Resource-Aware Cost-Sharing Mechanisms with Priors
Vasilis Gkatzelis, Emmanouil Pountourakis, Alkmini Sgouritsa

TL;DR
This paper introduces resource-aware cost-sharing mechanisms that leverage prior information about users to achieve low price of anarchy in selfish scheduling games, extending applicability beyond convex or concave cost functions.
Contribution
It demonstrates that incorporating minimal prior information about users enables resource-aware mechanisms to maintain low PoA across a broader range of cost functions.
Findings
A mechanism with knowledge of two users guarantees constant PoA.
Using probabilistic user presence, the mechanism achieves logarithmic expected PoA.
Enhanced mechanisms outperform previous models for non-convex, non-concave cost functions.
Abstract
In a decentralized system with machines, we study the selfish scheduling problem where each user strategically chooses which machine to use. Each machine incurs a cost, which is a function of the total load assigned to it, and some cost-sharing mechanism distributes this cost among the machine's users. The users choose a machine aiming to minimize their own share of the cost, so the cost-sharing mechanism induces a game among them. We approach this problem from the perspective of a designer who can select which cost-sharing mechanism to use, aiming to minimize the price of anarchy (PoA) of the induced games. Recent work introduced the class of \emph{resource-aware} cost-sharing mechanisms, whose decisions can depend on the set of machines in the system, but are oblivious to the total number of users. These mechanisms can guarantee low PoA bounds for instances where the cost…
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