Greedy Selfish Network Creation

We introduce and analyze greedy equilibria (GE) for the well-known model of selfish network creation by Fabrikant et al.[PODC'03]. GE are interesting for two reasons: (1) they model outcomes found by agents which prefer smooth adaptations over radical strategy-changes, (2) GE are outcomes found by agents which do not have enough computational resources to play optimally. In the model of Fabrikant et al. agents correspond to Internet Service Providers which buy network links to improve their quality of network usage. It is known that computing a best response in this model is NP-hard. Hence, poly-time agents are likely not to play optimally. But how good are networks created by such agents? We answer this question for very simple agents. Quite surprisingly, naive greedy play suffices to create remarkably stable networks. Specifically, we show that in the SUM version, where agents attempt to minimize their average distance to all other agents, GE capture Nash equilibria (NE) on trees and that any GE is in 3-approximate NE on general networks. For the latter we also provide a lower bound of 3/2 on the approximation ratio. For the MAX version, where agents attempt to minimize their maximum distance, we show that any GE-star is in 2-approximate NE and any GE-tree having larger diameter is in 6/5-approximate NE. Both bounds are tight. We contrast these positive results by providing a linear lower bound on the approximation ratio for the MAX version on general networks in GE. This result implies a locality gap of $\Omega(n)$ for the metric min-max facility location problem, where n is the number of clients.Comment: 28 pages, 8 figures. An extended abstract of this work was accepted at WINE'1

Interfacing the Network: An Embedded Approach to Network Instrument Creation

This paper discusses the design, construction, and development of a multi-site collaborative instrument, The Loop, developed by the JacksOn4 collective during 2009-10 and formally presented in Oslo at the arts.on.wires and NIME conferences in 2011. The development of this instrument is primarily a reaction to historical network performance that either attempts to present traditional acoustic practice in a distributed format or utilises the network as a conduit to shuttle acoustic and performance data amongst participant nodes. In both scenarios the network is an integral and indispensible part of the performance, however, the network is not perceived as an instrument, per se. The Loop is an attempt to create a single, distributed hybrid instrument retaining traditionally acoustic interfaces and resonant bodies that are mediated by the network. The embedding of the network into the body of the instrument raises many practical and theoretical discussions, which are explored in this paper through a reflection upon the notion of the distributed instrument and the way in which its design impacts the behaviour of the participants (performers and audiences); the mediation of musical expression across networks; the bi-directional relationship between instrument and design; as well as how the instrument assists in the realisation of the creators’ compositional and artistic goals

On a Bounded Budget Network Creation Game

We consider a network creation game in which each player (vertex) has a fixed budget to establish links to other players. In our model, each link has unit price and each agent tries to minimize its cost, which is either its local diameter or its total distance to other players in the (undirected) underlying graph of the created network. Two versions of the game are studied: in the MAX version, the cost incurred to a vertex is the maximum distance between the vertex and other vertices, and in the SUM version, the cost incurred to a vertex is the sum of distances between the vertex and other vertices. We prove that in both versions pure Nash equilibria exist, but the problem of finding the best response of a vertex is NP-hard. We take the social cost of the created network to be its diameter, and next we study the maximum possible diameter of an equilibrium graph with n vertices in various cases. When the sum of players' budgets is n-1, the equilibrium graphs are always trees, and we prove that their maximum diameter is Theta(n) and Theta(log n) in MAX and SUM versions, respectively. When each vertex has unit budget (i.e. can establish link to just one vertex), the diameter of any equilibrium graph in either version is Theta(1). We give examples of equilibrium graphs in the MAX version, such that all vertices have positive budgets and yet the diameter is Omega(sqrt(log n)). This interesting (and perhaps counter-intuitive) result shows that increasing the budgets may increase the diameter of equilibrium graphs and hence deteriorate the network structure. Then we prove that every equilibrium graph in the SUM version has diameter 2^O(sqrt(log n)). Finally, we show that if the budget of each player is at least k, then every equilibrium graph in the SUM version is k-connected or has diameter smaller than 4.Comment: 28 pages, 3 figures, preliminary version appeared in SPAA'1

Quality of Service in Network Creation Games

Network creation games model the creation and usage costs of networks formed by n selfish nodes. Each node v can buy a set of edges, each for a fixed price \alpha > 0. Its goal is to minimize its private costs, i.e., the sum (SUM-game, Fabrikant et al., PODC 2003) or maximum (MAX-game, Demaine et al., PODC 2007) of distances from $v$ to all other nodes plus the prices of the bought edges. The above papers show the existence of Nash equilibria as well as upper and lower bounds for the prices of anarchy and stability. In several subsequent papers, these bounds were improved for a wide range of prices \alpha. In this paper, we extend these models by incorporating quality-of-service aspects: Each edge cannot only be bought at a fixed quality (edge length one) for a fixed price \alpha. Instead, we assume that quality levels (i.e., edge lengths) are varying in a fixed interval [\beta,B], 0 < \beta <= B. A node now cannot only choose which edge to buy, but can also choose its quality x, for the price p(x), for a given price function p. For both games and all price functions, we show that Nash equilibria exist and that the price of stability is either constant or depends only on the interval size of available edge lengths. Our main results are bounds for the price of anarchy. In case of the SUM-game, we show that they are tight if price functions decrease sufficiently fast.Comment: An extended abstract of this paper has been accepted for publication in the proceedings of the 10th International Conference on Web and Internet Economics (WINE

Network Creation Games: Think Global - Act Local

We investigate a non-cooperative game-theoretic model for the formation of communication networks by selfish agents. Each agent aims for a central position at minimum cost for creating edges. In particular, the general model (Fabrikant et al., PODC'03) became popular for studying the structure of the Internet or social networks. Despite its significance, locality in this game was first studied only recently (Bil\`o et al., SPAA'14), where a worst case locality model was presented, which came with a high efficiency loss in terms of quality of equilibria. Our main contribution is a new and more optimistic view on locality: agents are limited in their knowledge and actions to their local view ranges, but can probe different strategies and finally choose the best. We study the influence of our locality notion on the hardness of computing best responses, convergence to equilibria, and quality of equilibria. Moreover, we compare the strength of local versus non-local strategy-changes. Our results address the gap between the original model and the worst case locality variant. On the bright side, our efficiency results are in line with observations from the original model, yet we have a non-constant lower bound on the price of anarchy.Comment: An extended abstract of this paper has been accepted for publication in the proceedings of the 40th International Conference on Mathematical Foundations on Computer Scienc

Geometric Network Creation Games

Network Creation Games are a well-known approach for explaining and analyzing the structure, quality and dynamics of real-world networks like the Internet and other infrastructure networks which evolved via the interaction of selfish agents without a central authority. In these games selfish agents which correspond to nodes in a network strategically buy incident edges to improve their centrality. However, past research on these games has only considered the creation of networks with unit-weight edges. In practice, e.g. when constructing a fiber-optic network, the choice of which nodes to connect and also the induced price for a link crucially depends on the distance between the involved nodes and such settings can be modeled via edge-weighted graphs. We incorporate arbitrary edge weights by generalizing the well-known model by Fabrikant et al.[PODC'03] to edge-weighted host graphs and focus on the geometric setting where the weights are induced by the distances in some metric space. In stark contrast to the state-of-the-art for the unit-weight version, where the Price of Anarchy is conjectured to be constant and where resolving this is a major open problem, we prove a tight non-constant bound on the Price of Anarchy for the metric version and a slightly weaker upper bound for the non-metric case. Moreover, we analyze the existence of equilibria, the computational hardness and the game dynamics for several natural metrics. The model we propose can be seen as the game-theoretic analogue of a variant of the classical Network Design Problem. Thus, low-cost equilibria of our game correspond to decentralized and stable approximations of the optimum network design.Comment: Accepted at 31st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA '19). 33 pages, 11 figure

Degree distributions of growing networks

The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree. The network is built by (i) creation of new nodes which each immediately attach to a pre-existing node, and (ii) creation of new links between pre-existing nodes. This process naturally generates correlated in- and out-degree distributions. When the node and link creation rates are linear functions of node degree, these distributions exhibit distinct power-law forms. By tuning the parameters in these rates to reasonable values, exponents which agree with those of the web graph are obtained

Encryption’s Importance to Economic and Infrastructure Security

Det övergripande syftet med den här avhandlingen var att utreda om network coopetition, samarbete mellan konkurrerande aktörer, kan öka värdeskapandet inom hälso- och sjukvården. Inom hälso- och sjukvården är network coopetition ett ämne som fått liten uppmärksamhet i tidigare studier. För att besvara syftet utvecklades en modell för network coopetition inom hälso- och sjukvården. Modellen applicerades sedan på en del av vårdkedjan för patienter i behov av neurokirurgisk vård. Resultaten från avhandlingen visar att: (1) Förutsättningarna för network coopetition i vårdkedjan för patienter i behov av neurokirurgisk vård är uppfyllda. (2) Det finns exempel på horisontell network coopetition i den studerade vårdkedjan. (3) Det existerar en diskrepans mellan hur aktörerna  ser  på  sitt  eget  och  de  andra  aktörernas  värdeskapande. (4)  Värdeskapandet bör utvärderas som ett gemensamt system där hänsyn tas till alla aktörer och utvärderas på process- nivå där hänsyn tas till alla intressenter. Dessa resultat leder fram till den övergripande slutsatsen är att network coopetition bör kunna öka värdeskapandet för högspecialiserade vårdkedjor med en stor andel inomlänspatienter.The overall purpose of this thesis was to investigate whether network coopetition, cooperation between competitive actors, can increase the value creation within the health care system. Within health care, network coopetition is a subject granted little attention in previous research. To fulfil the purpose a model for network coopetition within the health care system was developed. The model was the applied to one part of the chain of care for patients in need of neurosurgery. The results from this thesis show: (1) The conditions for network coopetition in the chain of care for patients in need of neurosurgery are fulfilled. (2) Examples of horizontal network coopetition have been found in the studied chain of care. (3) There is an existing discrepancy between how each actor recognizes its own and the other actors’ value creation. (4) The value creation ought to be evaluated as a common system where all actors are taken into account and at a process level where all stakeholders are considered. These results supports the final conclusion that network coopetition ought to be able to increase the value creation for highly specialized chain of cares with a large share of within-county patients