Congestion games with priority-based scheduling

We reconsider atomic and non-atomic affine congestion games under the assumption that players are partitioned into p priority classes and resources schedule their users according to a priority-based policy, breaking ties uniformly at random. We derive tight bounds on both the price of anarchy and the price of stability as a function of p, revealing an interesting separation between the general case of and the priority-free scenario of . In fact, while in absence of priorities the worst-case prices of anarchy and stability of non-atomic games are lower than their counterparts in atomic ones, the two classes share the same bounds when . Moreover, while the worst-case price of stability is lower than the worst-case price of anarchy in atomic games with no priorities, their values become equal when . Said differently, the presence of priorities simultaneously irons out any combinatorial difference between atomic and non-atomic requests and among different pure Nash equilibria to produce a unique representative worst-case situation. Notably, our results keep holding even under singleton strategies. Besides being of independent interest, priority-based scheduling shares tight connections with online load balancing and finds a natural application within the theory of coordination mechanisms and cost-sharing policies for congestion games. Under this perspective, a number of possible research directions also arise.