Congestion games with mixed objectives - Feldotto, Matthias; Leder, Lennart; Skopalik, Alexander (Journal of Combinatorial Optimization)
We study a new class of games which generalizes congestion games andits bottleneck variant. We introduce congestion games with mixed objectives to modelnetwork scenarios in which players seek to optimize for latency and bandwidths alike.We characterize the (non-)existence of pure Nash equilibria (PNE), the convergenceof improvement dynamics, the quality of equilibria and show the complexity of thedecision problem. For games that do not possess PNE we give bounds on the approx-imation ratio of approximate pure Nash equilibria.

Pure Nash Equilibria in Robust Congestion Games via Potential Functions - Kemper, Arne

Scenario-driven Strategy Analysis in a n-player Composition Game Model - Nachtigall, Marcel

Learning deterministic bandit behaviour form compositions - Kempf, Jérôme

Pure Nash equilibria in restricted budget games - Drees, Maximilian; Feldotto, Matthias; Riechers, Sören; Skopalik, Alexander (Journal of Combinatorial Optimization)
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.

Congestion Games with Complementarities - Feldotto, Matthias; Leder, Lennart; Skopalik, Alexander (Proceedings of the 10th International Conference on Algorithms and Complexity (CIAC))
We study a model of selfish resource allocation that seeks to incorporate dependencies among resources as they exist in 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.

Computing Approximate Pure Nash Equilibria in Shapley Value Weighted Congestion Games - Feldotto, Matthias; Gairing, Martin; Kotsialou, Grammateia; Skopalik, Alexander (Proceedings of the 13th International Conference on Web and Internet Economics (WINE))
We study the computation of approximate pure Nash equilibria in Shapley value (SV) weighted congestion games, introduced in [19]. This class of games considers weighted congestion games in which Shapley values are used as an alternative (to proportional shares) for distributing the total cost of each resource among its users. We focus on the interesting subclass of such games with polynomial resource cost functions and present an algorithm that computes approximate pure Nash equilibria with a polynomial number of strategy updates. Since computing a single strategy update is hard, we apply sampling techniques which allow us to achieve polynomial running time. The algorithm builds on the algorithmic ideas of [7], however, to the best of our knowledge, this is the first algorithmic result on computation of approximate equilibria using other than proportional shares as player costs in this setting. We present a novel relation that approximates the Shapley value of a player by her proportional share and vice versa. As side results, we upper bound the approximate price of anarchy of such games and significantly improve the best known factor for computing approximate pure Nash equilibria in weighted congestion games of [7].

Filtering Undesirable Flows in Networks - Polevoy, Gleb; Trajanovski, Stojan; Grosso, Paola; de Laat, Cees (Combinatorial Optimization and Applications: 11th International Conference, COCOA 2017, Shanghai, China, December 16-18, 2017, Proceedings, Part I)
Keywords: flow; filter; MMSA; set cover; approximation; local ratio algorithm

Reciprocation Effort Games - Polevoy, Gleb; de Weerdt, M.M. (Proceedings of the 29th Benelux Conference on Artificial Intelligence)
Keywords: interaction; reciprocation; contribute; shared effort; curbing; convergence; threshold; Nash equilibrium; social welfare; efficiency; price of anarchy; price of stability

Competition between Cooperative Projects - Polevoy, Gleb; de Weerdt, M.M. (Proceedings of the 29th Benelux Conference on Artificial Intelligence)
Keywords: agents; projects; contribute; shared effort game; competition; quota; threshold; Nash equilibrium; social welfare; efficiency; price of anarchy; price of stability

Sharing is Caring: Multiprocessor Scheduling with a Sharable Resource - Kling, Peter; Mäcker, Alexander; Riechers, Sören; Skopalik, Alexander (Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA))
We consider a scheduling problem on $m$ identical processors sharing an arbitrarily divisible resource. In addition to assigning jobs to processors, the scheduler must distribute the resource among the processors (e.g., for three processors in shares of 20%, 15%, and 65%) and adjust this distribution over time. Each job $j$ comes with a size $p_j \in \mathbb{R}$ and a resource requirement $r_j > 0$. Jobs do not benefit when receiving a share larger than $r_j$ of the resource. But providing them with a fraction of the resource requirement causes a linear decrease in the processing efficiency. We seek a (non-preemptive) job and resource assignment minimizing the makespan.Our main result is an efficient approximation algorithm which achieves an approximation ratio of $2 + 1/(m-2)$. It can be improved to an (asymptotic) ratio of $1 + 1/(m-1)$ if all jobs have unit size. Our algorithms also imply new results for a well-known bin packing problem with splittable items and a restricted number of allowed item parts per bin.Based upon the above solution, we also derive an approximation algorithm with similar guarantees for a setting in which we introduce so-called tasks each containing several jobs and where we are interested in the average completion time of tasks (a task is completed when all its jobs are completed).

Pure Nash Equilibria in Restricted Budget Games - Drees, Maximilian; Feldotto, Matthias; Riechers, Sören; Skopalik, Alexander (Proceedings of the 23rd International Computing and Combinatorics Conference (COCOON))
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.

Sortieren dynamischer Daten - Nachtigall, Simon

Robuste Optimierung in Congestion Games - Pukrop, Simon

Complexity of Signalling in Routing Games under Uncertainty - Bürmann, Jan

Bounding the Inefficiency of Equilibria in Congestion Games under Taxation - Vijayalakshmi, Vipin Ravindran

Making Gamification Easy for the Professor: Decoupling Game and Content with the StudyNow Mobile App - Feldotto, Matthias; John, Thomas; Kundisch, Dennis; Hemsen, Paul; Klingsieck, Katrin; Skopalik, Alexander (Proceedings of the 12th International Conference on Design Science Research in Information Systems and Technology (DESRIST))
Many university students struggle with motivational problems, and gamification has the potential to address these problems. However, gamification is hardly used in education, because current approaches to gamification require instructors to engage in the time-consuming preparation of their course contents for use in quizzes, mini-games and the like. Drawing on research on limited attention and present bias, we propose a "lean" approach to gamification, which relies on gamifying learning activities (rather than learning contents) and increasing their salience. In this paper, we present the app StudyNow that implements such a lean gamification approach. With this app, we aim to enable more students and instructors to benefit from the advantages of gamification.

Towards a Lean Approach for Gamifying Education - John, Thomas; Feldotto, Matthias; Hemsen, Paul; Klingsieck, Katrin; Kundisch, Dennis; Langendorf, Mike (Proceedings of the 25th European Conference on Information Systems (ECIS))
Many university students struggle with motivational problems, and gamification has the potential to address these problems. However, using gamification currently is rather tedious and time-consuming for instructors because current approaches to gamification require instructors to engage in the time-consuming preparation of course contents (e.g., for quizzes or mini-games). In reply to this issue, we propose a “lean” approach to gamification, which relies on gamifying learning activities rather than learning contents. The learning activities that are gamified in the lean approach can typically be drawn from existing course syllabi (e.g., attend certain lectures, hand in assignments, read book chapters and articles). Hence, compared to existing approaches, lean gamification substantially lowers the time requirements posed on instructors for gamifying a given course. Drawing on research on limited attention and the present bias, we provide the theoretical foundation for the lean gamification approach. In addition, we present a mobile application that implements lean gamification and outline a mixed-methods study that is currently under way for evaluating whether lean gamification does indeed have the potential to increase students’ motivation. We thereby hope to allow more students and instructors to benefit from the advantages of gamification.

Existence and Properties of Pure Nash Equilibria in Budget Games - Drees, Maximilian

Congestion Games with Mixed Objectives - Leder, Lennart

The Game of Reciprocation Habits - Polevoy, Gleb; de Weerdt, M.M.; Jonker, C.M. (Proceedings of the 2016 European Conference on Artificial Intelligence)
Keywords: agents; action; repeated reciprocation; fixed; floating; network; Nash equilibrium; social welfare; price of anarchy; price of stability; convex combination

The Convergence of Reciprocation - Polevoy, Gleb; de Weerdt, Mathijs; Jonker, Catholijn (Proceedings of the 2016 International Conference on Autonomous Agents and Multiagent Systems)
Keywords: agent's influence; behavior; convergence; perron-frobenius; reciprocal interaction; repeated reciprocation

Congestion Games with Mixed Objectives - Feldotto, Matthias; Leder, Lennart; Skopalik, Alexander (Proceedings of the 10th Annual International Conference on Combinatorial Optimization and Applications (COCOA))
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.

Über die Rolle von Informationen in Verkehrsnetzwerken - Handirk, Tobias

Routing Games With Progressive Filling - Harks, Tobias; Höfer, Martin; Schewior, Kevin; Skopalik, Alexander (IEEE/ACM Transactions on Networking)
Abstract—Max-min fairness (MMF) is a widely known approachto a fair allocation of bandwidth to each of the usersin a network. This allocation can be computed by uniformlyraising the bandwidths of all users without violating capacityconstraints. We consider an extension of these allocations byraising the bandwidth with arbitrary and not necessarily uniformtime-depending velocities (allocation rates). These allocationsare used in a game-theoretic context for routing choices, whichwe formalize in progressive filling games (PFGs). We present avariety of results for equilibria in PFGs. We show that these gamespossess pure Nash and strong equilibria. While computation ingeneral is NP-hard, there are polynomial-time algorithms forprominent classes of Max-Min-Fair Games (MMFG), includingthe case when all users have the same source-destination pair.We characterize prices of anarchy and stability for pure Nashand strong equilibria in PFGs and MMFGs when players havedifferent or the same source-destination pairs. In addition, weshow that when a designer can adjust allocation rates, it is possibleto design games with optimal strong equilibria. Some initial resultson polynomial-time algorithms in this direction are also derived.

Strategic Online Facility Location - Drees, Maximilian; Feldkord, Björn; Skopalik, Alexander (Proceedings of the 10th Annual International Conference on Combinatorial Optimization and Applications (COCOA))
In this paper we consider a strategic variant of the online facility location problem. Given is a graph in which each node serves two roles: it is a strategic client stating requests as well as a potential location for a facility. In each time step one client states a request which induces private costs equal to the distance to the closest facility. Before serving, the clients may collectively decide to open new facilities, sharing the corresponding price. Instead of optimizing the global costs, each client acts selfishly. The prices of new facilities vary between nodes and also change over time, but are always bounded by some fixed value α. Both the requests as well as the facility prices are given by an online sequence and are not known in advance.We characterize the optimal strategies of the clients and analyze their overall performance in comparison to a centralized offline solution. If all players optimize their own competitiveness, the global performance of the system is O(√α⋅α) times worse than the offline optimum. A restriction to a natural subclass of strategies improves this result to O(α). We also show that for fixed facility costs, we can find strategies such that this bound further improves to O(√α).

Systematic evaluation of peer-to-peer systems using PeerfactSim.KOM - Feldotto, Matthias; Graffi, Kalman (Concurrency and Computation: Practice and Experience)
Comparative evaluations of peer-to-peer protocols through simulations are a viable approach to judge the performance and costs of the individual protocols in large-scale networks. In order to support this work, we present the peer-to-peer system simulator PeerfactSim.KOM, which we extended over the last years. PeerfactSim.KOM comes with an extensive layer model to support various facets and protocols of peer-to-peer networking. In this article, we describe PeerfactSim.KOM and show how it can be used for detailed measurements of large-scale peer-to-peer networks. We enhanced PeerfactSim.KOM with a fine-grained analyzer concept, with exhaustive automated measurements and gnuplot generators as well as a coordination control to evaluate sets of experiment setups in parallel. Thus, by configuring all experiments and protocols only once and starting the simulator, all desired measurements are performed, analyzed, evaluated, and combined, resulting in a holistic environment for the comparative evaluation of peer-to-peer systems. An immediate comparison of different configurations and overlays under different aspects is possible directly after the execution without any manual post-processing.

Solving the aggregated bandits problem - Pfannschmidt, Karlson

Approximate Pure Nash Equilibria in Weighted Congestion Games: Existence, Efficient Computation, and Structure - Caragiannis, Ioannis; Fanelli, Angelo; Gravin, Nick; Skopalik, Alexander (Transactions on Economics and Computation)
We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of pure Nash equilibria is guaranteed by a potential function argument. Unfortunately, this proof of existence is inefficient and computing pure Nash equilibria in such games is a PLS-hard problem even when all players have unit weights. The situation gets worse when superlinear (e.g., quadratic) latency functions come into play; in this case, the Nash dynamics of the game may contain cycles and pure Nash equilibria may not even exist. Given these obstacles, we consider approximate pure Nash equilibria as alternative solution concepts. A ρ--approximate pure Nash equilibrium is a state of a (weighted congestion) game from which no player has any incentive to deviate in order to improve her cost by a multiplicative factor higher than ρ. Do such equilibria exist for small values of ρ? And if so, can we compute them efficiently?We provide positive answers to both questions for weighted congestion games with polynomial latency functions by exploiting an “approximation” of such games by a new class of potential games that we call Ψ-games. This allows us to show that these games have d!-approximate pure Nash equilibria, where d is the maximum degree of the latency functions. Our main technical contribution is an efficient algorithm for computing O(1)-approximate pure Nash equilibria when d is a constant. For games with linear latency functions, the approximation guarantee is 3+√5/2 + Oγ for arbitrarily small γ > 0; for latency functions with maximum degree d≥ 2, it is d2d+o(d). The running time is polynomial in the number of bits in the representation of the game and 1/γ. As a byproduct of our techniques, we also show the following interesting structural statement for weighted congestion games with polynomial latency functions of maximum degree d ≥ 2: polynomially-long sequences of best-response moves from any initial state to a dO(d2)-approximate pure Nash equilibrium exist and can be efficiently identified in such games as long as d is a constant.To the best of our knowledge, these are the first positive algorithmic results for approximate pure Nash equilibria in weighted congestion games. Our techniques significantly extend our recent work on unweighted congestion games through the use of Ψ-games. The concept of approximating nonpotential games by potential ones is interesting in itself and might have further applications.

Budget Games with priced strategies - Pautz, Jannis

On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games - Drees, Maximilian; Feldotto, Matthias; Riechers, Sören; Skopalik, Alexander (Proceedings of the 8th International Symposium on Algorithmic Game Theory (SAGT))
In 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 $α$ through unilateral strategy changes. There is a threshold $α_δ$ (where $δ$ is a parameter that limits the demand of each player on a specific resource) such that $α$-approximate pure Nash equilibria always exist for $α ≥ α_δ$, but not for $α < α_δ$. We give both upper and lower bounds on this threshold $α_δ$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $α$-approximate price of anarchy for BAGs is $α+1$. 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.

Multilevel Netzwerk Spiele mit konstanten Entfernungen im Highspeed-Netzwerk - Kothe, Nils

Inter-Datacenter Scheduling of Large Data Flows - Cohen, R.; Polevoy, Gleb (Cloud Computing, IEEE Transactions on)
Inter-datacenter transfers of non-interactive but timely large flows over a private (managed) network is an important problem faced by many cloud service providers. The considered flows are non-interactive because they do not explicitly target the end users. However, most of them must be performed on a timely basis and are associated with a deadline. We propose to schedule these flows by a centralized controller, which determines when to transmit each flow and which path to use. Two scheduling models are presented in this paper. In the first, the controller also determines the rate of each flow, while in the second bandwidth is assigned by the network according to the TCP rules. We develop scheduling algorithms for both models and compare their complexity and performance.
Keywords: Approximation algorithms; Approximation methods; Bandwidth; Cloud computing; Routing; Schedules; Scheduling

Bandwidth allocation in cellular networks with multiple interferences - Bar-Yehuda, Reuven; Polevoy, Gleb; Rawitz, Dror (Discrete Applied Mathematics)
Abstract We study the problem of bandwidth allocation with multiple interferences. In this problem the input consists of a set of users and a set of base stations. Each user has a list of requests, each consisting of a base station, a frequency demand, and a profit that may be gained by scheduling this request. The goal is to find a maximum profit set of user requests S that satisfies the following conditions: (i) S contains at most one request per user, (ii) the frequency sets allotted to requests in S that correspond to the same base station are pairwise non-intersecting, and (iii) the QoS received by any user at any frequency is reasonable according to an interference model. In this paper we consider two variants of bandwidth allocation with multiple interferences. In the first each request specifies a demand that can be satisfied by any subset of frequencies that is large enough. In the second each request specifies a specific frequency interval. Furthermore, we consider two interference models, multiplicative and additive. We show that these problems are extremely hard to approximate if the interferences depend on both the interfered and the interfering base stations. On the other hand, we provide constant factor approximation algorithms for both variants of bandwidth allocation with multiple interferences for the case where the interferences depend only on the interfering base stations. We also consider a restrictive special case that is closely related to the Knapsack problem. We show that this special case is NP-hard and that it admits an FPTAS.
Keywords: Local ratio

Routing Games with Progressive Filling - Harks, Tobias; Höfer, Martin; Schewior, Kevin; Skopalik, Alexander (Proceedings of the 33rd Annual IEEE International Conference on Computer Communications (INFOCOM'14))
Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider an extension of these allocations by raising the bandwidth with arbitrary and not necessarily uniform time-depending velocities (allocation rates). These allocations are used in a game-theoretic context for routing choices, which we formalize in progressive filling games (PFGs).We present a variety of results for equilibria in PFGs. We show that these games possess pure Nash and strong equilibria. While computation in general is NP-hard, there are polynomial-time algorithms for prominent classes of Max-Min-Fair Games (MMFG), including the case when all users have the same source-destination pair. We characterize prices of anarchy and stability for pure Nash and strong equilibria in PFGs and MMFGs when players have different or the same source-destination pairs. In addition, we show that when a designer can adjust allocation rates, it is possible to design games with optimal strong equilibria. Some initial results on polynomial-time algorithms in this direction are also derived.

Reputationssysteme für zusammengesetzte Dienstleistungen - Pahl, David

Nash Equilibria in Shared Effort Games - Polevoy, Gleb; Trajanovski, Stojan; de Weerdt, Mathijs M. (Proceedings of the 2014 International Conference on Autonomous Agents and Multi-agent Systems)
Keywords: competition; equilibrium; market; models; shared effort games; simulation

Improving Human Interaction in Crowdsensing - Polevoy, Gleb; de Weerdt, Mathijs M. (Proceedings of the 2014 International Conference on Autonomous Agents and Multi-agent Systems)
Keywords: dynamics; emotion modeling; negotiation; network interaction; shared effort game

Request Driven Social Sensing - King, Thomas C.; Liu, Qingzhi; Polevoy, Gleb; de Weerdt, Mathijs; Dignum, Virginia; van Riemsdijk, M. Birna; Warnier, Martijn (Proceedings of the 2014 International Conference on Autonomous Agents and Multi-agent Systems)
Keywords: crowd-sensing; crowdsourcing; data aggregation; game theory; norms; reciprocation; self interested agents; simulation

Signaling Competition and Social Welfare - Polevoy, Gleb; Smorodinsky, Rann; Tennenholtz, Moshe (ACM Trans. Econ. Comput.)
Keywords: Competition; efficiency; equilibrium; market; social welfare

Budget-restricted utility games with ordered strategic decisions - Drees, Maximilian; Riechers, Sören; Skopalik, Alexander (Proceedings of the 7th International Symposium on Algorithmic Game Theory (SAGT))
We introduce the concept of budget games. Players choose a set of tasks and each task has a certain demand on every resource in the game. Each resource has a budget. If the budget is not enough to satisfy the sum of all demands, it has to be shared between the tasks. We study strategic budget games, where the budget is shared proportionally. We also consider a variant in which the order of the strategic decisions influences the distribution of the budgets. The complexity of the optimal solution as well as existence, complexity and quality of equilibria are analysed. Finally, we show that the time an ordered budget game needs to convergence towards an equilibrium may be exponential.

Brief Announcement: A Model for Multilevel Network Games - Abshoff, Sebastian; Cord-Landwehr, Andreas; Jung, Daniel; Skopalik, Alexander (Proceedings of the 7th International Symposium on Algorithmic Game Theory (SAGT))
Today's networks, like the Internet, do not consist of one but a mixture of several interconnected networks. Each has individual qualities and hence the performance of a network node results from the networks' interplay.We introduce a new game theoretic model capturing the interplay between a high-speed backbone network and a low-speed general purpose network. In our model, n nodes are connected by a static network and each node can decide individually to become a gateway node. A gateway node pays a fixed price for its connection to the high-speed network, but can utilize the high-speed network to gain communication distance 0 to all other gateways. Communication distances in the low-speed network are given by the hop distances. The effective communication distance between any two nodes then is given by the shortest path, which is possibly improved by using gateways as shortcuts.Every node v has the objective to minimize its communication costs, given by the sum (SUM-game) or maximum (MAX-game) of the effective communication distances from v to all other nodes plus a fixed price α > 0, if it decides to be a gateway. For both games and different ranges of α, we study the existence of equilibria, the price of anarchy, and convergence properties of best-response dynamics.

Bounding the Potential Function in Congestion Games and Approximate Pure Nash Equilibria - Feldotto, Matthias; Gairing, Martin; Skopalik, Alexander (Proceedings of the 10th International Conference on Web and Internet Economics (WINE))
In this paper we study the potential function in congestion games. We consider both games with non-decreasing cost functions as well as games with non-increasing utility functions. We show that the value of the potential function $Φ(\sf s)$ of any outcome $\sf s$ of a congestion game approximates the optimum potential value $Φ(\sf s^*)$ by a factor $Ψ_{\mathcal{F}}$ which only depends on the set of cost/utility functions $\mathcal{F}$, and an additive term which is bounded by the sum of the total possible improvements of the players in the outcome $\sf s$. The significance of this result is twofold. On the one hand it provides Price-of-Anarchy-like results with respect to the potential function. On the other hand, we show that these approximations can be used to compute $(1+ε)·Ψ_{\mathcal{F}}$-approximate pure Nash equilibria for congestion games with non-decreasing cost functions. For the special case of polynomial cost functions, this significantly improves the guarantees from Caragiannis et al. [FOCS 2011]. Moreover, our machinery provides the first guarantees for general latency functions.

Approximate pure Nash equilibria in weighted congestion games - Hansknecht, Christoph; Klimm, Max; Skopalik, Alexander (Proceedings of the 17th. International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX))
We study the existence of approximate pure Nash equilibria in weighted congestion games and develop techniques to obtain approximate potential functions that prove the existence of alpha-approximate pure Nash equilibria and the convergence of alpha-improvement steps. Specifically, we show how to obtain upper bounds for approximation factor alpha for a given class of cost functions. For example for concave cost functions the factor is at most 3/2, for quadratic cost functions it is at most 4/3, and for polynomial cost functions of maximal degree d it is at at most d + 1. For games with two players we obtain tight bounds which are as small as for example 1.054 in the case of quadratic cost functions.

Approximate pure Nash equilibria in Social Context Congestion Games - Gairing, Martin; Kotsialou, Grammateia; Skopalik, Alexander (Proceedings of the 10th International Conference on Web and Internet Economics (WINE))
We study the existence of approximate pure Nash equilibriain social context congestion games. For any given set of allowed costfunctions F, we provide a threshold value μ(F), and show that for theclass of social context congestion games with cost functions from F, α-Nash dynamics are guaranteed to converge to α-approximate pure Nashequilibrium if and only if α > μ(F).Interestingly, μ(F) is related and always upper bounded by Roughgarden’sanarchy value [19].

A Simulation Framework for Analyzing Complex Infinitely Repeated Games - Feldotto, Matthias; Skopalik, Alexander (Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2014))
We discuss a technique to analyze complex infinitely repeated games using techniques from the fields of game theory and simulations. Our research is motivated by the analysis of electronic markets with thousands of participants and possibly complex strategic behavior. We consider an example of a global market of composed IT services to demonstrate the use of our simulation technique. We present our current work in this area and we want to discuss further approaches for the future.

Multilevel Network Games - Abshoff, Sebastian; Cord-Landwehr, Andreas; Jung, Daniel; Skopalik, Alexander (Proceedings of the 10th International Conference on Web and Internet Economics (WINE))
We consider a multilevel network game, where nodes can improvetheir communication costs by connecting to a high-speed network.The n nodes are connected by a static network and each node can decideindividually to become a gateway to the high-speed network. The goalof a node v is to minimize its private costs, i.e., the sum (SUM-game) ormaximum (MAX-game) of communication distances from v to all othernodes plus a fixed price α > 0 if it decides to be a gateway. Between gatewaysthe communication distance is 0, and gateways also improve othernodes’ distances by behaving as shortcuts. For the SUM-game, we showthat for α ≤ n − 1, the price of anarchy is Θ (n/√α) and in this rangeequilibria always exist. In range α ∈ (n−1, n(n−1)) the price of anarchyis Θ(√α), and for α ≥ n(n − 1) it is constant. For the MAX-game, weshow that the price of anarchy is either Θ (1 + n/√α), for α ≥ 1, orelse 1. Given a graph with girth of at least 4α, equilibria always exist.Concerning the dynamics, both games are not potential games. For theSUM-game, we even show that it is not weakly acyclic.

HSkip+: A Self-Stabilizing Overlay Network for Nodes with Heterogeneous Bandwidths - Feldotto, Matthias; Scheideler, Christian; Graffi, Kalman (Proceedings of the 14th IEEE International Conference on Peer-to-Peer Computing (P2P))
In this paper we present and analyze HSkip+, a self-stabilizing overlay network for nodes with arbitrary heterogeneous bandwidths. HSkip+ has the same topology as the Skip+ graph proposed by Jacob et al. [PODC 2009] but its self-stabilization mechanism significantly outperforms the self-stabilization mechanism proposed for Skip+. Also, the nodes are now ordered according to their bandwidths and not according to their identifiers. Various other solutions have already been proposed for overlay networks with heterogeneous bandwidths, but they are not self-stabilizing. In addition to HSkip+ being self-stabilizing, its performance is on par with the best previous bounds on the time and work for joining or leaving a network of peers of logarithmic diameter and degree and arbitrary bandwidths. Also, the dilation and congestion for routing messages is on par with the best previous bounds for such networks, so that HSkip+ combines the advantages of both worlds. Our theoretical investigations are backed by simulations demonstrating that HSkip+ is indeed performing much better than Skip+ and working correctly under high churn rates.

On the Admission of Dependent Flows in Powerful Sensor Networks - Cohen, R.; Nudelman, I.; Polevoy, Gleb (Networking, IEEE/ACM Transactions on)
In this paper, we define and study a new problem, referred to as the Dependent Unsplittable Flow Problem (D-UFP). We present and discuss this problem in the context of large-scale powerful (radar/camera) sensor networks, but we believe it has important applications on the admission of large flows in other networks as well. In order to optimize the selection of flows transmitted to the gateway, D-UFP takes into account possible dependencies between flows. We show that D-UFP is more difficult than NP-hard problems for which no good approximation is known. Then, we address two special cases of this problem: the case where all the sensors have a shared channel and the case where the sensors form a mesh and route to the gateway over a spanning tree.
Keywords: Approximation algorithms; Approximation methods; Bandwidth; Logic gates; Radar; Vectors; Wireless sensor networks; Dependent flow scheduling; sensor networks

On the Admission of Dependent Flows in Powerful Sensor Networks - Cohen, Reuven; Nudelman, Ilia; Polevoy, Gleb (Infocom'2012, Orlando, Florida)