In a typical overlay network for routing or content sharing, each node must select a fixed number of immediate overlay neighbors for routing traffic or content queries. A selfish node entering such a network would select neighbors so as to minimize the weighted sum of expected access costs to all its destinations. Previous work on selfish neighbor selection has built intuition with simple models where edges are undirected, access costs are modeled by hop-counts, and nodes have potentially

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... ded degrees. However, in practice, important constraints not captured by these models lead to richer games with substantively and fundamentally different outcomes. Our work models neighbor selection as a game involving directed links, constraints on the number of allowed neighbors, and costs reflecting both network latency and node preference. We express a node's "best response" wiring strategy as a k-median problem on asymmetric distance, and use this formulation to obtain pure Nash equilibria. We experimentally examine the properties of such stable wirings on synthetic topologies, as well as on real topologies and maps constructed from PlanetLab and AS-level Internet measurements. Our results indicate that selfish nodes can reap substantial performance benefits when connecting to overlay networks constructed by naive nodes. On the other hand, in overlays that are dominated by selfish nodes, the resulting stable wirings are optimized to such great extent that even uninformed newcomers can extract near-optimal performance through naive wiring strategies. or even most players do not play optimally -a setting which we believe to be typical. Interesting questions along these lines include an assessment of the advantage to a player from employing an optimizing strategy, when most other players do not, or more broadly, whether employing an optimizing strategy by a relatively small number of players could be enough to achieve global efficiencies. Scope and Contributions: In this paper, we formulate and answer such questions using a combination of modeling, analysis, and extensive simulations using synthetic and real datasets. Our starting point is the definition of a network creation game that is better suited for settings of P2P and overlay routing applications -settings that necessitate the relaxation and/or modification of some of the central modeling assumptions of prior work. In that regard, the central aspects of our model are: (1) Bounded Degree: Most protocols used for implementing overlay routing or content sharing impose hard constraints on the maximum number of overlay neighbors. For example, in popular versions of BitTorrent a client may select up to 35 nodes from a neighbors' list provided by the Tracker of a particular torrent file [4] . 1 In overlay routing systems [8], the number of immediate nodes has to be kept small so as to reduce the monitoring and reporting overhead imposed by the link-state routing protocol implemented at the overlay layer. Motivated by these systems, we explicitly model such hard constraints on node degrees. Notice that in the prior studies cited above, node degrees were implicitly bounded (as opposed to explicitly constrained) by virtue of the tradeoff between the additional cost of setting up more links and the decreased communication distance achieved through the addition of new links. We also note that some of these earlier network creation games were proposed in the context of physical communication networks. In such networks, the cost of acquiring a link is instrumental to the design and operation of a critical infrastructure. Such concerns do not apply in the case of overlay networks such as those we consider in this paper. Thus, we argue that models in which node degrees are outcomes of an underlying optimization process do not faithfully reflect the realities of systems and applications we consider. (2) Directed Edges: Another important consideration in the 1 KaZaA and FastTrack include neighbor constraints at multiple levels: ordinary nodes (ON) may select up to 5 super nodes (SN) from a larger list for establishing initial negotiation and then maintain connection with only one of these; SNs may connect to at most 50 other SNs (from a typical population of SNs ranging between 25K and 40K [5] ) and accept between 55 to 70 (or 100 to 160) children ONs (depending on their provisioning). New versions of Gnutella and Limewire involve a similar two-level architecture [6] with associated constraints. Similarly, DHT routing protocols like Chord [7] impose hard constraints on the number of first hop neighbors.