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

On the Price of Anarchy for flows over time

Dynamic network flows, or network flows over time, constitute an important model for real-world situations where steady states are unusual, such as urban traffic and the Internet. These applications immediately raise the issue of analyzing dynamic network flows from a game-theoretic perspective. In this paper we study dynamic equilibria in the deterministic fluid queuing model in single-source single-sink networks, arguably the most basic model for flows over time. In the last decade we have witnessed significant developments in the theoretical understanding of the model. However, several fundamental questions remain open. One of the most prominent ones concerns the Price of Anarchy, measured as the worst case ratio between the minimum time required to route a given amount of flow from the source to the sink, and the time a dynamic equilibrium takes to perform the same task. Our main result states that if we could reduce the inflow of the network in a dynamic equilibrium, then the Price of Anarchy is exactly e/(e − 1) ≈ 1.582. This significantly extends a result by Bhaskar, Fleischer, and Anshelevich (SODA 2011). Furthermore, our methods allow to determine that the Price of Anarchy in parallel-link networks is exactly 4/3. Finally, we argue that if a certain very natural monotonicity conjecture holds, the Price of Anarchy in the general case is exactly e/(e − 1)

LP-based Covering Games with Low Price of Anarchy

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3]

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)

On a Simple Hedonic Game with Graph-Restricted Communication

International audienceWe study a hedonic game for which the feasible coalitions are prescribed by a graph representing the agents' social relations. A group of agents can form a feasible coalition if and only if their corresponding vertices can be spanned with a star. This requirement guarantees that agents are connected, close to each other, and one central agent can coordinate the actions of the group. In our game everyone strives to join the largest feasible coalition. We study the existence and computational complexity of both Nash stable and core stable partitions. Then, we provide tight or asymptotically tight bounds on their quality, with respect to both the price of anarchy and stability, under two natural social functions, namely, the number of agents who are not in a singleton coalition, and the number of coalitions. We also derive refined bounds for games in which the social graph is restricted to be claw-free. Finally, we investigate the complexity of computing socially optimal partitions as well as extreme Nash stable ones

Implementing experiential learning activities in a large enrollment introductory food science and human nutrition course

Experiential learning activities are often viewed as impractical, and potentially unfeasible, instructional tools to employ in a large class. Research has shown, though, that the metacognitive skills that students utilize while participating in experiential learning activities enable students to assess their true level of understanding and mastery for the subject matter. The objective of this study was to evaluate whether students in a large (~660 person) Introduction to Food Science and Human Nutrition (FSHN 101) course improved their understanding of dietary intake and food safety after participating in two experiential learning activities developed for these course topics. The first activity, completed during class, asked students to select one day???s worth of food from a list of menu choices, calculate the nutritional value of their food choices, and then compare their daily nutritional intake to the dietary reference intakes for their gender, age category and health status. The second activity, completed via the course website, asked students to complete one food safety survey prior to the commencement of the course???s food microbiology section to assess the students' personal food safety behaviors and a second survey upon completion of the section to assess students' knowledge of recommended food safety practices. Students were asked to evaluate both the cognitive and affective aspects of the experiential learning activities by completing a reflective questionnaire after participating in each activity. Overall, students' responses revealed that the activities were effective learning tools and that the students liked engaging with the material on a personal application level. A Poster version of this article can be found in the IDEALS SoTL Presentations and Posters folder.published or submitted for publicationis peer reviewe

Resource competition on integral polymatroids

We study competitive resource allocation problems in which players distribute their demands integrally over 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 non-decreasing 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

Competitive routing over time

Abstract. Congestion games are a fundamental and widely studied model for selfish allocation problems like routing and load balancing. An intrinsic property of these games is that players allocate resources simultaneously and instantly. This is particularly unrealistic for many network routingscenarios, which are one ofthe prominentapplication scenarios of congestion games. In many networks, load travels along routes over time and allocation of edges happens sequentially. In this paper we consider two frameworks that enhance network congestion games with a notion of time. We propose temporal network congestion games that use coordination mechanisms — local policies that allow to sequentialize traffic on the edges. In addition, we consider congestion games with time-dependent costs, in whichtravel times are fixedbutqualityofservice oftransmission varies with load over time. We study existence and complexity properties of pure Nash equilibria and best-response strategies in both frameworks. In some cases our results can be used to characterize convergence for various distributed dynamics.