Colored Resource Allocation Games

We introduce Colored Resource Allocation Games as a new model for selfish routing and wavelength assignment in multifiber all-optical networks. Colored Resource Allocation Games are a generalization of congestion and bottleneck games where players have their strategies in multiple copies (colors). We focus on two main subclasses of these games depending on the player cost: in Colored Congestion Games the player cost is the sum of latencies of the resources allocated to the player, while in Colored Bottleneck Games the player cost is the maximum of these latencies. We investigate the pure price of anarchy for three different social cost functions and prove tight bounds for each separate case. Our bounds for the two standard social cost functions (maximum and average player cost) generalize earlier results. The third social cost function is particularly meaningful in the setting of multifiber all-optical networks, where it captures the objective of fiber cost minimization.