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

The central thesis of Olson's Logic Of Collective Action is that larger groups are less likely to achieve their goals than smaller groups. He offers an important definition of a collective good that many future authors will work with: "A common, collective or collectivegood is here defined as any good such that if person X . . in a group consumes it, it cannot feasibly be withheld from others in that group." Since the goal of a group is to further the interest of its members, the competition of individual and common interests in an organization mimics that of a free market: people always maximize self interest in a rational way. He argues against the popular idea that humans have an abstract and innate 'propensity' to organize. To support his thesis, Olson presents several key qualitative and quantitative differences between large and small groups. We extend the Olson's model to an infinitely repeated interaction snd sdhow that: 1) the willingness to contribute for collective good decreases when group size increases and do not exist economic incentive to enforce coordination 2) the willingness to contribute for collective good decreaseswhen social interaction is more difficult, keeping fixed the size. 3) the willingness to contribute for collective good decreaseswhen monitoring the others is more difficult, keeping fixed size and level of social intercation 4) a formal organization is necessary to reduce the negative impact that the group size has on the willingnes to contribute for a collective good.