TY - CONF
AB - Competing firms tend to select similar locations for their stores. This phenomenon, called the principle of minimum differentiation, was captured by Hotelling with a landmark model of spatial competition but is still the object of an ongoing scientific debate. Although consistently observed in practice, many more realistic variants of Hotelling's model fail to support minimum differentiation or do not have pure equilibria at all. In particular, it was recently proven for a generalized model which incorporates negative network externalities and which contains Hotelling's model and classical selfish load balancing as special cases, that the unique equilibria do not adhere to minimum differentiation. Furthermore, it was shown that for a significant parameter range pure equilibria do not exist. We derive a sharp contrast to these previous results by investigating Hotelling's model with negative network externalities from an entirely new angle: approximate pure subgame perfect equilibria. This approach allows us to prove analytically and via agent-based simulations that approximate equilibria having good approximation guarantees and that adhere to minimum differentiation exist for the full parameter range of the model. Moreover, we show that the obtained approximate equilibria have high social welfare.
AU - Feldotto, Matthias
AU - Lenzner, Pascal
AU - Molitor, Louise
AU - Skopalik, Alexander
ID - 10281
T2 - Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems
TI - From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation
ER -
TY - CONF
AB - We characterise the set of dominant strategy incentive compatible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilateral trade setting. In such a setting there is a single buyer and a single seller who holds a finite number k of identical items. The mechanism has to decide how many units of the item are transferred from the seller to the buyer and how much money is transferred from the buyer to the seller. We consider two classes of valuation functions for the buyer and seller: Valuations that are increasing in the number of units in possession, and the more specific class of valuations that are increasing and submodular.
Furthermore, we present some approximation results about the performance of certain such mechanisms, in terms of social welfare: For increasing submodular valuation functions, we show the existence of a deterministic 2-approximation mechanism and a randomised e/(1-e) approximation mechanism, matching the best known bounds for the single-item setting.
AU - Lazos, Philip
AU - Goldberg, Paul
AU - Skopalik, Alexander
AU - Gerstgrasser, Matthias
AU - de Keijzer, Bart
ID - 5471
T2 - Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence (AAAI)
TI - Multi-unit Bilateral Trade
ER -
TY - JOUR
AB - 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.
AU - Drees, Maximilian
AU - Feldotto, Matthias
AU - Riechers, Sören
AU - Skopalik, Alexander
ID - 1369
JF - Journal of Combinatorial Optimization
SN - 1382-6905
TI - Pure Nash equilibria in restricted budget games
ER -
TY - CONF
AB - We consider a market where final products or services are compositions of a number of basic services. Users are asked to evaluate the quality of the composed product after purchase. The quality of the basic service influences the performance of the composed services but cannot be observed directly. The question we pose is whether it is possible to use user evaluations on composed services to assess the quality of basic services. We discuss how to combine aggregation of evaluations across users and disaggregation of information on composed services to derive valuations for the single components. As a solution we propose to use the (weighted) average as aggregation device in connection with the Shapley value as disaggregation method, since this combination fulfills natural requirements in our context. In addition, we address some occurring computational issues: We give an approximate solution concept using only a limited number of evaluations which guarantees nearly optimal results with reduced running time. Lastly, we show that a slightly modified Shapley value and the weighted average are still applicable if the evaluation profiles are incomplete.
AU - Feldotto, Matthias
AU - Haake, Claus-Jochen
AU - Skopalik, Alexander
AU - Stroh-Maraun, Nadja
ID - 2831
SN - 978-1-4503-5916-0
T2 - Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018)
TI - Disaggregating User Evaluations Using the Shapley Value
ER -
TY - JOUR
AB - 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.
AU - Feldotto, Matthias
AU - Leder, Lennart
AU - Skopalik, Alexander
ID - 669
IS - 4
JF - Journal of Combinatorial Optimization
SN - 1382-6905
TI - Congestion games with mixed objectives
VL - 36
ER -
TY - CONF
AB - 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.
AU - Feldotto, Matthias
AU - Leder, Lennart
AU - Skopalik, Alexander
ID - 112
T2 - Proceedings of the 10th International Conference on Algorithms and Complexity (CIAC)
TI - Congestion Games with Complementarities
ER -
TY - CONF
AB - 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).
AU - Kling, Peter
AU - Mäcker, Alexander
AU - Riechers, Sören
AU - Skopalik, Alexander
ID - 59
T2 - Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)
TI - Sharing is Caring: Multiprocessor Scheduling with a Sharable Resource
ER -
TY - CONF
AB - 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.
AU - Drees, Maximilian
AU - Feldotto, Matthias
AU - Riechers, Sören
AU - Skopalik, Alexander
ID - 66
T2 - Proceedings of the 23rd International Computing and Combinatorics Conference (COCOON)
TI - Pure Nash Equilibria in Restricted Budget Games
ER -
TY - CONF
AB - 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].
AU - Feldotto, Matthias
AU - Gairing, Martin
AU - Kotsialou, Grammateia
AU - Skopalik, Alexander
ID - 113
T2 - Proceedings of the 13th International Conference on Web and Internet Economics (WINE)
TI - Computing Approximate Pure Nash Equilibria in Shapley Value Weighted Congestion Games
ER -
TY - CONF
AB - 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.
AU - Feldotto, Matthias
AU - John, Thomas
AU - Kundisch, Dennis
AU - Hemsen, Paul
AU - Klingsieck, Katrin
AU - Skopalik, Alexander
ID - 1094
T2 - Proceedings of the 12th International Conference on Design Science Research in Information Systems and Technology (DESRIST)
TI - Making Gamification Easy for the Professor: Decoupling Game and Content with the StudyNow Mobile App
ER -
TY - CONF
AB - 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).
AU - Drees, Maximilian
AU - Feldkord, Björn
AU - Skopalik, Alexander
ID - 149
T2 - Proceedings of the 10th Annual International Conference on Combinatorial Optimization and Applications (COCOA)
TI - Strategic Online Facility Location
ER -
TY - CONF
AB - 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.
AU - Feldotto, Matthias
AU - Leder, Lennart
AU - Skopalik, Alexander
ID - 209
T2 - Proceedings of the 10th Annual International Conference on Combinatorial Optimization and Applications (COCOA)
TI - Congestion Games with Mixed Objectives
ER -
TY - JOUR
AB - 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.
AU - Harks, Tobias
AU - Höfer, Martin
AU - Schewior, Kevin
AU - Skopalik, Alexander
ID - 159
IS - 4
JF - IEEE/ACM Transactions on Networking
TI - Routing Games With Progressive Filling
ER -
TY - CONF
AB - 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.
AU - Drees, Maximilian
AU - Feldotto, Matthias
AU - Riechers, Sören
AU - Skopalik, Alexander
ID - 271
T2 - Proceedings of the 8th International Symposium on Algorithmic Game Theory (SAGT)
TI - On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games
ER -
TY - JOUR
AB - 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.
AU - Caragiannis, Ioannis
AU - Fanelli, Angelo
AU - Gravin, Nick
AU - Skopalik, Alexander
ID - 320
IS - 1
JF - Transactions on Economics and Computation
TI - Approximate Pure Nash Equilibria in Weighted Congestion Games: Existence, Efficient Computation, and Structure
VL - 3
ER -
TY - CONF
AB - 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 $\Phi(\sf s)$ of any outcome $\sf s$ of a congestion game approximates the optimum potential value $\Phi(\sf s^*)$ by a factor $\Psi_{\mathcal{F}}$ 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 \emph{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 $(1+\varepsilon)\cdot\Psi_{\mathcal{F}}$-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.
AU - Feldotto, Matthias
AU - Gairing, Martin
AU - Skopalik, Alexander
ID - 453
T2 - Proceedings of the 10th International Conference on Web and Internet Economics (WINE)
TI - Bounding the Potential Function in Congestion Games and Approximate Pure Nash Equilibria
ER -
TY - CONF
AB - 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.
AU - Abshoff, Sebastian
AU - Cord-Landwehr, Andreas
AU - Jung, Daniel
AU - Skopalik, Alexander
ID - 395
T2 - Proceedings of the 10th International Conference on Web and Internet Economics (WINE)
TI - Multilevel Network Games
ER -
TY - CONF
AB - 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.
AU - Hansknecht, Christoph
AU - Klimm, Max
AU - Skopalik, Alexander
ID - 455
T2 - Proceedings of the 17th. International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX)
TI - Approximate pure Nash equilibria in weighted congestion games
ER -
TY - CONF
AB - 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.
AU - Feldotto, Matthias
AU - Skopalik, Alexander
ID - 462
T2 - Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2014)
TI - A Simulation Framework for Analyzing Complex Infinitely Repeated Games
ER -
TY - CONF
AB - 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.
AU - Drees, Maximilian
AU - Riechers, Sören
AU - Skopalik, Alexander
ED - Lavi, Ron
ID - 451
T2 - Proceedings of the 7th International Symposium on Algorithmic Game Theory (SAGT)
TI - Budget-restricted utility games with ordered strategic decisions
ER -