Document Open Access Logo

Networks of Complements

Authors Moshe Babaioff, Liad Blumrosen, Noam Nisan

PDF
Thumbnail PDF

File

LIPIcs.ICALP.2016.140.pdf
  • Filesize: 0.64 MB
  • 14 pages

Document Identifiers

Author Details

Moshe Babaioff
Liad Blumrosen
Noam Nisan

Cite As Get BibTex

Moshe Babaioff, Liad Blumrosen, and Noam Nisan. Networks of Complements. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 140:1-140:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ICALP.2016.140

Abstract

We consider a network of sellers, each selling a single product, where the graph structure represents pair-wise complementarities between products. We study how the network structure affects revenue and social welfare of equilibria of the pricing game between the sellers. We prove positive and negative results, both of "Price of Anarchy" and of "Price of Stability" type, for special families of graphs (paths, cycles) as well as more general ones (trees, graphs). We describe best-reply dynamics that converge to non-trivial equilibrium in several families of graphs, and we use these dynamics to prove the existence of approximately-efficient equilibria.

Subject Classification

Keywords
  • Complements
  • Pricing
  • Networks
  • Game Theory
  • Price of Stability

Metrics

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

References

  1. Moshe Babaioff, Robert Kleinberg, and Christos H. Papadimitriou. Congestion games with malicious players. Games and Economic Behavior, 67(1):22-35, 2009. Google Scholar
  2. Moshe Babaioff, Brendan Lucier, and Noam Nisan. Bertrand networks. In ACM Conference on Electronic Commerce (ACM-EC), 2013. Google Scholar
  3. Maria-Florina Balcan and Avrim Blum. Approximation algorithms and online mechanisms for item pricing. In Proceedings of the 7th ACM Conference on Electronic Commerce, EC'06, pages 29-35, 2006. Google Scholar
  4. Joseph Louis François Bertrand. theorie mathematique de la richesse sociale. Journal de Savants, 67:499–508, 1883. Google Scholar
  5. Yang Cai and Constantinos Daskalakis. On minmax theorems for multiplayer games. In Proceedings of the Twenty-second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA'11, pages 217-234, 2011. Google Scholar
  6. Xi Chen, Xiaotie Deng, and Shang-Hua Teng. Settling the complexity of computing two-player nash equilibria. J. ACM, 56(3):14:1-14:57, 2009. Google Scholar
  7. Margarida Corominas-Bosch. Bargaining in a network of buyers and sellers. Journal of Economic Theory, 115(1):35-77, 2004. Google Scholar
  8. Antoine Augustin Cournot. Recherches sur les principes mathematiques de la theori des Richesses. Trans. N.T. Bacon, New York: Macmillan, 1929, 1838. Google Scholar
  9. Argyrios Deligkas, John Fearnley, Rahul Savani, and Paul Spirakis. Computing approximate nash equilibria in polymatrix games. In Web and Internet Economics: 10th International Conference, WINE 2014, pages 58-71, 2014. Google Scholar
  10. C. Ellet. An essay on the laws of trade in reference to the works of internal improvement in the United States. Reprints of economic classics. A.M. Kelley, 1966. Google Scholar
  11. Andrew V. Goldberg, Jason D. Hartline, Anna R. Karlin, Michael Saks, and Andrew Wright. Competitive auctions. Games and Economic Behavior, 55(2):242-269, 2006. Google Scholar
  12. Venkatesan Guruswami, Jason D. Hartline, Anna R. Karlin, David Kempe, Claire Kenyon, and Frank McSherry. On profit-maximizing envy-free pricing. In Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA'05, pages 1164-1173, 2005. Google Scholar
  13. Sham M. Kakade, Michael Kearns, Luis E. Ortiz, Robin Pemantle, and Siddharth Suri. Economic properties of social networks. In Advances in Neural Information Processing Systems 17, pages 633-640. MIT Press, 2005. Google Scholar
  14. Michael Kearns. In Noam Nisan, Tim Roughgarden, Eva Tardos and Vijay Vazirani (Editors), Algorithmic Game Theory. Chapter 7. Graphical Games. Cambridge University Press, 2007. Google Scholar
  15. Michael J. Kearns, Michael L. Littman, and Satinder P. Singh. Graphical models for game theory. In Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence, UAI'01, pages 253-260, 2001. Google Scholar
  16. Jon Kleinberg and Éva Tardos. Balanced outcomes in social exchange networks. In Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, STOC'08, pages 295-304, 2008. Google Scholar
  17. E. Kranton and Deborah F. Minehart. A theory of buyer-seller networks. American Economic Review, 91:485-508, 2001. Google Scholar
  18. Robert Krauthgamer, Aranyak Mehta, and Atri Rudra. Pricing commodities. Theor. Comput. Sci., 412(7):602-613, 2011. Google Scholar
  19. Euiwoong Lee. Hardness of graph pricing through generalized max-dicut. In Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC'15, pages 391-399, 2015. Google Scholar
  20. E.w Lee, D. Buchfuhrer, L. Andrew, A. Tang, and S. Low. Progress on pricing with peering. In Proceedings of the 45th Annual Allerton Conference on Computing, Communications and Control, Allerton’07, pages 286-291, 2007. Google Scholar
  21. Daniel Lehmann, Liadan Ita O'Callaghan, and Yoav Shoham. Truth revelation in approximately efficient combinatorial auctions. In JACM 49(5), pages 577-602, Sept. 2002. Google Scholar
  22. C. St.J. A. Nash-Williams. Edge-disjoint spanning trees of finite graphs. Journal of the London Mathematical Society, s1-36(1):445-450, 1961. 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
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact