Bilò, Davide; Lenzner, Pascal On the Tree Conjecture for the Network Creation GameTheory of Computing Systems 2020: 422–443
Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al. (2003) is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of \($\alpha$\) per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all \($\alpha$\) and that for \($\alpha \geq n$\) all equilibrium networks are trees. We introduce a novel technique for analyzing stable networks for high edge-price \($\alpha$\) and employ it to improve on the best known bound for the latter conjecture. In particular we show that for \($\alpha>4n −13$\) all equilibrium networks must be trees, which implies a constant price of anarchy for this range of \($\alpha$\). Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees.
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
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.
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
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.
Echzell, Hagen; Friedrich, Tobias; Lenzner, Pascal; Melnichenko, Anna Flow-Based Network Creation GamesInternational Joint Conference on Artificial Intelligence (IJCAI) 2020: 139–145
Network Creation Games (NCGs) model the creation of decentralized communication networks like the Internet. In such games strategic agents corresponding to network nodes selfishly decide with whom to connect to optimize some objective function. Past research intensively analyzed models where the agents strive for a central position in the network. This models agents optimizing the network for low-latency applications like VoIP. However, with today's abundance of streaming services it is important to ensure that the created network can satisfy the increased bandwidth demand. To the best of our knowledge, this natural problem of the decentralized strategic creation of networks with sufficient bandwidth has not yet been studied. We introduce Flow-Based NCGs where the selfish agents focus on bandwidth instead of latency. In essence, budget-constrained agents create network links to maximize their minimum or average network flow value to all other network nodes. Equivalently, this can also be understood as agents who create links to increase their connectivity and thus also the robustness of the network. For this novel type of NCG we prove that pure Nash equilibria exist, we give a simple algorithm for computing optimal networks, we show that the Price of Stability is~1 and we prove an (almost) tight bound of 2 on the Price of Anarchy. Last but not least, we show that our models do not admit a potential function.
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
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.