This document describes a modified public goods game between 4 players where at least 2 players must contribute for the public good to be available. If the public good is available, each player gets a payoff of 1 from it. Each player knows their own contribution cost ci but has incomplete information about other players' costs, which they believe are uniformly distributed between 0 and 1. The document asks to find all symmetric pure strategy perfect Bayesian equilibria of this game.

1. 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.