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)

Bandwidth allocation in cellular networks with multiple interferences - Bar-Yehuda, Reuven; Polevoy, Gleb; Rawitz, Dror (DIALM-PODC)