Document Open Access Logo

Fair Tree Connection Games with Topology-Dependent Edge Cost

Authors Davide Bilò , Tobias Friedrich , Pascal Lenzner , Anna Melnichenko , Louise Molitor



PDF
Thumbnail PDF

File

LIPIcs.FSTTCS.2020.15.pdf
  • Filesize: 0.68 MB
  • 15 pages

Document Identifiers

Author Details

Davide Bilò
  • Department of Humanities and Social Sciences, University of Sassari, Via Roma 151, 07100 Sassari (SS), Italy
Tobias Friedrich
  • Hasso Plattner Institute, University of Potsdam, Prof.-Dr.-Helmert-Straße 2-3, 14482 Potsdam, Germany
Pascal Lenzner
  • Hasso Plattner Institute, University of Potsdam, Prof.-Dr.-Helmert-Straße 2-3, 14482 Potsdam, Germany
Anna Melnichenko
  • Hasso Plattner Institute, University of Potsdam, Prof.-Dr.-Helmert-Straße 2-3, 14482 Potsdam, Germany
Louise Molitor
  • Hasso Plattner Institute, University of Potsdam, Prof.-Dr.-Helmert-Straße 2-3, 14482 Potsdam, Germany

Acknowledgements

We thank Warut Suksompong for many interesting discussions. Moreover, we are grateful to our anonymous reviewers for their valuable suggestions. This work has been partly supported by COST Action CA16228 European Network for Game Theory (GAMENET).

Cite AsGet BibTex

Davide Bilò, Tobias Friedrich, Pascal Lenzner, Anna Melnichenko, and Louise Molitor. Fair Tree Connection Games with Topology-Dependent Edge Cost. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 15:1-15:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.FSTTCS.2020.15

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • Theory of computation → Quality of equilibria
  • Theory of computation → Convergence and learning in games
  • Theory of computation → Network formation
Keywords
  • Network Design Games
  • Spanning Tree Games
  • Fair Cost Sharing
  • Price of Anarchy
  • Nash Equilibrium
  • Algorithmic Game Theory
  • Combinatorics

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Susanne Albers and Pascal Lenzner. On Approximate Nash Equilibria in Network Design. Internet Mathematics, 9(4):384-405, 2013. Google Scholar
  2. Carme Àlvarez and Arnau Messegué. On the Price of Anarchy for High-Price Links. In WINE'19, pages 316-329. Springer, 2019. Google Scholar
  3. Nir Andelman, Michal Feldman, and Yishay Mansour. Strong price of anarchy. Games and Economic Behavior, 65(2):289-317, 2009. Google Scholar
  4. Elliot Anshelevich, Anirban Dasgupta, Jon Kleinberg, Eva Tardos, Tom Wexler, and Tim Roughgarden. The Price of Stability for Network Design with Fair Cost Allocation. SIAM Journal on Computing, 38(4):1602-1623, 2008. Google Scholar
  5. Elliot Anshelevich, Anirban Dasgupta, Éva Tardos, and Tom Wexler. Near-Optimal Network Design with Selfish Agents. Theory of Computing, 4(1):77-109, 2008. Google Scholar
  6. Venkatesh Bala and Sanjeev Goyal. A Noncooperative Model of Network Formation. Econometrica, 68(5):1181-1229, 2000. Google Scholar
  7. Davide Bilò and Pascal Lenzner. On the Tree Conjecture for the Network Creation Game. Theory of Computing Systems, 64(3):422-443, 2020. Google Scholar
  8. Vittorio Bilò, Michele Flammini, and Luca Moscardelli. The Price of Stability for Undirected Broadcast Network Design with Fair Cost Allocation is Constant. Games and Economic Behavior, 2014. Google Scholar
  9. Davide Bilò, Tobias Friedrich, Pascal Lenzner, Anna Melnichenko, and Louise Molitor. Fair tree connection games with topology-dependent edge cost, 2020. URL: http://arxiv.org/abs/2009.10988.
  10. Charles G. Bird. On Cost Allocation for a Spanning Tree: A Game Theoretic Approach. Networks, 6(4):335-350, 1976. Google Scholar
  11. Ankit Chauhan, Pascal Lenzner, Anna Melnichenko, and Louise Molitor. Selfish Network Creation with Non-uniform Edge Cost. In SAGT'17, pages 160-172. Springer, 2017. Google Scholar
  12. Chandra Chekuri, Julia Chuzhoy, Liane Lewin-Eytan, Joseph Naor, and Ariel Orda. Non-cooperative Multicast and Facility Location Games. IEEE Journal on Selected Areas in Communications, 25(6):1193-1206, 2007. Google Scholar
  13. Armin Claus and Daniel J. Kleitman. Cost Allocation for a Spanning Tree. Networks, 3(4):289-304, 1973. Google Scholar
  14. Erik D. Demaine, Mohammad Taghi Hajiaghayi, Hamid Mahini, and Morteza Zadimoghaddam. The Price of Anarchy in Network Creation Games. ACM Transactions on Algorithms, 8(2):13, 2012. Google Scholar
  15. Shayan Ehsani, Saber Shokat Fadaee, MohammadAmin Fazli, Abbas Mehrabian, Sina Sadeghian Sadeghabad, Mohammad Ali Safari, and Morteza Saghafian. A Bounded Budget Network Creation Game. ACM Transactions on Algorithms, 11(4):1-25, 2015. Google Scholar
  16. Stephan Eidenbenz, Sritesh Kumar, and Sibylle Zust. Equilibria in Topology Control Games for Ad hoc Networks. Mobile Networks and Applications, 11(2):143-159, 2006. Google Scholar
  17. Bruno Escoffier, Laurent Gourvès, Jérôme Monnot, and Stefano Moretti. Cost Allocation Protocols for Network Formation on Connection Situations. In ICST'12, pages 228-234, 2012. Google Scholar
  18. Alex Fabrikant, Ankur Luthra, Elitza Maneva, Christos H. Papadimitriou, and Scott Shenker. On a network creation game. In PODC'03, pages 347-351. ACM, 2003. Google Scholar
  19. Michal Feldman, Kevin Lai, and Li Zhang. The Proportional-share Allocation Market for Computational Resources. IEEE Transactions on Parallel and Distributed Systems, 20(8):1075-1088, 2008. Google Scholar
  20. Amos Fiat, Haim Kaplan, Meital Levy, Svetlana Olonetsky, and Ronen Shabo. On the Price of Stability for Designing Undirected Networks with Fair Cost Allocations. In ICALP'06, pages 608-618. Springer, 2006. Google Scholar
  21. Laurent Gourvès and Jérôme Monnot. Three Selfish Spanning Tree Games. In WINE'08, pages 465-476. Springer, 2008. Google Scholar
  22. Daniel Granot and Gur Huberman. Minimum Cost Spanning Tree Games. Mathematical programming, 21(1):1-18, 1981. Google Scholar
  23. Daniel Granot and Gur Huberman. On the Core and Nucleolus of Minimum Cost Spanning Tree Games. Mathematical programming, 29(3):323-347, 1984. Google Scholar
  24. Martin Hoefer. Non-Cooperative Tree Creation. Algorithmica, 53(1):104-131, 2009. Google Scholar
  25. Martin Hoefer and Piotr Krysta. Geometric Network Design with Selfish Agents. In COCOON'05, pages 167-178, 2005. Google Scholar
  26. Matthew O. Jackson and Asher Wolinsky. A Strategic Model of Social and Economic Networks. Journal of Economic Theory, 71(1):44-74, 1996. Google Scholar
  27. Elias Koutsoupias and Christos Papadimitriou. Worst-case equilibria. In STACS'99, pages 404-413. Springer-Verlag, 1999. Google Scholar
  28. Thomas L. Magnanti and Richard T. Wong. Network Design and Transportation Planning: Models and Algorithms. Transportation Science, 18(1):1-55, 1984. Google Scholar
  29. Akaki Mamageishvili, Matúš Mihalák, and Dominik Müller. Tree Nash Equilibria in the Network Creation Game. In WAW'13, pages 118-129. Springer, 2013. Google Scholar
  30. Matúš Mihalák and Jan Christoph Schlegel. The Price of Anarchy in Network Creation Games is (Mostly) Constant. In SAGT'10, pages 276-287. Springer, 2010. Google Scholar
  31. Kimaya Mittal, Elizabeth M. Belding, and Subhash Suri. A Game-theoretic Analysis of Wireless Access Point Selection by Mobile Users. Computer Communications, 31(10):2049-2062, 2008. Google Scholar
  32. Dov Monderer and Lloyd S. Shapley. Potential Games. Games and Economic Behavior, 14(1):124-143, 1996. Google Scholar
  33. Hervé Moulin and Scott Shenker. Strategyproof Sharing of Submodular Costs: Budget Balance versus Efficiency. Economic Theory, 18(3):511-533, 2001. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail