Random Priority: A Probabilistic Resolution of the 
Tragedy of the Commons


Herv‚ CrŠs, (H.E.C. School of Management)


Herv‚ Moulin, (Duke University)





Abstract:

The celebrated "tragedy of the commons" arises when a certain technology with increasing marginal cost is the common property of its users.  Examples include the exploitation of fisheries and other natural resources, as well as queuing problems where users want a service and the externalities result from congestion.
In a very simple model of the tragedy we compare two natural mechanisms where users have free access to the technology.  In one mechanism, Average Cost, each user pays the same average cost; in the other, Random Priority, users are randomly ordered (without bias) and successively offered to buy at the "true" marginal cost.
Both mechanisms, AC and RP, lead to inefficient overproduction, but the question is which one leads to a less severe "tragedy"?  We show that RP tends to overproduce less but that which game collects more social surplus depend much on the configuration of the demand (namely the social value of the goods produced).  Specifically, a spread demand may favor AC but a concentrated demand (fairly homogeneous users) strongly favors RP; moreover, the more crowded the commons the more RP outperforms AC.
In order to study the expected equilibrium outcome under RP, we introduce a probabilistic variant of serial cost sharing, of which the outcome is both Pareto superior and very close to the outcome of RP.  The Probabilistic Serial game is more involved than the RP game but its equilibrium outcome is easy to compute.






JEL Classification: D60, D62, D72

Keywords: tragedy of the commons, increasing marginal costs, cooperative production, sequencing