TY - THES
AB - This thesis investigates approximate pure Nash equilibria in different game-theoretic models. In such an outcome, no player can improve her objective by more than a given factor through a deviation to another strategy. In the first part, we investigate two variants of Congestion Games in which the existence of pure Nash equilibria is guaranteed through a potential function argument. However, the computation of such equilibria might be hard. We construct and analyze approximation algorithms that enable the computation of states with low approximation factors in polynomial time. To show their guarantees we use sub games among players, bound the potential function values of arbitrary states and exploit a connection between Shapley and proportional cost shares. Furthermore, we apply and analyze sampling techniques for the computation of approximate Shapley values in different settings. In the second part, we concentrate on the existence of approximate pure Nash equilibria in games in which no pure Nash equilibria exist in general. In the model of Coevolving Opinion Formation Games, we bound the approximation guarantees for natural states nearly independent of the specific definition of the players' neighborhoods by applying a concept of virtual costs. For the special case of only one influential neighbor, we even show lower approximation factors for a natural strategy. Then, we investigate a two-sided Facility Location Game among facilities and clients on a line with an objective function consisting of distance and load. We show tight bounds on the approximation factor for settings with three facilities and infinitely many clients. For the general scenario with an arbitrary number of facilities, we bound the approximation factor for two promising candidates, namely facilities that are uniformly distributed and which are paired.
AU - Feldotto, Matthias
ID - 8080
TI - Approximate Pure Nash Equilibria in Congestion, Opinion Formation and Facility Location Games
ER -
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 - GEN
AU - Kemper, Arne
ID - 1186
TI - Pure Nash Equilibria in Robust Congestion Games via Potential Functions
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 - GEN
AU - Nachtigall, Marcel
ID - 1187
TI - Scenario-driven Strategy Analysis in a n-player Composition Game Model
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 - GEN
AU - Kempf, Jérôme
ID - 1188
TI - Learning deterministic bandit behaviour form compositions
ER -
TY - CONF
AB - We study the classic bin packing problem in a fully-dynamic setting, where new items can arrive and old items may depart. We want algorithms with low asymptotic competitive ratio while repacking items sparingly between updates. Formally, each item i has a movement cost c_i >= 0, and we want to use alpha * OPT bins and incur a movement cost gamma * c_i, either in the worst case, or in an amortized sense, for alpha, gamma as small as possible. We call gamma the recourse of the algorithm. This is motivated by cloud storage applications, where fully-dynamic bin packing models the problem of data backup to minimize the number of disks used, as well as communication incurred in moving file backups between disks. Since the set of files changes over time, we could recompute a solution periodically from scratch, but this would give a high number of disk rewrites, incurring a high energy cost and possible wear and tear of the disks. In this work, we present optimal tradeoffs between number of bins used and number of items repacked, as well as natural extensions of the latter measure.
AU - Feldkord, Björn
AU - Feldotto, Matthias
AU - Gupta, Anupam
AU - Guruganesh, Guru
AU - Kumar, Amit
AU - Riechers, Sören
AU - Wajc, David
ED - Chatzigiannakis, Ioannis
ED - Kaklamanis, Christos
ED - Marx, Dániel
ED - Sannella, Donald
ID - 2484
SN - 1868-8969
T2 - 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
TI - Fully-Dynamic Bin Packing with Little Repacking
VL - 107
ER -
TY - GEN
AU - Koop, Samuel
ID - 3851
TI - Congestion Games mit gewichteten Strategien
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 - GEN
AU - Bürmann, Jan
ID - 1080
TI - Complexity of Signalling in Routing Games under Uncertainty
ER -
TY - GEN
AU - Nachtigall, Simon
ID - 1073
TI - Sortieren dynamischer Daten
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 - GEN
AU - Vijayalakshmi, Vipin Ravindran
ID - 1081
TI - Bounding the Inefficiency of Equilibria in Congestion Games under Taxation
ER -
TY - GEN
AU - Pukrop, Simon
ID - 1074
TI - Robuste Optimierung in 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 -