Group specific public goods, orchestration of interest groups and free riding

We consider a two group contest over a group specific public good where each member of a group has a different benefit from the good. Our model can be interpreted in two ways: Each of the players has a non-linear investment cost in the contest, or alternatively, the returns to effort are decreasing as reflected in the contest success function. In the first part of the paper we show conditions under which freeriding decreases and consider the different properties of the equilibrium. In the second part of the paper we develop the properties of the optimal formation of the group and its affect on the equilibrium outcome.