Coordination Mechanisms

Abstract

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.

The Price of Optimum in a Matching Game

“…In this context, the price of anarchy (PoA) [6,7], defined as the value of the worst Nash equilibrium relative to the social optimum, is a well established measure of the performance deterioration. A game with a high PoA needs regulation and several ways to improve the system performance exist in the literature, including coordination mechanisms [8] and Stackelberg strategies [3,4,[9][10][11][12][13][14]. This paper deals with the latter.…”

Strategic Scheduling Games: Equilibria and Efficiency

“…Following [19] we define a coordination mechanism as the set of scheduling policies (algorithms), that are deployed on the machines; these indirectly define the individual completion times functions c j : M |J | → + of the players. Thus choosing a coordination mechanism is equivalent to choosing completion time functions for players in J .…”

“…It is a non-preemptive ordering policy that achieves P oA = 4 3 − 1 3m on identical machines and at most O(log m) on uniformly related and restricted assignment machines. The first bound emerges by the analysis of the longest-first greedy algorithm by Graham [32] (upper bound) and by the analysis of Christodoulou et al [19] (lower bound). The second comes from the analysis of [34].…”

“…The idea is to specify local operational rules per resource, so as to coordinate users towards globally efficient system utilization. The deployment of such local rules was formalized in [19], under the notion of coordination mechanisms and demonstrated for scheduling and network congestion games. In scheduling, local policies are scheduling algorithms deployed on the machines; their set is referred to as a coordination mechanism.…”

“…In section 3 we discuss several results regarding the most studied coordination mechanisms from the literature. These include the scheduling model (preemptive mechanism) introduced in [36] and further studied in [23,20,28,9,24,46] (subsection 3.1), non-preemptive ordering mechanisms studied in [5,19,34,22] (subsection 3.2) and a brief account of mechanisms for the most general scheduling environment of unrelated machines (subsection 3.5) [34,10,14]. In section 4 we revisit nonpreemptive ordering mechanisms in the context of truthfulness [19,18], where agents may misreport their processing loads to the mechanism so as to minimize their completion time in the outcome of the game.…”