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Network Investment Game with Wardrop Followers [article]

Daniel Schmand, Marc Schröder, Alexander Skopalik
2019 arXiv   pre-print
We study a two-sided network investment game consisting of two sets of players, called providers and users. The game is set in two stages. In the first stage, providers aim to maximize their profit by investing in bandwidth of cloud computing services. The investments of the providers yield a set of usable services for the users. In the second stage, each user wants to process a task and therefore selects a bundle of services so as to minimize the total processing time. We assume the total
more » ... ssing time to be separable over the chosen services and the processing time of each service to depend on the utilization of the service and the installed bandwidth. We provide insights on how competition between providers affects the total costs of the users and show that every game on a series-parallel graph can be reduced to an equivalent single edge game when analyzing the set of subgame perfect Nash equilibria.
arXiv:1904.10417v1 fatcat:teunzsonlfbrrfysyzdreicqge

Additive Stabilizers for Unstable Graphs [article]

Karthekeyan Chandrasekaran, Corinna Gottschalk, Jochen Könemann, Britta Peis, Daniel Schmand, Andreas Wierz
2016 arXiv   pre-print
Stabilization of graphs has received substantial attention in recent years due to its connection to game theory. Stable graphs are exactly the graphs inducing a matching game with non-empty core. They are also the graphs that induce a network bargaining game with a balanced solution. A graph with weighted edges is called stable if the maximum weight of an integral matching equals the cost of a minimum fractional weighted vertex cover. If a graph is not stable, it can be stabilized in different
more » ... ays. Recent papers have considered the deletion or addition of edges and vertices in order to stabilize a graph. In this work, we focus on a fine-grained stabilization strategy, namely stabilization of graphs by fractionally increasing edge weights. We show the following results for stabilization by minimum weight increase in edge weights (min additive stabilizer): (i) Any approximation algorithm for min additive stabilizer that achieves a factor of O(|V|^1/24-ϵ) for ϵ>0 would lead to improvements in the approximability of densest-k-subgraph. (ii) Min additive stabilizer has no o(|V|) approximation unless NP=P. Results (i) and (ii) together provide the first super-constant hardness results for any graph stabilization problem. On the algorithmic side, we present (iii) an algorithm to solve min additive stabilizer in factor-critical graphs exactly in poly-time, (iv) an algorithm to solve min additive stabilizer in arbitrary-graphs exactly in time exponential in the size of the Tutte set, and (v) a poly-time algorithm with approximation factor at most √(|V|) for a super-class of the instances generated in our hardness proofs.
arXiv:1608.06797v1 fatcat:7dp574xwgvdf5hz6amnelmnujm

Asynchronous Opinion Dynamics in Social Networks [article]

Petra Berenbrink, Martin Hoefer, Dominik Kaaser, Pascal Lenzner, Malin Rau, Daniel Schmand
2022 arXiv   pre-print
Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. The model by Hegselmann and Krause is a well-known theoretical model to study such opinion formation processes in social networks. In contrast to many other theoretical models, it does not converge towards a situation where all agents agree on the same opinion. Instead, it assumes that people find an opinion reasonable if and only if it is close to their own.
more » ... e system converges towards a stable situation where agents sharing the same opinion form a cluster, and agents in different clusters do not We focus on the social variant of the Hegselmann-Krause model where agents are connected by a social network and their opinions evolve in an iterative process. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion. By this, the set of influencing neighbors of an agent may change over time. To the best of our knowledge, social Hegselmann-Krause systems with asynchronous opinion updates have only been studied with the complete graph as social network. We show that such opinion dynamics with random agent activation are guaranteed to converge for any social network. We provide an upper bound of 𝒪(n|E|^2 (ε/δ)^2) on the expected number of opinion updates until convergence, where |E| is the number of edges of the social network. For the complete social network we show a bound of 𝒪(n^3(n^2 + (ε/δ)^2)) that represents a major improvement over the previously best upper bound of 𝒪(n^9 (ε/δ)^2). Our bounds are complemented by simulations that indicate asymptotically matching lower bounds.
arXiv:2201.12923v1 fatcat:rgq7ufm2ejb2tbin5ughlbx3qm

Strategic Payments in Financial Networks [article]

Nils Bertschinger and Martin Hoefer and Daniel Schmand
2019 arXiv   pre-print
In their seminal work on systemic risk in financial markets, Eisenberg and Noe proposed and studied a model with n firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the
more » ... ssible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation – if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of Ω(n) away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems.
arXiv:1908.01714v2 fatcat:7x2htw2oifdc7li5eckh7gtnvm

Sharing Non-anonymous Costs of Multiple Resources Optimally [chapter]

Max Klimm, Daniel Schmand
2015 Lecture Notes in Computer Science  
In cost sharing games, the existence and efficiency of pure Nash equilibria fundamentally depends on the method that is used to share the resources' costs. We consider a general class of resource allocation problems in which a set of resources is used by a heterogeneous set of selfish users. The cost of a resource is a (non-decreasing) function of the set of its users. Under the assumption that the costs of the resources are shared by uniform cost sharing protocols, i.e., protocols that use
more » ... local information of the resource's cost structure and its users to determine the cost shares, we exactly quantify the inefficiency of the resulting pure Nash equilibria. Specifically, we show tight bounds on prices of stability and anarchy for games with only submodular and only supermodular cost functions, respectively, and an asymptotically tight bound for games with arbitrary set-functions. While all our upper bounds are attained for the well-known Shapley cost sharing protocol, our lower bounds hold for arbitrary uniform cost sharing protocols and are even valid for games with anonymous costs, i.e., games in which the cost of each resource only depends on the cardinality of the set of its users.
doi:10.1007/978-3-319-18173-8_20 fatcat:blceikiywbb2dngiag5m5bhwya

Sharing Non-Anonymous Costs of Multiple Resources Optimally [article]

Max Klimm, Daniel Schmand
2015 arXiv   pre-print
In cost sharing games, the existence and efficiency of pure Nash equilibria fundamentally depends on the method that is used to share the resources' costs. We consider a general class of resource allocation problems in which a set of resources is used by a heterogeneous set of selfish users. The cost of a resource is a (non-decreasing) function of the set of its users. Under the assumption that the costs of the resources are shared by uniform cost sharing protocols, i.e., protocols that use
more » ... local information of the resource's cost structure and its users to determine the cost shares, we exactly quantify the inefficiency of the resulting pure Nash equilibria. Specifically, we show tight bounds on prices of stability and anarchy for games with only submodular and only supermodular cost functions, respectively, and an asymptotically tight bound for games with arbitrary set-functions. While all our upper bounds are attained for the well-known Shapley cost sharing protocol, our lower bounds hold for arbitrary uniform cost sharing protocols and are even valid for games with anonymous costs, i.e., games in which the cost of each resource only depends on the cardinality of the set of its users.
arXiv:1412.4456v2 fatcat:d6rnam2wejdgbaonohv4sxeily

Strategic Payments in Financial Networks

Nils Bertschinger, Martin Hoefer, Daniel Schmand, Michael Wagner
2020 Innovations in Theoretical Computer Science  
In their seminal work on systemic risk in financial markets, Eisenberg and Noe [13] proposed and studied a model with n firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the
more » ... permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation -if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of Ω(n) away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems. ACM Subject Classification Theory of computation → Algorithmic game theory and mechanism design
doi:10.4230/lipics.itcs.2020.46 dblp:conf/innovations/BertschingerHS20 fatcat:n7rlhhtoinhzjj4ko4dyphviva

The Online Best Reply Algorithm for Resource Allocation Problems [article]

Max Klimm, Daniel Schmand, Andreas Tönnis
2019 arXiv   pre-print
Bjelde, Klimm and Schmand [7] analyzed the solution quality of local minima of the social cost function both for weighted and unweighted resource allocation problems, see Table 1 .  ... 
arXiv:1805.02526v2 fatcat:bsa6dvinvjgypknxa2or4ovw44

Competitive Packet Routing with Priority Lists

Tobias Harks, Britta Peis, Daniel Schmand, Bjoern Tauer, Laura Vargas Koch
2018 ACM Transactions on Economics and Computation  
In competitive packet routing games, packets are routed selfishly through a network and scheduling policies at edges determine which packages are forwarded first if there is not enough capacity on an edge to forward all packages at once. We analyze the impact of priority lists on the worst-case quality of pure Nash equilibria. A priority list is an ordered list of players that may or may not depend on the edge. Whenever the number of packets entering an edge exceeds the inflow capacity, packets
more » ... are processed in list order. We derive several new bounds on the price of anarchy and stability for global and local priority policies. We also consider the question of the complexity of computing an optimal priority list. It turns out that even for very restricted cases, i.e., for routing on a tree, the computation of an optimal priority list is APX-hard.
doi:10.1145/3184137 fatcat:ycbw2obd6nb65me5fztzrejlzm

Network Investment Games with Wardrop Followers

Daniel Schmand, Marc Schröder, Alexander Skopalik, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
We study a two-sided network investment game consisting of two sets of players, called providers and users. The game is set in two stages. In the first stage, providers aim to maximize their profit by investing in bandwidth of cloud computing services. The investments of the providers yield a set of usable services for the users. In the second stage, each user wants to process a task and therefore selects a bundle of services so as to minimize the total processing time. We assume the total
more » ... ssing time to be separable over the chosen services and the processing time of each service to depend on the utilization of the service and the installed bandwidth. We provide insights on how competition between providers affects the total costs of the users and show that every game on a series-parallel graph can be reduced to an equivalent single edge game when analyzing the set of subgame perfect Nash equilibria. ACM Subject Classification Theory of computation → Algorithmic game theory and mechanism design; Theory of computation → Network games
doi:10.4230/lipics.icalp.2019.151 dblp:conf/icalp/Schmand0S19 fatcat:yunk7mbkozc45fsrihro6sjwva

Hiring Secretaries over Time: The Benefit of Concurrent Employment [article]

Yann Disser, John Fearnley, Martin Gairing, Oliver Göbel, Max Klimm, Daniel Schmand, Alexander Skopalik, Andreas Tönnis
2017 arXiv   pre-print
We consider a stochastic online problem where n applicants arrive over time, one per time step. Upon arrival of each applicant their cost per time step is revealed, and we have to fix the duration of employment, starting immediately. This decision is irrevocable, i.e., we can neither extend a contract nor dismiss a candidate once hired. In every time step, at least one candidate needs to be under contract, and our goal is to minimize the total hiring cost, which is the sum of the applicants'
more » ... ts multiplied with their respective employment durations. We provide a competitive online algorithm for the case that the applicants' costs are drawn independently from a known distribution. Specifically, the algorithm achieves a competitive ratio of 2.965 for the case of uniform distributions. For this case, we give an analytical lower bound of 2 and a computational lower bound of 2.148. We then adapt our algorithm to stay competitive even in settings with one or more of the following restrictions: (i) at most two applicants can be hired concurrently; (ii) the distribution of the applicants' costs is unknown; (iii) the total number n of time steps is unknown. On the other hand, we show that concurrent employment is a necessary feature of competitive algorithms by proving that no algorithm has a competitive ratio better than Ω(√(n) / n) if concurrent employment is forbidden.
arXiv:1604.08125v2 fatcat:6paucepbkja6njbewxdkxxbr7u

A Greedy Algorithm for the Social Golfer and the Oberwolfach Problem [article]

Daniel Schmand, Marc Schröder, Laura Vargas Koch
2021 arXiv   pre-print
Email addresses: schmand@uni-bremen.de (Daniel Schmand), m.schroder@maastrichtuniversity.nl (Marc Schröder), laura.vargas@oms.rwth-aachen.de (Laura Vargas Koch) Appleton (1995) even mentions playing  ... 
arXiv:2007.10704v3 fatcat:zrw7tczeeverfni743s6z3jguu

Robust flows over time: models and complexity results

Corinna Gottschalk, Arie M. C. A. Koster, Frauke Liers, Britta Peis, Daniel Schmand, Andreas Wierz
2017 Mathematical programming  
School of Business and Economics, RWTH Aachen University, Germany, E-mail: {gottschalk, peis, schmand, wierz}@oms.rwth-aachen.de · 2 Lehrstuhl II für Mathematik, RWTH Aachen University, Germany, E-mail  ... 
doi:10.1007/s10107-017-1170-3 fatcat:euea3svlpjfmpb2n6yyzyqkrhi

Competitive Packet Routing with Priority Lists

Tobias Harks, Britta Peis, Daniel Schmand, Laura Koch
unpublished
In competitive packet routing games, packets are routed selfishly through a network and scheduling policies at edges determine which packages are forwarded first if there is not enough capacity on an edge to forward all packages at once. We analyze the impact of priority lists on the worst-case quality of pure Nash equilibria. A priority list is an ordered list of players that may or may not depend on the edge. Whenever the number of packets entering an edge exceeds the inflow capacity, packets
more » ... are processed in list order. We derive several new bounds on the price of anarchy and stability for global and local priority policies. We also consider the question of the complexity of computing an optimal priority list. It turns out that even for very restricted cases, i.e., for routing on a tree, the computation of an optimal priority list is APX-hard.
fatcat:3yw46kuszncvvekjpj3p4jup2y

Stochastic Probing with Increasing Precision

Martin Hoefer, Kevin Schewior, Daniel Schmand
2021 Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence   unpublished
We consider a selection problem with stochastic probing. There is a set of items whose values are drawn from independent distributions. The distributions are known in advance. Each item can be \emph{tested} repeatedly. Each test reduces the uncertainty about the realization of its value. We study a testing model, where the first test reveals if the realized value is smaller or larger than the median of the underlying distribution. Subsequent tests allow to further narrow down the interval in
more » ... ch the realization is located. There is a limited number of possible tests, and our goal is to design near-optimal testing strategies that allow to maximize the expected value of the chosen item. We study both identical and non-identical distributions and develop polynomial-time algorithms with constant approximation factors in both scenarios.
doi:10.24963/ijcai.2021/560 fatcat:i4iacoogqbgjzknru62cwwjk6i
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