@phdthesis{8080,
abstract = {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.},
author = {Feldotto, Matthias},
title = {{Approximate Pure Nash Equilibria in Congestion, Opinion Formation and Facility Location Games}},
doi = {10.17619/UNIPB/1-588},
year = {2019},
}
@inproceedings{10281,
abstract = {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.},
author = {Feldotto, Matthias and Lenzner, Pascal and Molitor, Louise and Skopalik, Alexander},
booktitle = {Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems},
location = {Montreal QC, Canada},
pages = {1949----1951},
publisher = {International Foundation for Autonomous Agents and Multiagent Systems},
title = {{ From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation}},
year = {2019},
}
@inproceedings{5471,
abstract = {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.},
author = {Lazos, Philip and Goldberg, Paul and Skopalik, Alexander and Gerstgrasser, Matthias and de Keijzer, Bart},
booktitle = {Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence (AAAI)},
location = {Honolulu, Hawaii, USA},
title = {{ Multi-unit Bilateral Trade}},
year = {2019},
}
@inproceedings{2831,
abstract = {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.},
author = {Feldotto, Matthias and Haake, Claus-Jochen and Skopalik, Alexander and Stroh-Maraun, Nadja},
booktitle = {Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018)},
isbn = {978-1-4503-5916-0},
location = {Irvine, California, USA},
pages = {5:1--5:6},
title = {{Disaggregating User Evaluations Using the Shapley Value}},
doi = {10.1145/3230654.3230659},
year = {2018},
}
@misc{1186,
author = {Kemper, Arne},
publisher = {Universität Paderborn},
title = {{Pure Nash Equilibria in Robust Congestion Games via Potential Functions}},
year = {2018},
}
@article{1369,
abstract = {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.},
author = {Drees, Maximilian and Feldotto, Matthias and Riechers, Sören and Skopalik, Alexander},
issn = {1382-6905},
journal = {Journal of Combinatorial Optimization},
publisher = {Springer Nature},
title = {{Pure Nash equilibria in restricted budget games}},
doi = {10.1007/s10878-018-0269-7},
year = {2018},
}
@misc{1187,
author = {Nachtigall, Marcel},
publisher = {Universität Paderborn},
title = {{Scenario-driven Strategy Analysis in a n-player Composition Game Model}},
year = {2018},
}
@article{669,
abstract = {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.},
author = {Feldotto, Matthias and Leder, Lennart and Skopalik, Alexander},
issn = {1382-6905},
journal = {Journal of Combinatorial Optimization},
number = {4},
pages = {1145--1167},
publisher = {Springer Nature},
title = {{Congestion games with mixed objectives}},
doi = {10.1007/s10878-017-0189-y},
volume = {36},
year = {2018},
}
@inproceedings{2484,
abstract = {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.},
author = {Feldkord, Björn and Feldotto, Matthias and Gupta, Anupam and Guruganesh, Guru and Kumar, Amit and Riechers, Sören and Wajc, David},
booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, Dániel and Sannella, Donald},
isbn = {978-3-95977-076-7},
issn = {1868-8969},
location = {Prag},
pages = {51:1--51:24},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
title = {{Fully-Dynamic Bin Packing with Little Repacking}},
doi = {10.4230/LIPIcs.ICALP.2018.51},
volume = {107},
year = {2018},
}
@misc{1188,
author = {Kempf, Jérôme},
publisher = {Universität Paderborn},
title = {{Learning deterministic bandit behaviour form compositions}},
year = {2018},
}
@misc{3851,
author = {Koop, Samuel},
publisher = {Universität Paderborn},
title = {{Congestion Games mit gewichteten Strategien}},
year = {2018},
}
@inproceedings{112,
abstract = {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.},
author = {Feldotto, Matthias and Leder, Lennart and Skopalik, Alexander},
booktitle = {Proceedings of the 10th International Conference on Algorithms and Complexity (CIAC)},
pages = {222----233},
title = {{Congestion Games with Complementarities}},
doi = {10.1007/978-3-319-57586-5_19},
year = {2017},
}
@inproceedings{66,
abstract = {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.},
author = {Drees, Maximilian and Feldotto, Matthias and Riechers, Sören and Skopalik, Alexander},
booktitle = {Proceedings of the 23rd International Computing and Combinatorics Conference (COCOON)},
pages = {175----187},
title = {{Pure Nash Equilibria in Restricted Budget Games}},
doi = {10.1007/978-3-319-62389-4_15},
year = {2017},
}
@inproceedings{59,
abstract = {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).},
author = {Kling, Peter and Mäcker, Alexander and Riechers, Sören and Skopalik, Alexander},
booktitle = {Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)},
pages = {123----132},
title = {{Sharing is Caring: Multiprocessor Scheduling with a Sharable Resource}},
doi = {10.1145/3087556.3087578},
year = {2017},
}
@misc{1073,
author = {Nachtigall, Simon},
publisher = {Universität Paderborn},
title = {{Sortieren dynamischer Daten}},
year = {2017},
}
@misc{1080,
author = {Bürmann, Jan},
publisher = {Universität Paderborn},
title = {{Complexity of Signalling in Routing Games under Uncertainty}},
year = {2017},
}
@inproceedings{113,
abstract = {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].},
author = {Feldotto, Matthias and Gairing, Martin and Kotsialou, Grammateia and Skopalik, Alexander},
booktitle = {Proceedings of the 13th International Conference on Web and Internet Economics (WINE)},
title = {{Computing Approximate Pure Nash Equilibria in Shapley Value Weighted Congestion Games}},
doi = {10.1007/978-3-319-71924-5_14},
year = {2017},
}
@misc{1074,
author = {Pukrop, Simon},
publisher = {Universität Paderborn},
title = {{Robuste Optimierung in Congestion Games}},
year = {2017},
}
@misc{1081,
author = {Vijayalakshmi, Vipin Ravindran},
publisher = {Universität Paderborn},
title = {{Bounding the Inefficiency of Equilibria in Congestion Games under Taxation}},
year = {2017},
}
@inproceedings{1094,
abstract = {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.},
author = {Feldotto, Matthias and John, Thomas and Kundisch, Dennis and Hemsen, Paul and Klingsieck, Katrin and Skopalik, Alexander},
booktitle = {Proceedings of the 12th International Conference on Design Science Research in Information Systems and Technology (DESRIST)},
pages = {462--467},
title = {{Making Gamification Easy for the Professor: Decoupling Game and Content with the StudyNow Mobile App}},
doi = {10.1007/978-3-319-59144-5_32},
year = {2017},
}