Bounded-Distance Network Creation Games
Davide Bil\`o, Luciano Gual\`a, and Guido Proietti

TL;DR
This paper introduces a new network creation game model where players' costs depend on maintaining bounded distances, analyzing the structure of equilibria, computational complexity, and the efficiency loss measured by the Price of Anarchy.
Contribution
It defines the MaxBD and SumBD models with bounded-distance constraints, studies their equilibrium properties, and provides bounds on the Price of Anarchy under various conditions.
Findings
Computing best responses is NP-hard.
Equilibria can be arbitrarily bad with non-uniform bounds.
Price of Anarchy bounds depend on uniform distance bounds.
Abstract
A network creation game simulates a decentralized and non-cooperative building of a communication network. Informally, there are players sitting on the network nodes, which attempt to establish a reciprocal communication by activating, incurring a certain cost, any of their incident links. The goal of each player is to have all the other nodes as close as possible in the resulting network, while buying as few links as possible. According to this intuition, any model of the game must then appropriately address a balance between these two conflicting objectives. Motivated by the fact that a player might have a strong requirement about its centrality in the network, in this paper we introduce a new setting in which if a player maintains its (either maximum or average) distance to the other nodes within a given associated bound, then its cost is simply equal to the number of activated…
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Taxonomy
TopicsGame Theory and Applications · Game Theory and Voting Systems · Economic theories and models
