On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum

Efficiency in Multi-objective Games

In a multi-objective game, each agent individually evaluates each overall action-profile on multiple objectives. I generalize the price of anarchy to multi-objective games and provide a polynomial-time algorithm to assess it. This work asserts that policies on tobacco promote a higher economic efficiency

Extended Smoothed Boundary Method for Solving Partial Differential Equations with General Boundary Conditions on Complex Boundaries

In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original differential equations such that the equations are solved in the region where a domain parameter takes a specified value while boundary conditions are imposed on the region where the value of the domain parameter varies smoothly across a short distance. The mathematical derivations are straightforward and generically applicable to a wide variety of partial differential equations. To demonstrate the general applicability of the approach, we provide four examples herein: (1) the diffusion equation with both Neumann and Dirichlet boundary conditions; (2) the diffusion equation with both surface diffusion and reaction; (3) the mechanical equilibrium equation; and (4) the equation for phase transformation with the presence of additional boundaries. The solutions for several of these cases are validated against corresponding analytical and semi-analytical solutions. The potential of the approach is demonstrated with five applications: surface-reaction-diffusion kinetics with a complex geometry, Kirkendall-effect-induced deformation, thermal stress in a complex geometry, phase transformations affected by substrate surfaces, and a self-propelled droplet.Comment: This document is the revised version of arXiv:0912.1288v

A modification of Honoré's triple-link model in the synoptic problem

In New Testament studies, the synoptic problem is concerned with the relationships between the gospels of Matthew, Mark and Luke. In an earlier paper a careful specification in probabilistic terms was set up of Honoré's triple-link model. In the present paper, a modification of Honoré's model is proposed. As previously, counts of the numbers of verbal agreements between the gospels are examined to investigate which of the possible triple-link models appears to give the best fit to the data, but now using the modified version of the model and additional sets of data

Nash Social Welfare in Selfish and Online Load Balancing

In load balancing problems there is a set of clients, each wishing to select a resource from a set of permissible ones, in order to execute a certain task. Each resource has a latency function, which depends on its workload, and a client's cost is the completion time of her chosen resource. Two fundamental variants of load balancing problems are {\em selfish load balancing} (aka. {\em load balancing games}), where clients are non-cooperative selfish players aimed at minimizing their own cost solely, and {\em online load balancing}, where clients appear online and have to be irrevocably assigned to a resource without any knowledge about future requests. We revisit both selfish and online load balancing under the objective of minimizing the {\em Nash Social Welfare}, i.e., the geometric mean of the clients' costs. To the best of our knowledge, despite being a celebrated welfare estimator in many social contexts, the Nash Social Welfare has not been considered so far as a benchmarking quality measure in load balancing problems. We provide tight bounds on the price of anarchy of pure Nash equilibria and on the competitive ratio of the greedy algorithm under very general latency functions, including polynomial ones. For this particular class, we also prove that the greedy strategy is optimal as it matches the performance of any possible online algorithm

The mitochondrial genome of Angiostrongylus mackerrasae as a basis for molecular, epidemiological and population genetic studies

BACKGROUND: Angiostrongylus mackerrasae is a metastrongyloid nematode endemic to Australia, where it infects the native bush rat, Rattus fuscipes. This lungworm has an identical life cycle to that of Angiostrongylus cantonensis, a leading cause of eosinophilic meningitis in humans. The ability of A. mackerrasae to infect non-rodent hosts, specifically the black flying fox, raises concerns as to its zoonotic potential. To date, data on the taxonomy, epidemiology and population genetics of A. mackerrasae are unknown. Here, we describe the mitochondrial (mt) genome of A. mackerrasae with the aim of starting to address these knowledge gaps. METHODS: The complete mitochondrial (mt) genome of A. mackerrasae was amplified from a single morphologically identified adult worm, by long-PCR in two overlapping amplicons (8 kb and 10 kb). The amplicons were sequenced using the MiSeq Illumina platform and annotated using an in-house pipeline. Amino acid sequences inferred from individual protein coding genes of the mt genomes were concatenated and then subjected to phylogenetic analysis using Bayesian inference. RESULTS: The mt genome of A. mackerrasae is 13,640 bp in size and contains 12 protein coding genes (cox1-3, nad1-6, nad4L, atp6 and cob), and two ribosomal RNA (rRNA) and 22 transfer RNA (tRNA) genes. CONCLUSIONS: The mt genome of A. mackerrasae has similar characteristics to those of other Angiostrongylus species. Sequence comparisons reveal that A. mackerrasae is closely related to A. cantonensis and the two sibling species may have recently diverged compared with all other species in the genus with a highly specific host selection. This mt genome will provide a source of genetic markers for explorations of the epidemiology, biology and population genetics of A. mackerrasae