The failures of collective action: a formal game-theoretic revisitation of the Olson theory

In Section 2 we study the problem of whether group goods which are in fixed supply and subject to a fixed cost of production will be supplied or not supplied in a static one-stage game of free cooperation, showing how the final outcome depends on the size of the group. In Section 3 we carry the previous analysis into a dynamic repeated game of free cooperation, showing how the final outcome depends both on the size of the group and on the value given to the future by the group members. In Section 4 we study how the outcome of the previ ous section is affected when we move from a state of free cooperation to one of enforced cooperation under an organized group. Finally, in Section 5 we extend the analysis of Section 2 to the case of group goods which are in variable supply and subject to a variable cost of produc tion, showing how under a static one-stage game of free cooperation the supply of the goods is inefficiently low, and how this insufficiency increases to the point of complete collapse when the group becomes very large