We introduce the notion of coordination mechanisms to improve the performance in systems with independent selfish and non-colluding agents. The quality of a coordination mechanism is measured by its price of anarchy-the worst-case performance of a Nash equilibrium over the (centrally controlled) social optimum. We give upper and lower bounds for the price of anarchy for selfish task allocation and congestion games.

We present the rst poly-logarithmic competitive online algorithm for minimum metric bipartite matching. Via induction and a careful use of potential functions, we show that a simple randomized greedy algorithm is competitive on a hierarchically separated tree. Application of recent results on randomized embedding of metrics into trees yield the poly-logarithmic result for general metrics.

a b s t r a c tWe introduce the notion of coordination mechanisms to improve the performance in systems with independent selfish and non-colluding agents. The quality of a coordination mechanism is measured by its price of anarchy-the worst-case performance of a Nash equilibrium over the (centrally controlled) social optimum. We give upper and lower bounds for the price of anarchy for selfish task allocation and congestion games.

Abstract. We study the online matching problem when the metric space is a single straight line. For this case, the offline matching problem is trivial but the online problem has been open and the best known competitive ratio was the trivial Θ(n) where n is the number of requests. It was conjectured that the generalized Work Function Algorithm has constant competitive ratio for this problem. We show that it is in fact Ω(log n) and O(n), and make some progress towards proving a better upper bound by establishing some structural properties of the solutions. Our technique for the upper bound doesn't use a potential function but it reallocates the online cost in a way that the comparison with the offline cost becomes more direct.

No abstract