The worst absolute surplus loss in the problem of commons: random priority versus average cost

A good is produced with increasing marginal cost. A group of agents want at most one unit of that good. The two classic methods that solve this problem are average cost and random priority. In the first method users request a unit ex ante and every agent who gets a unit pay average cost of the number of produced units. Under random priority users are ordered without bias and the mechanism successively offers the units at price equal to marginal cost. We compare these mechanisms by the worst absolute surplus loss and find that random priority unambiguously performs better than average cost for any cost function and any number of agents. Fixing the cost function, we show that the ratio of worst absolute surplus losses will be bounded by positive constants for any number of agents, hence the above advantage of random priority is not very large. I especially thank Herve Moulin for helpful comments and suggestions. I also appreciate the feedback from Justin Leroux and an anonymous referee.