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

On the Structure of Equilibria in Basic Network Formation

We study network connection games where the nodes of a network perform edge swaps in order to improve their communication costs. For the model proposed by Alon et al. (2010), in which the selfish cost of a node is the sum of all shortest path distances to the other nodes, we use the probabilistic method to provide a new, structural characterization of equilibrium graphs. We show how to use this characterization in order to prove upper bounds on the diameter of equilibrium graphs in terms of the size of the largest $k$-vicinity (defined as the the set of vertices within distance $k$ from a vertex), for any $k \geq 1$ and in terms of the number of edges, thus settling positively a conjecture of Alon et al. in the cases of graphs of large $k$-vicinity size (including graphs of large maximum degree) and of graphs which are dense enough. Next, we present a new swap-based network creation game, in which selfish costs depend on the immediate neighborhood of each node; in particular, the profit of a node is defined as the sum of the degrees of its neighbors. We prove that, in contrast to the previous model, this network creation game admits an exact potential, and also that any equilibrium graph contains an induced star. The existence of the potential function is exploited in order to show that an equilibrium can be reached in expected polynomial time even in the case where nodes can only acquire limited knowledge concerning non-neighboring nodes.Comment: 11 pages, 4 figure

Selfish Network Creation with Non-Uniform Edge Cost

Network creation games investigate complex networks from a game-theoretic point of view. Based on the original model by Fabrikant et al. [PODC'03] many variants have been introduced. However, almost all versions have the drawback that edges are treated uniformly, i.e. every edge has the same cost and that this common parameter heavily influences the outcomes and the analysis of these games. We propose and analyze simple and natural parameter-free network creation games with non-uniform edge cost. Our models are inspired by social networks where the cost of forming a link is proportional to the popularity of the targeted node. Besides results on the complexity of computing a best response and on various properties of the sequential versions, we show that the most general version of our model has constant Price of Anarchy. To the best of our knowledge, this is the first proof of a constant Price of Anarchy for any network creation game.Comment: To appear at SAGT'1

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

Patterns and drivers of climatic niche dynamics during biological invasions of island-endemic amphibians, reptiles, and birds

Shifts between native and alien climatic niches pose a major challenge for predicting biological invasions. This is particularly true for insular species because geophysical barriers could constrain the realization of their fundamental niches, which may lead to underestimates of their invasion potential. To investigate this idea, we estimated the frequency of shifts between native and alien climatic niches and the magnitude of climatic mismatches using 80,148 alien occurrences of 46 endemic insular amphibian, reptile, and bird species. Then, we assessed the influence of nine potential predictors on climatic mismatches across taxa, based on species' characteristics, native range physical characteristics, and alien range properties. We found that climatic mismatch is common during invasions of endemic insular birds and reptiles: 78.3% and 55.1% of their respective alien records occurred outside of the environmental space of species' native climatic niche. In comparison, climatic mismatch was evident for only 16.2% of the amphibian invasions analyzed. Several predictors significantly explained climatic mismatch, and these varied among taxonomic groups. For amphibians, only native range size was associated with climatic mismatch. For reptiles, the magnitude of climatic mismatch was higher for species with narrow native altitudinal ranges, occurring in topographically complex or less remote islands, as well as for species with larger distances between their native and alien ranges. For birds, climatic mismatch was significantly larger for invasions on continents with higher phylogenetic diversity of the recipient community, and when the invader was more evolutionarily distinct. Our findings highlight that apparently common niche shifts of insular species may jeopardize our ability to forecast their potential invasions using correlative methods based on climatic variables. Also, we show which factors provide additional insights on the actual invasion potential of insular endemic amphibians, reptiles, and birds

Capacity of countries to reduce biological invasions

The extent and impacts of biological invasions on biodiversity are largely shaped by an array of socio-economic and environmental factors, which exhibit high variation among countries. Yet, a global analysis of how these factors vary across countries is currently lacking. Here, we investigate how five broad, country-specific socio-economic and environmental indices (Governance, Trade, Environmental Performance, Lifestyle and Education, Innovation) explain country-level (1) established alien species (EAS) richness of eight taxonomic groups, and (2) proactive or reactive capacity to prevent and manage biological invasions and their impacts. These indices underpin many aspects of the invasion process, including the introduction, establishment, spread and management of alien species. They are also general enough to enable a global comparison across countries, and are therefore essential for defining future scenarios for biological invasions. Models including Trade, Governance, Lifestyle and Education, or a combination of these, best explained EAS richness across taxonomic groups and national proactive or reactive capacity. Historical (1996 or averaged over 1996–2015) levels of Governance and Trade better explained both EAS richness and the capacity of countries to manage invasions than more recent (2015) levels, revealing a historical legacy with important implications for the future of biological invasions. Using Governance and Trade to define a two-dimensional socio-economic space in which the position of a country captures its capacity to address issues of biological invasions, we identified four main clusters of countries in 2015. Most countries had an increase in Trade over the past 25 years, but trajectories were more geographically heterogeneous for Governance. Declines in levels of Governance are concerning as they may be responsible for larger levels of invasions in the future. By identifying the factors influencing EAS richness and the regions most susceptible to changes in these factors, our results provide novel insights to integrate biological invasions into scenarios of biodiversity change to better inform decision-making for policy and the management of biological invasions

European scenarios for future biological invasions

1. Invasive alien species are one of the major threats to global biodiversity, ecosystem integrity, nature's contributions to people and human health. While scenarios about potential future developments have been available for other global change drivers for quite some time, we largely lack an understanding of how biological invasions might unfold in the future across spatial scales. 2. Based on previous work on global invasion scenarios, we developed a workflow to downscale global scenarios to a regional and policy-relevant context. We applied this workflow at the European scale to create four European scenarios of biological invasions until 2050 that consider different environmental, socio-economic and socio-cultural trajectories, namely the European Alien Species Narratives (Eur-ASNs). 3. We compared the Eur-ASNs with their previously published global counterparts (Global-ASNs), assessing changes in 26 scenario variables. This assessment showed a high consistency between global and European scenarios in the logic and assumptions of the scenario variables. However, several discrepancies in scenario variable trends were detected that could be attributed to scale differences. This suggests that the workflow is able to capture scale-dependent differences across scenarios. 4. We also compared the Global- and Eur-ASNs with the widely used Global and European Shared Socioeconomic Pathways (SSPs), a set of scenarios developed in the context of climate change to capture different future socio-economic trends. Our comparison showed considerable divergences in the scenario space occupied by the different scenarios, with overall larger differences between the ASNs and SSPs than across scales (global vs. European) within the scenario initiatives. 5. Given the differences between the ASNs and SSPs, it seems that the SSPs do not adequately capture the scenario space relevant to understanding the complex future of biological invasions. This underlines the importance of developing independent but complementary scenarios focussed on biological invasions. The downscaling workflow we implemented and presented here provides a tool to develop such scenarios across different regions and contexts. This is a major step towards an improved understanding of all major drivers of global change, including biological invasions

High-harmonic generation from a confined atom

The order of high harmonics emitted by an atom in an intense laser field is limited by the so-called cutoff frequency. Solving the time-dependent Schr\"odinger equation, we show that this frequency can be increased considerably by a parabolic confining potential, if the confinement parameters are suitably chosen. Furthermore, due to confinement, the radiation intensity remains high throughout the extended emission range. All features observed can be explained with classical arguments.Comment: 4 pages(tex files), 4 figures(eps files); added references and comment

Theory for the ultrafast ablation of graphite films

The physical mechanisms for damage formation in graphite films induced by femtosecond laser pulses are analyzed using a microscopic electronic theory. We describe the nonequilibrium dynamics of electrons and lattice by performing molecular dynamics simulations on time-dependent potential energy surfaces. We show that graphite has the unique property of exhibiting two distinct laser induced structural instabilities. For high absorbed energies (> 3.3 eV/atom) we find nonequilibrium melting followed by fast evaporation. For low intensities above the damage threshold (> 2.0 eV/atom) ablation occurs via removal of intact graphite sheets.Comment: 5 pages RevTeX, 3 PostScript figures, submitted to Phys. Re

Relativistic treatment of harmonics from impurity systems in quantum wires

Within a one particle approximation of the Dirac equation we investigate a defect system in a quantum wire. We demonstrate that by minimally coupling a laser field of frequency omega to such an impurity system, one may generate harmonics of multiples of the driving frequency. In a multiple defect system one may employ the distance between the defects in order to tune the cut-off frequency.Comment: 9 pages Latex, 8 eps figures, section added, numerics improve