**Les Cahiers de Recherche - HEC Paris**
# No 662:

Free Access to the Commons: Random Priority versus Average Cost

*Herve CRES and Herve MOULIN*
**Abstract:** A technology with increasing marginal costs produces
indivisible units of service. Each agent wants at most one unit of service.
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 overproductions. Which one leads
to a less severe tragedy ? We show that RP tends to overproduce less but
that which game collects more social surplus depends much on the
configuration of the demand (namely the social value of the goods
produced).

We give general results as well as canonical examples,
describing demand and cost profiles for which one mechanism outperforms the
other. We find that the key element for the comparison is the crowding
ratio, i.e., the number of potential users over the number of units of
output users can afford: (1) we prove that the more crowded the commons,
the more RP outperforms AC, and (2) we exhibit a threshold value of 2.4 for
the crowding ratio beyond which RP strongly outperforms AC, and beneath
which AC only mildly outperforms RP. Thus the Random Priority mechanism
offers a (partial) probabilistic resolution of the tragedy of crowded
commons.

**Keywords:** tragedy of the commons; increasing marginal cost; scheduling; cooperative production; priority; (follow links to similar papers)

**JEL-Codes:** D60; D62; D72; (follow links to similar papers)

65 pages, November 2, 1998

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