On Green Sustainability of Resource Selection Games with Equitable Cost-Sharing

As increasing concern for environmental sustainability urges to bring attention to green-aware multi-agent systems, we put forward a game-theoretic model in which agents compete for the usage of power-consuming resources and are charged a cost proportional to their fair share of the power consumption. Using the widely adopted cube-root rule for CMOS-based devices, our model becomes a congestion game in which two distinct parts coexist, namely, congestion games with polynomial latency functions and fair cost-sharing games. The interplay between these two components is governed by two resource-specific constants regulating the static and dynamic power consumption of each resource. Our findings show that, despite these games being highly inefficient in the general case (a super-constant price of stability), performance at equilibrium significantly improves (a constant price of anarchy) when the ratio between the static and dynamic power consumption of each resource remains bounded by a constant. This suggests that, in uncoordinated green-aware multi-agent systems, technology plays a fundamental role in shaping the efficiency of stable solutions.