, Volume 36, Issue 3, pp 379-405
Date: 22 Aug 2007

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

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Abstract

We compute the price of anarchy (PoA) of three familiar demand games, i.e., the smallest ratio of the equilibrium to efficient surplus, over all convex preferences quasi-linear in money. For any convex cost, the PoA is at least \(\frac{1}{n}\) in the average and serial games, where n is the number of users. It is zero in the incremental game for piecewise linear cost functions. With quadratic costs, the PoA of the serial game is \(\theta (\frac{1}{\log n})\) , and \(\theta (\frac{1}{n})\) for the average and incremental games. This generalizes if the marginal cost is convex or concave, and its elasticity is bounded.