Bridging the Gap Between Central and Local Decision-Making: The Efficacy of Collaborative Equilibria in Altruistic Congestion Games

TL;DR

The main contributions are in constructing tractable linear programs that provide bounds on the price of anarchy of collaborative equilibria in altruistic congestion games and bridge the gap between the known efficiency guarantees of centralized and distributed decision-making paradigms.

Abstract

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.

Figures (2)

• Figure 1: Price of Anarchy with different collaborative decision-making paradigms in various classes of congestion games. In each plot is the $k$-strong price of anarchy within the respective class of altruistic congestion games with latency functions formed by linear combinations of the functions in $\mathcal{L}$. The bounds are generated by the linear programs in \ref{['thm:alt']}. In each setting, increasing the amount of collaboration ($k$) improves the equilibrium efficiency guarantee.
• Figure 2: Game construction for worst-case $k$-strong price of anarchy. Three of the $n$ players' action sets are shown (color-coded in yellow, green, and purple, respectively) on three of $n!$ rings for the label $(a,x,b)=(2,1,1)$. A ring has $n$ positions, one for each player. For a label $(a,x,b)$, we generate $n!$ rings for all the orderings of players over positions. This is repeated for each label. Players still only have two actions, but each action covers resources from each ring. The value of a resource with label $(a,x,b)$ is equal to a value of $\theta^\star(a,x,b)$, which we can set as equal to a solution to \ref{['opt:lb']}.

Theorems & Definitions (4)

• Definition 1
• Proposition III.1
• proof
• Theorem III.2