2023 [ nach oben ]

Bläsius, Thomas; Friedrich, Tobias; Krejca, Martin; Molitor, Louise The Impact of Geometry on Monochrome Regions in the Flip Schelling ProcessComputational Geometry (CGTA) 2023: 101902
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Schelling's classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We introduce an agent-based saturated open-city variant, the Flip Schelling Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to change their types; similar to a new agent arriving as soon as another agent leaves the vertex. We investigate the probability that an edge u,v is monochrome, i.e., that both vertices u and v have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and, moreover, that large common neighborhoods are more decisive. As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random geometric graphs, we show that the existence of an edge u,v makes a highly decisive common neighborhood for u and v more likely. Based on this, we prove the existence of a constant c>0 such that the expected fraction of monochrome edges after the FSP is at least 1/2+c. (2) For Erdős–Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most 1/2+o(1). Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.
@article{blasius2023impact, abstract = {Schelling's classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We introduce an agent-based saturated open-city variant, the Flip Schelling Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to change their types; similar to a new agent arriving as soon as another agent leaves the vertex. We investigate the probability that an edge {u,v} is monochrome, i.e., that both vertices u and v have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and, moreover, that large common neighborhoods are more decisive. As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random geometric graphs, we show that the existence of an edge {u,v} makes a highly decisive common neighborhood for u and v more likely. Based on this, we prove the existence of a constant c>0 such that the expected fraction of monochrome edges after the FSP is at least 1/2+c. (2) For Erdős–Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most 1/2+o(1). Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.}, author = {Bläsius, Thomas and Friedrich, Tobias and Krejca, Martin and Molitor, Louise}, journal = {Computational Geometry (CGTA)}, keywords = {sys:relevantfor:ae cgta louisemolitor martinskrejca thomasblaesius tobiasfriedrich year2023}, pages = 101902, title = {The Impact of Geometry on Monochrome Regions in the Flip Schelling Process}, volume = 108, year = 2023 }

2022 [ nach oben ]

Bilò, Davide; Bilò, Vittorio; Lenzner, Pascal; Molitor, Louise Topological Influence and Locality in Swap Schelling GamesAutonomous Agents and Multi-Agent Systems (AGNT) 2022
[ Abstract ] [ BibTeX ]
 
Residential segregation is a wide-spread phenomenon that can be observed in almost every major city. In these urban areas residents with different racial or socioeconomic background tend to form homogeneous clusters. Schelling's famous agent-based model for residential segregation explains how such clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slight bias towards agents preferring similar neighbors. Very recently, Schelling's model has been investigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight bounds on the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, which are commonly used in empirical studies. For grids we also show that locality has a severe impact on the game dynamics.
@article{bilo2022topological, abstract = {Residential segregation is a wide-spread phenomenon that can be observed in almost every major city. In these urban areas residents with different racial or socioeconomic background tend to form homogeneous clusters. Schelling's famous agent-based model for residential segregation explains how such clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slight bias towards agents preferring similar neighbors. Very recently, Schelling's model has been investigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight bounds on the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, which are commonly used in empirical studies. For grids we also show that locality has a severe impact on the game dynamics.}, author = {Bilò, Davide and Bilò, Vittorio and Lenzner, Pascal and Molitor, Louise}, journal = {Autonomous Agents and Multi-Agent Systems (AGNT)}, keywords = {agnt louisemolitor pascallenzner year2022}, title = {Topological Influence and Locality in Swap Schelling Games}, year = 2022 }

Angrick, Sebastian; Bals, Ben; Hastrich, Niko; Kleissl, Maximilian; Schmidt, Jonas; Doskoč, Vanja; Katzmann, Maximilian; Molitor, Louise; Friedrich, Tobias Towards Explainable Real Estate Valuation via Evolutionary AlgorithmsGenetic and Evolutionary Computation Conference (GECCO) 2022
[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
 
Human lives are increasingly influenced by algorithms, which therefore need to meet higher standards not only in accuracy but also with respect to explainability. This is especially true for high-stakes areas such as real estate valuation. Unfortunately, the methods applied there often exhibit a trade-off between accuracy and explainability. One explainable approach is case-based reasoning (CBR), whereeach decision is supported by specific previous cases. However, such methods can be wanting in accuracy. The unexplainable machine learning approaches are often observed to provide higher accuracy but are not scrutable in their decision-making. In this paper, we apply evolutionary algorithms (EAs) to CBR predictors in order to improve their performance. In particular, we deploy EAs to the similarity functions (used in CBR to find comparable cases), which are fitted to the data set at hand. As a consequence, we achieve higher accuracy than state-of-the-art deep neural networks (DNNs), while keeping interpretability and explainability. These results stem from our empirical evaluation on a large data set of real estate offers where we compare known similarity functions, their EA-improved counterparts, and DNNs. Surprisingly, DNNs are only on par with standard CBR techniques. However, using EA-learned similarity functions does yield an improved performance.
@inproceedings{angrick2022towards, abstract = {Human lives are increasingly influenced by algorithms, which therefore need to meet higher standards not only in accuracy but also with respect to explainability. This is especially true for high-stakes areas such as real estate valuation. Unfortunately, the methods applied there often exhibit a trade-off between accuracy and explainability. One explainable approach is case-based reasoning (CBR), whereeach decision is supported by specific previous cases. However, such methods can be wanting in accuracy. The unexplainable machine learning approaches are often observed to provide higher accuracy but are not scrutable in their decision-making. In this paper, we apply evolutionary algorithms (EAs) to CBR predictors in order to improve their performance. In particular, we deploy EAs to the similarity functions (used in CBR to find comparable cases), which are fitted to the data set at hand. As a consequence, we achieve higher accuracy than state-of-the-art deep neural networks (DNNs), while keeping interpretability and explainability. These results stem from our empirical evaluation on a large data set of real estate offers where we compare known similarity functions, their EA-improved counterparts, and DNNs. Surprisingly, DNNs are only on par with standard CBR techniques. However, using EA-learned similarity functions does yield an improved performance.}, author = {Angrick, Sebastian and Bals, Ben and Hastrich, Niko and Kleissl, Maximilian and Schmidt, Jonas and Doskoč, Vanja and Katzmann, Maximilian and Molitor, Louise and Friedrich, Tobias}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {benbals gecco jonasschmidt louisemolitor maximiliankatzmann maximiliankleissl nikohastrich sebastianangrick tobiasfriedrich vanjadoskoc year2022}, title = {Towards Explainable Real Estate Valuation via Evolutionary Algorithms}, year = 2022 }

Bilò, Davide; Bilò, Vittorio; Lenzner, Pascal; Molitor, Louise Tolerance is Necessary for Stability: Single-Peaked Swap Schelling GamesInternational Joint Conference on Artificial Intelligence (IJCAI) 2022
[ Abstract ] [ BibTeX ] [ Download ]
 
Residential segregation in metropolitan areas is a phenomenon that can be observed all over the world. Recently, this was investigated via game-theoretic models. There, selfish agents of two types are equipped with a monotone utility function that ensures higher utility if an agent has more same-type neighbors. The agents strategically choose their location on a given graph that serves as residential area to maximize their utility. However, sociological polls suggest that real-world agents are actually favoring mixed-type neighborhoods, and hence should be modeled via non-monotone utility functions. To address this, we study Swap Schelling Games with single-peaked utility functions. Our main finding is that tolerance, i.e., agents favoring fifty-fifty neighborhoods or being in the minority, is necessary for equilibrium existence on almost regular or bipartite graphs. Regarding the quality of equilibria, we derive (almost) tight bounds on the Price of Anarchy and the Price of Stability. In particular, we show that the latter is constant on bipartite and almost regular graphs.
@inproceedings{bilo2022tolerance, abstract = {Residential segregation in metropolitan areas is a phenomenon that can be observed all over the world. Recently, this was investigated via game-theoretic models. There, selfish agents of two types are equipped with a monotone utility function that ensures higher utility if an agent has more same-type neighbors. The agents strategically choose their location on a given graph that serves as residential area to maximize their utility. However, sociological polls suggest that real-world agents are actually favoring mixed-type neighborhoods, and hence should be modeled via non-monotone utility functions. To address this, we study Swap Schelling Games with single-peaked utility functions. Our main finding is that tolerance, i.e., agents favoring fifty-fifty neighborhoods or being in the minority, is necessary for equilibrium existence on almost regular or bipartite graphs. Regarding the quality of equilibria, we derive (almost) tight bounds on the Price of Anarchy and the Price of Stability. In particular, we show that the latter is constant on bipartite and almost regular graphs.}, author = {Bilò, Davide and Bilò, Vittorio and Lenzner, Pascal and Molitor, Louise}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai louisemolitor pascallenzner year2022}, title = {Tolerance is Necessary for Stability: Single-Peaked Swap Schelling Games}, year = 2022 }

2021 [ nach oben ]

Böther, Maximilian; Schiller, Leon; Fischbeck, Philipp; Molitor, Louise; Krejca, Martin S.; Friedrich, Tobias Evolutionary Minimization of Traffic CongestionGenetic and Evolutionary Computation Conference (GECCO) 2021: 937–945
Best Paper Award (RWA Track)
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Traffic congestion is a major issue that can be solved by suggesting drivers alternative routes they are willing to take. This concept has been formalized as a strategic routing problem in which a single alternative route is suggested to an existing one. We extend this formalization and introduce the Multiple-Routes problem, which is given a start and a destination and then aims at finding up to \(n\) different routes that the drivers strategically disperse over, minimizing the overall travel time of the system. Due to the NP-hard nature of the problem, we introduce the Multiple-Routes evolutionary algorithm (MREA) as a heuristic solver. We study several mutation and crossover operators and evaluate them on real-world data of the city of Berlin, Germany. We find that a combination of all operators yields the best result, improving the overall travel time by a factor between 1.8 and 3, in the median, compared to all drivers taking the fastest route. For the base case \(n=2\), we compare our MREA to the highly tailored optimal solver by Bläsius etal. [ATMOS 2020] and show that, in the median, our approach finds solutions of quality at least \(99.69\%\) of an optimal solution while only requiring \(40\%\) of the time.
@inproceedings{boether2021evolutionary, abstract = {Traffic congestion is a major issue that can be solved by suggesting drivers alternative routes they are willing to take. This concept has been formalized as a strategic routing problem in which a single alternative route is suggested to an existing one. We extend this formalization and introduce the Multiple-Routes problem, which is given a start and a destination and then aims at finding up to \(n\) different routes that the drivers strategically disperse over, minimizing the overall travel time of the system. Due to the NP-hard nature of the problem, we introduce the Multiple-Routes evolutionary algorithm (MREA) as a heuristic solver. We study several mutation and crossover operators and evaluate them on real-world data of the city of Berlin, Germany. We find that a combination of all operators yields the best result, improving the overall travel time by a factor between 1.8 and 3, in the median, compared to all drivers taking the fastest route. For the base case \(n=2\), we compare our MREA to the highly tailored optimal solver by Bläsius etal. [ATMOS 2020] and show that, in the median, our approach finds solutions of quality at least \(99.69\%\) of an optimal solution while only requiring \(40\%\) of the time.}, author = {Böther, Maximilian and Schiller, Leon and Fischbeck, Philipp and Molitor, Louise and Krejca, Martin S. and Friedrich, Tobias}, booktitle = {Genetic and Evolutionary Computation Conference (GECCO)}, keywords = {gecco leonschiller louisemolitor martinskrejca maximilianboether philippfischbeck tobiasfriedrich year2021}, note = {Best Paper Award (RWA Track)}, pages = {937–945}, title = {Evolutionary Minimization of Traffic Congestion}, year = 2021 }

Krogmann, Simon; Lenzner, Pascal; Molitor, Louise; Skopalik, Alexander Two-Stage Facility Location Games with Strategic Clients and FacilitiesInternational Joint Conference on Artificial Intelligence (IJCAI) 2021: 292–298
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
We consider non-cooperative facility location games where both facilities and clients act strategically and heavily influence each other. This contrasts established game-theoretic facility location models with non-strategic clients that simply select the closest opened facility. In our model, every facility location has a set of attracted clients and each client has a set of shopping locations and a weight that corresponds to her spending capacity. Facility agents selfishly select a location for opening their facility to maximize the attracted total spending capacity, whereas clients strategically decide how to distribute their spending capacity among the opened facilities in their shopping range. We focus on a natural client behavior similar to classical load balancing: our selfish clients aim for a distribution that minimizes their maximum waiting times for getting serviced, where a facility’s waiting time corresponds to its total attracted client weight. We show that subgame perfect equilibria exist and give almost tight constant bounds on the Price of Anarchy and the Price of Stability, which even hold for a broader class of games with arbitrary client behavior. Since facilities and clients influence each other, it is crucial for the facilities to anticipate the selfish clients’ behavior when selecting their location. For this, we provide an efficient algorithm that also implies an efficient check for equilibrium. Finally, we show that computing a socially optimal facility placement is NP-hard and that this result holds for all feasible client weight distributions.
@inproceedings{krogmann2021twostage, abstract = {We consider non-cooperative facility location games where both facilities and clients act strategically and heavily influence each other. This contrasts established game-theoretic facility location models with non-strategic clients that simply select the closest opened facility. In our model, every facility location has a set of attracted clients and each client has a set of shopping locations and a weight that corresponds to her spending capacity. Facility agents selfishly select a location for opening their facility to maximize the attracted total spending capacity, whereas clients strategically decide how to distribute their spending capacity among the opened facilities in their shopping range. We focus on a natural client behavior similar to classical load balancing: our selfish clients aim for a distribution that minimizes their maximum waiting times for getting serviced, where a facility’s waiting time corresponds to its total attracted client weight. We show that subgame perfect equilibria exist and give almost tight constant bounds on the Price of Anarchy and the Price of Stability, which even hold for a broader class of games with arbitrary client behavior. Since facilities and clients influence each other, it is crucial for the facilities to anticipate the selfish clients’ behavior when selecting their location. For this, we provide an efficient algorithm that also implies an efficient check for equilibrium. Finally, we show that computing a socially optimal facility placement is NP-hard and that this result holds for all feasible client weight distributions.}, author = {Krogmann, Simon and Lenzner, Pascal and Molitor, Louise and Skopalik, Alexander}, booktitle = {International Joint Conference on Artificial Intelligence (IJCAI)}, keywords = {ijcai louisemolitor pascallenzner simonkrogmann year2021}, pages = {292-298}, title = {Two-Stage Facility Location Games with Strategic Clients and Facilities}, year = 2021 }

Bläsius, Thomas; Friedrich, Tobias; Krejca, Martin; Molitor, Louise The Impact of Geometry on Monochrome Regions in the Flip Schelling ProcessInternational Symposium on Algorithms and Computation, (ISAAC) 2021 2021: 29:1–29:17
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Schelling’s classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We consider an agent-based saturated open-city variant, the Flip-Schelling-Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to changes their types; similar to a new agent arriving as soon as another agent leaves the vertex. We investigate the probability that an edge u,vis monochrome, i.e., that both vertices u and v have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and moreover, that large common neighborhoods are more decisive. As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random geometric graphs, we show that the existence of an edge u,v makes a highly decisive common neighborhood for u and v more likely. Based on this, we prove the existence of a constant c > 0 such that the expected fraction of monochrome edges after the FSP is at least 1/2 + c. (2) For Erdős–Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most 1/2 + o (1). Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.
@inproceedings{blasius2021impact, abstract = {Schelling’s classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We consider an agent-based saturated open-city variant, the Flip-Schelling-Process (FSP), in which agents, placed on a graph, have one out of two types and, based on the predominant type in their neighborhood, decide whether to changes their types; similar to a new agent arriving as soon as another agent leaves the vertex. We investigate the probability that an edge {u,v}is monochrome, i.e., that both vertices u and v have the same type in the FSP, and we provide a general framework for analyzing the influence of the underlying graph topology on residential segregation. In particular, for two adjacent vertices, we show that a highly decisive common neighborhood, i.e., a common neighborhood where the absolute value of the difference between the number of vertices with different types is high, supports segregation and moreover, that large common neighborhoods are more decisive. As an application, we study the expected behavior of the FSP on two common random graph models with and without geometry: (1) For random geometric graphs, we show that the existence of an edge {u,v} makes a highly decisive common neighborhood for u and v more likely. Based on this, we prove the existence of a constant c > 0 such that the expected fraction of monochrome edges after the FSP is at least 1/2 + c. (2) For Erdős–Rényi graphs we show that large common neighborhoods are unlikely and that the expected fraction of monochrome edges after the FSP is at most 1/2 + o (1). Our results indicate that the cluster structure of the underlying graph has a significant impact on the obtained segregation strength.}, author = {Bläsius, Thomas and Friedrich, Tobias and Krejca, Martin and Molitor, Louise}, booktitle = {International Symposium on Algorithms and Computation, (ISAAC) 2021}, keywords = {sys:relevantfor:ae isaac louisemolitor martinskrejca thomasblaesius tobiasfriedrich year2021}, pages = {29:1–29:17}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {The Impact of Geometry on Monochrome Regions in the Flip Schelling Process}, volume = 212, year = 2021 }

2020 [ nach oben ]

Bläsius, Thomas; Böther, Maximilian; Fischbeck, Philipp; Friedrich, Tobias; Gries, Alina; Hüffner, Falk; Kißig, Otto; Lenzner, Pascal; Molitor, Louise; Schiller, Leon; Wells, Armin; Wietheger, Simon A Strategic Routing Framework and Algorithms for Computing Alternative PathsAlgorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS) 2020: 10:1–10:14
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Traditional navigation services find the fastest route for a single driver. Though always using the fastest route seems desirable for every individual, selfish behavior can have undesirable effects such as higher energy consumption and avoidable congestion, even leading to higher overall and individual travel times. In contrast, strategic routing aims at optimizing the traffic for all agents regarding a global optimization goal. We introduce a framework to formalize real-world strategic routing scenarios as algorithmic problems and study one of them, which we call Single Alternative Path (SAP), in detail. There, we are given an original route between a single origin–destination pair. The goal is to suggest an alternative route to all agents that optimizes the overall travel time under the assumption that the agents distribute among both routes according to a psychological model, for which we introduce the concept of Pareto-conformity. We show that the SAP problem is NP-complete, even for such models. Nonetheless, assuming Pareto-conformity, we give multiple algorithms for different variants of SAP, using multi-criteria shortest path algorithms as subroutines.Moreover, we prove that several natural models are in fact Pareto-conform. The implementation and evaluation of our algorithms serve as a proof of concept, showing that SAP can be solved in reasonable time even though the algorithms have exponential running time in the worst case.
@inproceedings{blasius2020strategic, abstract = {Traditional navigation services find the fastest route for a single driver. Though always using the fastest route seems desirable for every individual, selfish behavior can have undesirable effects such as higher energy consumption and avoidable congestion, even leading to higher overall and individual travel times. In contrast, strategic routing aims at optimizing the traffic for all agents regarding a global optimization goal. We introduce a framework to formalize real-world strategic routing scenarios as algorithmic problems and study one of them, which we call Single Alternative Path (SAP), in detail. There, we are given an original route between a single origin–destination pair. The goal is to suggest an alternative route to all agents that optimizes the overall travel time under the assumption that the agents distribute among both routes according to a psychological model, for which we introduce the concept of Pareto-conformity. We show that the SAP problem is NP-complete, even for such models. Nonetheless, assuming Pareto-conformity, we give multiple algorithms for different variants of SAP, using multi-criteria shortest path algorithms as subroutines.Moreover, we prove that several natural models are in fact Pareto-conform. The implementation and evaluation of our algorithms serve as a proof of concept, showing that SAP can be solved in reasonable time even though the algorithms have exponential running time in the worst case.}, author = {Bläsius, Thomas and Böther, Maximilian and Fischbeck, Philipp and Friedrich, Tobias and Gries, Alina and Hüffner, Falk and Kißig, Otto and Lenzner, Pascal and Molitor, Louise and Schiller, Leon and Wells, Armin and Wietheger, Simon}, booktitle = {Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS)}, keywords = {sys:relevantfor:ae alinagries arminwells atmos falkhueffner leonschiller louisemolitor maximilianboether ottokissig pascallenzner philippfischbeck simonwietheger thomasblaesius tobiasfriedrich year2020}, pages = {10:1–10:14}, title = {A Strategic Routing Framework and Algorithms for Computing Alternative Paths}, volume = 85, year = 2020 }

Bilò, Davide; Friedrich, Tobias; Lenzner, Pascal; Melnichenko, Anna; Molitor, Louise Fair Tree Connection Games with Topology-Dependent Edge CostFoundations of Software Technology and Theoretical Computer Science (FSTTCS) 2020: 15:1–15:15
[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
 
How do rational agents self-organize when trying to connect to a common target? We study this question with a simple tree formation game which is related to the well-known fair single-source connection game by Anshelevich et al.(FOCS'04) and selfish spanning tree games by Gourvès and Monnot (WINE'08). In our game agents correspond to nodes in a network that activate a single outgoing edge to connect to the common target node (possibly via other nodes). Agents pay for their path to the common target, and edge costs are shared fairly among all agents using an edge. The main novelty of our model is dynamic edge costs that depend on the in-degree of the respective endpoint. This reflects that connecting to popular nodes that have increased internal coordination costs is more expensive since they can charge higher prices for their routing service. In contrast to related models, we show that equilibria are not guaranteed to exist, but we prove the existence for infinitely many numbers of agents. Moreover, we analyze the structure of equilibrium trees and employ these insights to prove a constant upper bound on the Price of Anarchy as well as non-trivial lower bounds on both the Price of Anarchy and the Price of Stability. We also show that in comparison with the social optimum tree the overall cost of an equilibrium tree is more fairly shared among the agents. Thus, we prove that self-organization of rational agents yields on average only slightly higher cost per agent compared to the centralized optimum, and at the same time, it induces a more fair cost distribution. Moreover, equilibrium trees achieve a beneficial trade-off between a low height and low maximum degree, and hence these trees might be of independent interest from a combinatorics point-of-view. We conclude with a discussion of promising extensions of our model.
@inproceedings{bilo2020connection, abstract = {How do rational agents self-organize when trying to connect to a common target? We study this question with a simple tree formation game which is related to the well-known fair single-source connection game by Anshelevich et al.(FOCS'04) and selfish spanning tree games by Gourvès and Monnot (WINE'08). In our game agents correspond to nodes in a network that activate a single outgoing edge to connect to the common target node (possibly via other nodes). Agents pay for their path to the common target, and edge costs are shared fairly among all agents using an edge. The main novelty of our model is dynamic edge costs that depend on the in-degree of the respective endpoint. This reflects that connecting to popular nodes that have increased internal coordination costs is more expensive since they can charge higher prices for their routing service. In contrast to related models, we show that equilibria are not guaranteed to exist, but we prove the existence for infinitely many numbers of agents. Moreover, we analyze the structure of equilibrium trees and employ these insights to prove a constant upper bound on the Price of Anarchy as well as non-trivial lower bounds on both the Price of Anarchy and the Price of Stability. We also show that in comparison with the social optimum tree the overall cost of an equilibrium tree is more fairly shared among the agents. Thus, we prove that self-organization of rational agents yields on average only slightly higher cost per agent compared to the centralized optimum, and at the same time, it induces a more fair cost distribution. Moreover, equilibrium trees achieve a beneficial trade-off between a low height and low maximum degree, and hence these trees might be of independent interest from a combinatorics point-of-view. We conclude with a discussion of promising extensions of our model.}, author = {Bilò, Davide and Friedrich, Tobias and Lenzner, Pascal and Melnichenko, Anna and Molitor, Louise}, booktitle = {Foundations of Software Technology and Theoretical Computer Science (FSTTCS)}, keywords = {annamelnichenko fsttcs louisemolitor pascallenzner tobiasfriedrich year2020}, pages = {15:1–15:15}, publisher = {Schloss Dagstuhl–Leibniz-Zentrum f{ü}r Informatik}, title = {Fair Tree Connection Games with Topology-Dependent Edge Cost}, volume = 182, year = 2020 }

Bilò, Davide; Bilò, Vittorio; Lenzner, Pascal; Molitor, Louise Topological Influence and Locality in Swap Schelling GamesInternational Symposium on Mathematical Foundations of Computer Science (MFCS) 2020: 15:1–15:15
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
Residential segregation is a wide-spread phenomenon that can be observed in almost everymajor city. In these urban areas residents with different racial or socioeconomic backgroundtend to form homogeneous clusters. Schelling’s famous agent-based model for residentialsegregation explains how such clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slightbias towards agents preferring similar neighbors. Very recently, Schelling’s model has beeninvestigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight boundson the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, whichare commonly used in empirical studies. For grids we also show that locality has a severeimpact on the game dynamics.
@inproceedings{bilo2020topological, abstract = {Residential segregation is a wide-spread phenomenon that can be observed in almost everymajor city. In these urban areas residents with different racial or socioeconomic backgroundtend to form homogeneous clusters. Schelling’s famous agent-based model for residentialsegregation explains how such clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slightbias towards agents preferring similar neighbors. Very recently, Schelling’s model has beeninvestigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight boundson the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, whichare commonly used in empirical studies. For grids we also show that locality has a severeimpact on the game dynamics.}, author = {Bilò, Davide and Bilò, Vittorio and Lenzner, Pascal and Molitor, Louise}, booktitle = {International Symposium on Mathematical Foundations of Computer Science (MFCS)}, editor = {Esparza, Javier and Kr{{á}}l', Daniel}, keywords = {louisemolitor mfcs pascallenzner year2020}, pages = {15:1–15:15}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{{ü}}r Informatik}, series = {LIPIcs}, title = {Topological Influence and Locality in Swap Schelling Games}, volume = 170, year = 2020 }

2019 [ nach oben ]

Feldotto, Matthias; Lenzner, Pascal; Molitor, Louise; Skopalik, Alexander From Hotelling to Load Balancing: Approximation and the Principle of Minimum DifferentiationAutonomous Agents and Multiagent Systems (AAMAS) 2019: 1949–1951
[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]
 
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.
@inproceedings{feldotto2019hotelling, 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 = {Autonomous Agents and Multiagent Systems (AAMAS)}, keywords = {aamas alexanderskopalik louisemolitor matthiasfeldotto pascallenzner year2019}, pages = {1949-1951}, title = {From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation}, year = 2019 }

Echzell, Hagen; Friedrich, Tobias; Lenzner, Pascal; Molitor, Louise; Pappik, Marcus; Schöne, Friedrich; Sommer, Fabian; Stangl, David Convergence and Hardness of Strategic Schelling SegregationWeb and Internet Economics (WINE) 2019: 156–170
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The phenomenon of residential segregation was captured by Schelling's famous segregation model where two types of agents are placed on a grid and an agent is content with her location if the fraction of her neighbors which have the same type as her is at least \(\tau\), for some \(0<\tau<1\). Discontent agents simply swap their location with a randomly chosen other discontent agent or jump to a random empty cell. We analyze a generalized game-theoretic model of Schelling segregation which allows more than two agent types and more general underlying graphs modeling the residential area. For this we show that both aspects heavily influence the dynamic properties and the tractability of finding an optimal placement. We map the boundary of when improving response dynamics (IRD), i.e., the natural approach for finding equilibrium states, are guaranteed to converge. For this we prove several sharp threshold results where guaranteed IRD convergence suddenly turns into the strongest possible non-convergence result: a violation of weak acyclicity. In particular, we show such threshold results also for Schelling's original model, which is in contrast to the standard assumption in many empirical papers. Furthermore, we show that in case of convergence, IRD find an equilibrium in \(O(m)\) steps, where \(m\) is the number of edges in the underlying graph and show that this bound is met in empirical simulations starting from random initial agent placements.
@inproceedings{echzell2019convergence, abstract = {The phenomenon of residential segregation was captured by Schelling's famous segregation model where two types of agents are placed on a grid and an agent is content with her location if the fraction of her neighbors which have the same type as her is at least \(\tau\), for some \(0<\tau<1\). Discontent agents simply swap their location with a randomly chosen other discontent agent or jump to a random empty cell. We analyze a generalized game-theoretic model of Schelling segregation which allows more than two agent types and more general underlying graphs modeling the residential area. For this we show that both aspects heavily influence the dynamic properties and the tractability of finding an optimal placement. We map the boundary of when improving response dynamics (IRD), i.e., the natural approach for finding equilibrium states, are guaranteed to converge. For this we prove several sharp threshold results where guaranteed IRD convergence suddenly turns into the strongest possible non-convergence result: a violation of weak acyclicity. In particular, we show such threshold results also for Schelling's original model, which is in contrast to the standard assumption in many empirical papers. Furthermore, we show that in case of convergence, IRD find an equilibrium in \(O(m)\) steps, where \(m\) is the number of edges in the underlying graph and show that this bound is met in empirical simulations starting from random initial agent placements.}, author = {Echzell, Hagen and Friedrich, Tobias and Lenzner, Pascal and Molitor, Louise and Pappik, Marcus and Schöne, Friedrich and Sommer, Fabian and Stangl, David}, booktitle = {Web and Internet Economics (WINE)}, keywords = {louisemolitor marcuspappik pascallenzner tobiasfriedrich wine year2019}, pages = {156-170}, title = {Convergence and Hardness of Strategic Schelling Segregation}, year = 2019 }

2018 [ nach oben ]

Chauhan, Ankit; Lenzner, Pascal; Molitor, Louise Schelling Segregation with Strategic AgentsSymposium on Algorithmic Game Theory (SAGT) 2018
[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
 
Schelling’s segregation model is a landmark model in sociology. It shows the counter-intuitive phenomenon that residential segregation between individuals of different groups can emerge even when all involved individuals are tolerant. Although the model is widely studied, no pure game-theoretic version where rational agents strategically choose their location exists. We close this gap by introducing and analyzing generalized game-theoretic models of Schelling segregation, where the agents can also have individual location preferences. For our models we investigate the convergence behavior and the efficiency of their equilibria. In particular, we prove guaranteed convergence to an equilibrium in the version which is closest to Schelling’s original model. Moreover, we provide tight bounds on the Price of Anarchy.
@inproceedings{chauhan2018schelling, abstract = {Schelling’s segregation model is a landmark model in sociology. It shows the counter-intuitive phenomenon that residential segregation between individuals of different groups can emerge even when all involved individuals are tolerant. Although the model is widely studied, no pure game-theoretic version where rational agents strategically choose their location exists. We close this gap by introducing and analyzing generalized game-theoretic models of Schelling segregation, where the agents can also have individual location preferences. For our models we investigate the convergence behavior and the efficiency of their equilibria. In particular, we prove guaranteed convergence to an equilibrium in the version which is closest to Schelling’s original model. Moreover, we provide tight bounds on the Price of Anarchy.}, author = {Chauhan, Ankit and Lenzner, Pascal and Molitor, Louise}, booktitle = {Symposium on Algorithmic Game Theory (SAGT)}, keywords = {ankitchauhan louisemolitor pascallenzner sagt year2018}, title = {Schelling Segregation with Strategic Agents}, year = 2018 }

2017 [ nach oben ]

Chauhan, Ankit; Lenzner, Pascal; Melnichenko, Anna; Molitor, Louise Selfish Network Creation with Non-Uniform Edge CostSymposium on Algorithmic Game Theory (SAGT) 2017: 160–172
[ Abstract ] [ BibTeX ] [ DOI ] [ Download ]
 
Network creation games investigate complex networks from a game-theoretic point of view. Based on the original model by Fabrikant et al. [PODC’03] many variants have been introduced. However, almost all versions have the drawback that edges are treated uniformly, i.e. every edge has the same cost and that this common parameter heavily influences the outcomes and the analysis of these games. We propose and analyze simple and natural parameter-free network creation games with non-uniform edge cost. Our models are inspired by social networks where the cost of forming a link is proportional to the popularity of the targeted node. Besides results on the complexity of computing a best response and on various properties of the sequential versions, we show that the most general version of our model has con- stant Price of Anarchy. To the best of our knowledge, this is the first proof of a constant Price of Anarchy for any network creation game.
@inproceedings{chauhan2017selfish, abstract = {Network creation games investigate complex networks from a game-theoretic point of view. Based on the original model by Fabrikant et al. [PODC’03] many variants have been introduced. However, almost all versions have the drawback that edges are treated uniformly, i.e. every edge has the same cost and that this common parameter heavily influences the outcomes and the analysis of these games. We propose and analyze simple and natural parameter-free network creation games with non-uniform edge cost. Our models are inspired by social networks where the cost of forming a link is proportional to the popularity of the targeted node. Besides results on the complexity of computing a best response and on various properties of the sequential versions, we show that the most general version of our model has con- stant Price of Anarchy. To the best of our knowledge, this is the first proof of a constant Price of Anarchy for any network creation game.}, author = {Chauhan, Ankit and Lenzner, Pascal and Melnichenko, Anna and Molitor, Louise}, booktitle = {Symposium on Algorithmic Game Theory (SAGT)}, keywords = {ankitchauhan annamelnichenko louisemolitor pascallenzner sagt year2017}, pages = {160-172}, title = {Selfish Network Creation with Non-Uniform Edge Cost}, year = 2017 }