Game Theory Question 3

3. Consider a modified public good game between four players in which for the public good

to be available at least two players out of the four have to contribute. If the public good

is available each player gets a payoff of 1 from it. The cost of contributing for player i is

equal to ci. Each player knows his or her own cost and has incomplete information about

the other players costs believing that the cost of each opponent is uniformly distributed on

the interval [0; 1] independently of each other. Find all symmetric PBE of this game.