Problem 2. Public good provision Two players have to simultaneously decide how much to contribute to the provision of a public good. If player 1 contributes r and player 2 contributes y, then the value of the public good is 2(x + y + ry), which they each receive. They can choose any non-negative number as their contribution. The cost of contributing a for player 1 is a2. The cost of contributing y for player 2 is ty, where the value of t is private information for player 2. Player 1 believes that t = 1 with probability p and t = 2 with probability 1 -p. This belief is common knowledge. (a) What are the set of actions, types and beliefs of both players? (b) Find the Bayesian Nash equilibrium of the game. (c) Compare the quantities chosen by both players. Interpret (important). (d) What happens as p - 1