Fair Tree Connection Games with Topology-Dependent Edge Cost
Davide Bil\`o, Tobias Friedrich, Pascal Lenzner, Anna Melnichenko,, Louise Molitor

TL;DR
This paper introduces a tree formation game with topology-dependent edge costs, analyzing the existence, structure, and efficiency of equilibria, and demonstrating that self-organized networks are nearly optimal and fairly distributed.
Contribution
It presents a novel dynamic cost model for tree formation games, proving equilibrium existence for many agents, and analyzing their efficiency and fairness properties.
Findings
Equilibria may not always exist, but do for infinitely many agents.
Equilibrium trees have bounded Price of Anarchy and Price of Stability.
Self-organized trees are nearly as cost-effective and fair as optimal centralized solutions.
Abstract
How do rational agents self-organize when trying to connect to a common target? We study this question with a simple tree formation game which is related to the well-known fair single-source connection game by Anshelevich et al. (FOCS'04) and selfish spanning tree games by Gourv\`es and Monnot (WINE'08). In our game agents correspond to nodes in a network that activate a single outgoing edge to connect to the common target node (possibly via other nodes). Agents pay for their path to the common target, and edge costs are shared fairly among all agents using an edge. The main novelty of our model is dynamic edge costs that depend on the in-degree of the respective endpoint. This reflects that connecting to popular nodes that have increased internal coordination costs is more expensive since they can charge higher prices for their routing service. In contrast to related models, we show…
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