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

Resource Competition on Integral Polymatroids

We study competitive resource allocation problems in which players distribute their demands integrally on a set of resources subject to player-specific submodular capacity constraints. Each player has to pay for each unit of demand a cost that is a nondecreasing and convex function of the total allocation of that resource. This general model of resource allocation generalizes both singleton congestion games with integer-splittable demands and matroid congestion games with player-specific costs. As our main result, we show that in such general resource allocation problems a pure Nash equilibrium is guaranteed to exist by giving a pseudo-polynomial algorithm computing a pure Nash equilibrium.Comment: 17 page

Congestion Games with Complementarities

We study a model of selfish resource allocation that seeks to incorporate dependencies among resources as they exist in modern networked environments. Our model is inspired by utility functions with constant elasticity of substitution (CES) which is a well-studied model in economics. We consider congestion games with different aggregation functions. In particular, we study $L_p$ norms and analyze the existence and complexity of (approximate) pure Nash equilibria. Additionally, we give an almost tight characterization based on monotonicity properties to describe the set of aggregation functions that guarantee the existence of pure Nash equilibria.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-57586-5_1

Effect of Periodontal Treatment on HbA1c among Patients with Prediabetes

Evidence is limited regarding whether periodontal treatment improves hemoglobin A1c (HbA1c) among people with prediabetes and periodontal disease, and it is unknown whether improvement of metabolic status persists >3 mo. In an exploratory post hoc analysis of the multicenter randomized controlled trial “Antibiotika und Parodontitis” (Antibiotics and Periodontitis)—a prospective, stratified, double-blind study—we assessed whether nonsurgical periodontal treatment with or without an adjunctive systemic antibiotic treatment affects HbA1c and high-sensitivity C-reactive protein (hsCRP) levels among periodontitis patients with normal HbA1c (≤5.7%, n = 218), prediabetes (5.7% 1 mm in both groups. In the normal HbA1c group, HbA1c values remained unchanged at 5.0% (95% CI, 4.9% to 6.1%) during the observation period. Among periodontitis patients with prediabetes, HbA1c decreased from 5.9% (95% CI, 5.9% to 6.0%) to 5.4% (95% CI, 5.3% to 5.5%) at 15.5 mo and increased to 5.6% (95% CI, 5.4% to 5.7%) after 27.5 mo. At 27.5 mo, 46% of periodontitis patients with prediabetes had normal HbA1c levels, whereas 47.9% remained unchanged and 6.3% progressed to diabetes. Median hsCRP values were reduced in the normal HbA1c and prediabetes groups from 1.2 and 1.4 mg/L to 0.7 and 0.7 mg/L, respectively. Nonsurgical periodontal treatment may improve blood glucose values among periodontitis patients with prediabetes (ClinicalTrials.gov NCT00707369)

Human Embryonic and Fetal Mesenchymal Stem Cells Differentiate toward Three Different Cardiac Lineages in Contrast to Their Adult Counterparts

Mesenchymal stem cells (MSCs) show unexplained differences in differentiation potential. In this study, differentiation of human (h) MSCs derived from embryonic, fetal and adult sources toward cardiomyocytes, endothelial and smooth muscle cells was investigated. Labeled hMSCs derived from embryonic stem cells (hESC-MSCs), fetal umbilical cord, bone marrow, amniotic membrane and adult bone marrow and adipose tissue were co-cultured with neonatal rat cardiomyocytes (nrCMCs) or cardiac fibroblasts (nrCFBs) for 10 days, and also cultured under angiogenic conditions. Cardiomyogenesis was assessed by human-specific immunocytological analysis, whole-cell current-clamp recordings, human-specific qRT-PCR and optical mapping. After co-culture with nrCMCs, significantly more hESC-MSCs than fetal hMSCs stained positive for α-actinin, whereas adult hMSCs stained negative. Furthermore, functional cardiomyogenic differentiation, based on action potential recordings, was shown to occur, but not in adult hMSCs. Of all sources, hESC-MSCs expressed most cardiac-specific genes. hESC-MSCs and fetal hMSCs contained significantly higher basal levels of connexin43 than adult hMSCs and co-culture with nrCMCs increased expression. After co-culture with nrCFBs, hESC-MSCs and fetal hMSCs did not express α-actinin and connexin43 expression was decreased. Conduction velocity (CV) in co-cultures of nrCMCs and hESC-MSCs was significantly higher than in co-cultures with fetal or adult hMSCs. In angiogenesis bioassays, only hESC-MSCs and fetal hMSCs were able to form capillary-like structures, which stained for smooth muscle and endothelial cell markers.Human embryonic and fetal MSCs differentiate toward three different cardiac lineages, in contrast to adult MSCs. Cardiomyogenesis is determined by stimuli from the cellular microenvironment, where connexin43 may play an important role

Congestion Games with Mixed Objectives

We study a new class of games which generalizes congestion games and its bottleneck variant. We introduce congestion games with mixed objectives to model network scenarios in which players seek to optimize for latency and bandwidths alike. We characterize the existence of pure Nash equilibria (PNE) and the convergence of improvement dynamics. For games that do not possess PNE we give bounds on the approximation ratio of approximate pure Nash equilibria.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-48749-6_4

Pure Nash Equilibria in Restricted Budget Games

In budget games, players compete over resources with finite budgets. For every resource, a player has a specific demand and as a strategy, he chooses a subset of resources. If the total demand on a resource does not exceed its budget, the utility of each player who chose that resource equals his demand. Otherwise, the budget is shared proportionally. In the general case, pure Nash equilibria (NE) do not exist for such games. In this paper, we consider the natural classes of singleton and matroid budget games with additional constraints and show that for each, pure NE can be guaranteed. In addition, we introduce a lexicographical potential function to prove that every matroid budget game has an approximate pure NE which depends on the largest ratio between the different demands of each individual player

A Unifying Tool for Bounding the Quality of Non-cooperative Solutions in Weighted Congestion Games

We present a general technique, based on a primal-dual formulation, for analyzing the quality of self-emerging solutions in weighted congestion games. With respect to traditional combinatorial approaches, the primal-dual schema has at least three advantages: first, it provides an analytic tool which can always be used to prove tight upper bounds for all the cases in which we are able to characterize exactly the polyhedron of the solutions under analysis; secondly, in each such a case the complementary slackness conditions give us an hint on how to construct matching lower bounding instances; thirdly, proofs become simpler and easy to check. For the sake of exposition, we first apply our technique to the problems of bounding the prices of anarchy and stability of exact and approximate pure Nash equilibria, as well as the approximation ratio of the solutions achieved after a one-round walk starting from the empty strategy profile, in the case of affine latency functions and we show how all the known upper bounds for these measures (and some of their generalizations) can be easily reobtained under a unified approach. Then, we use the technique to attack the more challenging setting of polynomial latency functions. In particular, we obtain the first known upper bounds on the price of stability of pure Nash equilibria and on the approximation ratio of the solutions achieved after a one-round walk starting from the empty strategy profile for unweighted players in the cases of quadratic and cubic latency functions. We believe that our technique, thanks to its versatility, may prove to be a powerful tool also in several other applications