We study the evolutiona of the shape of public goods functions. Benefits produced by public good generally have a sigmoid shape that implies saturation at high frequencies of contributors.Saturating payoff functions are determined by several parameters, and it is generally assumed that these parameters are fixed. We study instead how the parameters themselves evolve. Our central questions are the following. What kind of payoff function evolves if payoff parameters are under selection? Do cooperators and defectors coexist if payoff functions can evolve? How does payoff function evolution modifies average population fitness? Is it possible that evolution leads to a state where population fitness is close to the optimum?
