Conflicting Congestion Effects in Resource Allocation Games

Michal Feldman, Tami Tamir
2012 Operations Research  
We study strategic resource allocation settings, where jobs are self-interested players who choose resources with the objective of minimizing their individual cost. Our framework departs from the existing game theoretic models of resource allocation in two fundamental ways. First, while most of the previous work has considered cost structures with either negative congestion effects or positive ones, we introduce cost functions that encompass both effects. Second, we do not assume the existence
more » ... f a fixed set of resources; rather, jobs can always activate new resources, but activating a new resource is costly. Specifically, in our model there is a set of heterogeneous jobs and an unlimited supply of identical resources. The cost of a job is the load on its chosen resource plus its share in the resource's activation cost, which is proportional to its length. We provide results with respect to equilibrium existence and the inefficiency introduced due to self-interested behavior. We show that if the resource's activation cost is shared equally among its users, a pure Nash equilibrium (NE) might not exist. In contrast, under the proportional sharing rule, a pure NE always exists and we provide a poly-time algorithm for computing it. The algorithm is a variant of the LPT (Longest processing time) algorithm, whose analysis requires the establishment of a new non-trivial property of schedules obtained by this rule. With respect to the inefficiency of equilibria, we prove that there is no universal bound for the worst-case inefficiency (as quantified by the "price of anarchy" measure). Yet, the best-case inefficiency (quantified by the "price of stability" measure) is bounded by 5 4 and this is tight. These results add another layer to the growing literature on the price of anarchy and stability, which studies the extent to which selfish behavior affects system efficiency. Finally, we observe that unlike congestion games, best-response dynamics are not guaranteed to converge to a Nash equilibrium.
doi:10.1287/opre.1120.1051 fatcat:zl2krqpc35dqpfbe3ponahu32m