Multilevel Network Games
Sebastian Abshoff, Andreas Cord-Landwehr, Daniel Jung, and Alexander, Skopalik

TL;DR
This paper studies multilevel network games where nodes can become gateways to a high-speed network, analyzing equilibrium existence, efficiency, and dynamics for different cost models and parameters.
Contribution
It provides a comprehensive analysis of equilibrium properties, price of anarchy, and dynamics in multilevel network games with SUM and MAX cost functions.
Findings
Price of anarchy varies with the cost parameter
Equilibria exist under certain girth conditions
SUM-game is not weakly acyclic
Abstract
We consider a multilevel network game, where nodes can improve their communication costs by connecting to a high-speed network. The nodes are connected by a static network and each node can decide individually to become a gateway to the high-speed network. The goal of a node is to minimize its private costs, i.e., the sum (SUM-game) or maximum (MAX-game) of communication distances from to all other nodes plus a fixed price if it decides to be a gateway. Between gateways the communication distance is , and gateways also improve other nodes' distances by behaving as shortcuts. For the SUM-game, we show that for , the price of anarchy is and in this range equilibria always exist. In range the price of anarchy is , and for it is constant. For the…
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Taxonomy
TopicsGame Theory and Applications · Opinion Dynamics and Social Influence · Economic theories and models
