Scheduling with Opting Out: Improving upon Random Priority

In a scheduling problem where agents can opt out, we show that the familiar Random Priority (RP) a rule can be improved upon by another mechanism dubbed Probabilistic Serial (PS). Both mechanisms are nonmanipulable in a strong sense, but the latter is Pareto superior to the former and serves a larger (expected number of agents. The PS equilibrium outcome is easier to compute than the RP outcome; on the other hand RP is easier to implement than PS. We show that the improvement of PS over RP is significant but small: at most a couple of percentage points in the relative welfare gain and the relative difference in quantity served. We conjecture that the latter never exceeds 8.33 %. Both gains vanish when the number of agents is large.

Commons with Increasing Marginal Costs: Random Priority versus Average Cost

Indivisible units are produced with increasing marginal costs. Under average cost, each user pays average cost. Under random priority, users are randomly ordered (without bias) and successively offered to buy at the true marginal cost. Both average cost (AC) and random priority (RP) inefficiently overproduce. RP tends to overproduce less, but which game collects more surplus depends much on the demand configuration. We show that a key to compare the welfare properties of the two mechanisms is the crowding factor, i.e., the number of potential users over the number of units of output users can afford: The more crowded the commons, the more RP outperforms AC. In the quadratic cost case, beyond the threshold value of 2.4 for the crowding factor, RP strongly outperforms AC; beneath it AC only mildly outperforms RP. Thus the RP mechanism manages crowded commons better than AC.

Commons with increasing marginal costs: random priority versus average cost

ndivisible units are produced with increasing marginal costs. Under average cost, each user pays average cost. Under random priority, users are randomly ordered (without bias) and successively offered to buy at the true marginal cost. Both average cost (AC) and random priority (RP) inefficiently overproduce. RP tends to overproduce less, but which game collects more surplus depends much on the demand configuration. We show that a key to compare the welfare properties of the two mechanisms is the crowding factor, i.e., the number of potential users over the number of units of output users can afford: The more crowded the commons, the more RP outperforms AC. In the quadratic cost case, beyond the threshold value of 2.4 for the crowding factor, RP strongly outperforms AC; beneath it AC only mildly outperforms RP. Thus the RP mechanism manages crowded commons better than AC

An efficient and almost budget balanced cost sharing method

For a convex technology C we characterize cost sharing games where the Nash equilibrium demands maximize total surplus. Budget balance is possible if and only if C is polynomial of degree n−1n−1 or less. For general C, the residual* cost shares are balanced if at least one demand is null, a characteristic property. If the cost function is totally monotone, a null demand receives cash and total payments may exceed actual cost. The ratio of excess payment to efficient surplus is at most View the MathML sourcemin{2logn,1}. For power cost functions, C(a)=apC(a)=ap, p>1p>1, the ratio of budget imbalance to efficient surplus vanishes as View the MathML source1np−1. For analytic cost functions, the ratio converges to zero exponentially along a given sequence of users. All asymptotic properties are lost if the cost function is not smooth

Free access to the commons : random priority versus average cost

Available from INIST (FR), Document Supply Service, under shelf-number : DO 6409 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc

The price of anarchy of serial, average and incremental cost sharing

Price of anarchy, Cost sharing, Average cost, Serial cost, Incremental cost, C60, C72, D60,