Two sports teams, Aston CC (A) and Birmingham CC (B) are trying negotiate a trade where Aston CC receives a given player from Birmingham CC, and similarly Birmingham CC will receive a given player from Aston CC. Each team can either accept the trade (T) or reject the trade (R). The two players being discussed in the trade are both potentially injured. Each team has a prior belief of the probability that the player they are trading for is injured. Aston CC believes the player they are trading for is injured with probability 2/3. Birmingham CC believes the player they are trading for is injured with probability 1/5. This situation can be modelled as an incomplete information game. a) Find the probabilities of being in each type of game using the prior beliefs using the information in the question. b) For the payoff matrices given below: T R T R T R T -3|1|T|-5| 1 | T|5 | -1 R|3|2|R[3]|2 |R|-3]|-2 (PiPp) (PaPg') (Py'Ps) (Py'Pg') Figure 1: Payoff matrices for each type of game. P} is the probability that Aston believes the player they are trading for is injured. Similarly, P4/ is the probability that Aston believes the player they are trading for is not injured. P is the probability that Birmingham believes the player they are trading for is injured. Similarly, P}' is the probability that Birmingham believes the player they are trading for is not injured. The payoffs are assigned for various reasons, including legal fees to propose a trade, and happiness with their given player. Find the Nash equilibria for each game. Explicitly state why they are the Nash equilibria. Note: This is a zero-sum game. c) Write the table of all the expected payoffs for each given strategy of the players and each given type of game. d) Use your answer in part ) to determine whether there is a pure strategy Bayes-Nash equilibria. Discuss your