4. Two players have to simultaneously and independently decide how much to contribute to a pure public good. If the contributions of players 1 and 2 are 1:1 and m, then the amount of public good produced is 2(sz + 332 + $11132). Assume that 331 and $2 are both positive. Player 1 incurs a cost of at? and so his utility is 11,1031, 1'2) = 2((171 + 132 + {1311:2) 1'? Player 2 pays a cost of mg and so her cost is u2(a:1, :02) = 2(x1 + $2 + an) tr; The number if is private information to player 2. Player 1 knows that it is 2 with probability 1/2 and 3 with probability 1/2. (i) Dene carefully the strategies of the two players in this Bayesian game. (2 marks) (ii) Derive the pure strategy Bayesian Nash equilibrium of the game. (8 marks)