Problem 2 We consider the following problem of public good provision. Two players, Anton and Barbara, have to contribute to a public good, but each would prefer the other player to incur the its cost. They choose their contribution simultaneously. The strategy of each player is \"contribute\" (C) and \"not contribute\" (NC). Each player derive a benet equal to 1 if at least one of them contributed, and 0 if no player contributes. Anton's cost of contributing is CA and Barbara's cost is (33. Each player know his/ her cost but not the cost of the other player. The payoifs are depicted in Table 4. Barbara O NO C 1 1 1 1 Anton CA3 CB CA3 NC 1,1 CB 0, 0 Table 4: Public good provision For each player, the cost of contributing is drawn from a uniform distribution over [0, 2] .1 Recall that in a Bayesian game a player's strategy is a strategy for the game (C or N C) for each possible type, i.e., for each possible value of his/ her cost of contributing. We are looking for a BayesNash equilibrium. To this end, denote by 22- the probability that player 1' contributes to the public good. 1. Find a condition on c,- depending on 2,1; under which player i will contribute. 2. From the previous question we can deduce that players' equilibrium strategies are cuto strategies, i.e., a player i contributes if his/her cost 0; is below some cutoff c2\". Hence, 2,- = Prob(c,