Q1. Consider two players, A and B, involved in a gun fight. However, the players have asymmetric information about each otherâ€™s ability to shoot. Player A does not know if Player B is a good shooter (type G) or a bad shooter (type B) for sure, but he knows that Player B could be a type G with probability p. Player B is perfectly informed about Player Aâ€™s type. Each player can choose to fight or to concede. The payoffs of the players are defined as follows. If player A chooses to concede, he yields â€˜0â€™ pay off irrespective of the other playerâ€™s action. If A fights, he yields a payoff of 1 if the opponent concedes; if both players fight, then their payoff is (-1,1) if player B is type G and (1, -1) if player B is type B.
a.Represent this situation as a Bayesian Game (10 marks)
b.Find its Bayesian-Nash Equilibrium if p<1/2 and p>1/2. (15 marks)