Bridging the Gap Between Central and Local Decision-Making: The Efficacy of Collaborative Equilibria in Altruistic Congestion Games
Congestion games are popular models often used to study the system-level inefficiencies caused by selfish agents, typically measured by the price of anarchy. One may expect that aligning the agents' preferences with the system-level objective--altruistic behavior--would improve efficiency, but recent works have shown that altruism can lead to more significant inefficiency than selfishness in congestion games. In this work, we study to what extent the localness of decision-making causes inefficiency by considering collaborative decision-making paradigms that exist between centralized and distributed in altruistic congestion games. In altruistic congestion games with convex latency functions, the system cost is a super-modular function over the player's joint actions, and the Nash equilibria of the game are local optima in the neighborhood of unilateral deviations. When agents can collaborate, we can exploit the common-interest structure to consider equilibria with stronger local optimality guarantees in the system objective, e.g., if groups of k agents can collaboratively minimize the system cost, the system equilibria are the local optima over k-lateral deviations. Our main contributions are in constructing tractable linear programs that provide bounds on the price of anarchy of collaborative equilibria in altruistic congestion games. Our findings bridge the gap between the known efficiency guarantees of centralized and distributed decision-making paradigms while also providing insights into the benefit of inter-agent collaboration in multi-agent systems.