3. [7 points] Consider the following game between four players. Each player i has an initial endowment of 20 units of money. This money can be split between a private account (xi) and a public account (yi). The payoff of each player consists of the amount she allocated to her private account plus 2 times the minimum of all contributions to the public account, i.e., i = xi + 2min(y1, y2, y3, y4) (0.1)

a) What is the payoff function for player i = 1? [2 points]

b) Find the pure strategy Nash equilibria under the assumption that all participants are fully rational and only interested in their own earnings. [3 points]

c) Give a reason why one of the equilibrium may be a focal point for the players (you 2 must state which equilibrium you think is a focal point). [2 points]