>o. If player i fights, but player j not, then player i gets payoff I, while player j gets payoff O. If both players do not fight, each gets payoff k. (a) (I mark) Draw the Bayesian normal form representation Of this game. (b) (I mark) A Strategy in a static Bayesian game is a function that specifies an action for each type Of a player. Write down all the possible strategies for player i. marks) Assume that A plays fight if tA = 2 and cave otherwise. (i) If B is Of type 2, what should B do? (ii) If B is Of type I , what should B do? (d) (2 marks) Is there a Bayesian Nash equilibrium in which each player fights if and Only if she is Of type 2? If so, what is the equilibrium probability Of a fight? (e) (2 marks) Assume that A never fights. (i) If B is Of type 2, what should B do? (ii) If B is Of type I, what should B do? (f) (2 marks) Is there a Bayesian Nash equilibrium in which no player ever fights?