Assignment:
Carolyn and Maurice are playing the game “Chicken”. Both Carolyn and Maurice know that Maurice knows who won the Wimbledon tennis tournament yesterday (out of three possible tennis players, Jim, John, and Arthur, who each had a probability of one-third of winning the tournament), but Carolyn does not know who won the tournament.
(a) Describe this situation as a game with incomplete information, and find the set of Bayesian equilibria of this game.
(b) Answer the first two questions of this exercise, under the assumption that both Carolyn and Maurice only know whether or not Jim has won the tournament.
(c) Answer the first two questions of this exercise, under the assumption that Maurice only knows whether or not Jim has won the tournament, while Carolyn only knows whether or not John has won the tournament.
Provide complete and step by step solution for the question and show calculations and use formulas.