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 - JOUR
AU - Feldkord, Björn
AU - Meyer auf der Heide, Friedhelm
ID - 13873
IS - 3
JF - ACM Transactions on Parallel Computing (TOPC)
TI - The Mobile Server Problem
VL - 6
ER -
TY - CONF
AU - Feldkord, Björn
AU - Knollmann, Till
AU - Malatyali, Manuel
AU - Meyer auf der Heide, Friedhelm
ID - 12870
T2 - Proceedings of the 17th Workshop on Approximation and Online Algorithms (WAOA) (accepted)
TI - Managing Multiple Mobile Resources
ER -
TY - GEN
AU - Pukrop, Simon
ID - 10344
TI - Scheduling Algorithms for Multi-Operation Jobs with Setups on a Single Machine
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 - JOUR
AU - Meyer auf der Heide, Friedhelm
ID - 13937
IS - 2
JF - Mathematische Semesterberichte
TI - Paul Curzon, Peter W. McOwan: Computational Thinking; Die Welt des algorithmischen Denkens – in Spielen, Zaubertricks und Rätseln
VL - 66
ER -
TY - CONF
AU - Jansen, Klaus
AU - Maack, Marten
AU - Mäcker, Alexander
ID - 8866
T2 - Proceedings of the 33rd IEEE International Parallel and Distributed Processing Symposium (IPDPS)
TI - Scheduling on (Un-)Related Machines with Setup Times
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 - CHAP
AU - Kling, Peter
AU - Meyer auf der Heide, Friedhelm
ID - 13939
T2 - Distributed Computing by Mobile Entities, Current Research in Moving and Computing
TI - Continuous Protocols for Swarm Robotics
VL - 11340
ER -
TY - JOUR
AU - Abu-Khzam, Faisal N.
AU - Li, Shouwei
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
ID - 13946
JF - Theoretical Computer Science
TI - Efficient parallel algorithms for parameterized problems
VL - 786
ER -
TY - CONF
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
ID - 13942
T2 - Proceedings of the 8th International Conference on Operations Research and Enterprise Systems
TI - Online Algorithms for Leasing Vertex Cover and Leasing Non-metric Facility Location
ER -
TY - THES
AU - Mäcker, Alexander
ID - 14851
TI - On Scheduling with Setup Times
ER -
TY - CONF
AU - Meyer auf der Heide, Friedhelm
AU - Schaefer, Johannes Sebastian
ID - 7570
SN - 9781450357999
T2 - Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures - SPAA '18
TI - Brief Announcement: Communication in Systems of Home Based Mobile Agents
ER -
TY - GEN
AU - Kolpaczki, Patrick Irenäus
ID - 5404
TI - Online Algorithmen für das k-Page Migration Problem
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 - CONF
AU - Hamann, Heiko
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
AU - Wahby, Mostafa
ID - 2850
T2 - Ninth International Conference on Fun with Algorithms (FUN)
TI - Pick, Pack, & Survive: Charging Robots in a Modern Warehouse based on Online Connected Dominating Sets
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
AU - Jung, Daniel
AU - Kolb, Christina
AU - Scheideler, Christian
AU - Sundermeier, Jannik
ID - 4565
SN - 9781450357999
T2 - Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures (SPAA)
TI - Brief Announcement: Competitive Routing in Hybrid Communication Networks
ER -
TY - JOUR
AU - Li, Shouwei
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
ID - 2848
IS - 5
JF - Algorithmica
TI - Towards Flexible Demands in Online Leasing Problems.
VL - 80
ER -