Network Connection Games with Disconnected Equilibria
Ulrik Brandes, Martin Hoefer, Bobo Nick

TL;DR
This paper extends a network creation game to include disconnected equilibria, analyzing their existence, structure, and costs, and revealing how coordination can significantly improve social outcomes.
Contribution
It introduces a penalized version of the network creation game allowing disconnected equilibria and characterizes their properties and social efficiency.
Findings
Pure Nash equilibria always exist in the penalized game.
The price of anarchy can grow linearly with the number of players.
Strong equilibria have a bounded price of anarchy, at most 4.
Abstract
In this paper we extend a popular non-cooperative network creation game (NCG) to allow for disconnected equilibrium networks. There are n players, each is a vertex in a graph, and a strategy is a subset of players to build edges to. For each edge a player must pay a cost \alpha, and the individual cost for a player represents a trade-off between edge costs and shortest path lengths to all other players. We extend the model to a penalized game (PCG), for which we reduce the penalty counted towards the individual cost for a pair of disconnected players to a finite value \beta. Our analysis concentrates on existence, structure, and cost of disconnected Nash and strong equilibria. Although the PCG is not a potential game, pure Nash equilibria always and pure strong equilibria very often exist. We provide tight conditions under which disconnected Nash (strong) equilibria can evolve.…
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Taxonomy
TopicsGame Theory and Applications · Opinion Dynamics and Social Influence · Complex Network Analysis Techniques
