Skip to main content
SpringerLink
Log in

The Vertex Cover Game

  • Conference paper
  • First Online:
Frontiers of Dynamic Games

Part of the book series: Trends in Mathematics ((TM))

  • 357 Accesses

Abstract

The paper describes the vertex cover game (Gusev, Omega 97:102102, 2020) and shows its properties. The peculiarity of such a game is that it takes into account all the covers of the graph. Since the number of coverings is large, methods of decomposition and its analysis are developed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alrasheed, H.: δ-Hyperbolicity and the core-periphery structure in graphs. In: Machine Learning Techniques for Online Social Networks (pp. 23–43). Springer, Cham (2018)

    Google Scholar 

  2. Alvarez-Mozos, M., Alonso-Meijide, J.M., Fiestras-Janeiro, M.G.: On the externality-free Shapley-Shubik index. Games Econ. Behav. 105, 148–154 (2017)

    Article  MathSciNet  Google Scholar 

  3. Alonso-Meijide, J.M., Freixas, J., Molinero, X.: Computation of several power indices by generating functions. Appl. Math. Comput. 219(8), 3395–3402 (2012)

    MathSciNet  MATH  Google Scholar 

  4. An, Q., Wen, Y., Ding, T., Li, Y.: Resource sharing and payoff allocation in a three-stage system: Integrating network DEA with the Shapley value method. Omega 85, 16–25 (2019)

    Article  Google Scholar 

  5. Bhadury, J., Mighty, E.J., Damar, H.: Maximizing workforce diversity in project teams: A network flow approach. Omega 28(2), 143–153 (2000)

    Article  Google Scholar 

  6. Brams, S.J., Affuso, P.J.: Power and size: A new paradox. Theory Decis. 7(1–2), 29–56 (1976)

    Article  MathSciNet  Google Scholar 

  7. Chen, N.: On the approximability of influence in social networks. SIAM J. Discrete Math. 23(3), 1400–1415 (2009)

    Article  MathSciNet  Google Scholar 

  8. Dong, Y., Liu, Y., Liang, H., Chiclana, F., Herrera-Viedma, E.: Strategic weight manipulation in multiple attribute decision making. Omega 75, 154–164 (2018)

    Article  Google Scholar 

  9. Dubey, P.: On the uniqueness of the Shapley value. Int. J. Game Theory 4(3), 131–139 (1975)

    Article  MathSciNet  Google Scholar 

  10. Dubey, P., Einy, E., Haimanko, O.: Compound voting and the Banzhaf index. Games Econ. Behav. 51(1), 20–30 (2005)

    Article  MathSciNet  Google Scholar 

  11. Filiol, E., Franc, E., Gubbioli, A., Moquet, B., Roblot, G.: Combinatorial optimisation of worm propagation on an unknown network. Int. J. Comput. Sci. 2, 124 (2007)

    Google Scholar 

  12. Gallardo, J.M., Jiménez, N., Jiménez-Losada, A.: A Shapley measure of power in hierarchies. Inf. Sci. 372, 98–110 (2016)

    Article  Google Scholar 

  13. Gusev, V.V.: The vertex cover game: Application to transport networks. Omega 97, 102102 (2020)

    Article  Google Scholar 

  14. Hadas, Y., Gnecco, G., Sanguineti, M.: An approach to transportation network analysis via transferable utility games. Transp. Res. B Methodol. 105, 120–143 (2017)

    Article  Google Scholar 

  15. Harsanyi, J.C.: A simplified bargaining model for the n-person cooperative game. Int. Econ. Rev. 4(2), 194–220 (1963)

    Article  Google Scholar 

  16. Hu, S., Li, R., Zhao, P., Yin, M.: A hybrid metaheuristic algorithm for generalized vertex cover problem. Memetic Comput. 10(2), 165–176 (2018)

    Article  Google Scholar 

  17. Karp, R.M.: Reducibility among combinatorial problems. In: Complexity of Computer Computations (pp. 85–103). Springer, Boston, MA (1972)

    Google Scholar 

  18. Kurz, S.: A note on limit results for the Penrose-Banzhaf index (2018), Available at SSRN 3229289

    Google Scholar 

  19. Lusher, D., Koskinen, J., Robins, G. (eds.) Exponential Random Graph Models for Social Networks: Theory, Methods, and Applications, p. 337. Cambridge University Press, Cambridge (2013)

    Google Scholar 

  20. Molinero, X., Riquelme, F., Serna, M.: Cooperation through social influence. Eur. J. Oper. Res. 242(3), 960–974 (2015)

    Article  MathSciNet  Google Scholar 

  21. Owen, G.: Game Theory. Academic Press (3rd edn.), San Diego, USA (1995)

    Google Scholar 

  22. Shapley, L.S.: A value for n-person games. Contrib. Theory Games 2(28), 307–317 (1953)

    MathSciNet  MATH  Google Scholar 

  23. Tamura, H., Sugawara, H., Sengoku, M., Shinoda, S.: Multiple cover problem on undirected flow networks. Electron. Commun. Japan (Part III: Fundamental Electronic Science) 84(1), 67–74 (2001)

    Google Scholar 

  24. Wu, Q., Ren, H., Gao, W., Ren, J.: Benefit allocation for distributed energy network participants applying game theory based solutions. Energy 119, 384–391 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

The paper was prepared within the framework of the HSE University Basic Research Program

Author information

Authors and Affiliations

  1. HSE University, St. Petersburg, Russian Federation

    Vasily V. Gusev

Authors
  1. Vasily V. Gusev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vasily V. Gusev .

Editor information

Editors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    Leon A. Petrosyan

  2. Institute of Applied Mathematical Research, Russian Academy of Sciences, Petrozavodsk, Russia

    Vladimir V. Mazalov

  3. Graduate School of Management, St. Petersburg State University, St. Petersburg, Russia

    Nikolay A. Zenkevich

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gusev, V.V. (2021). The Vertex Cover Game. In: Petrosyan, L.A., Mazalov, V.V., Zenkevich, N.A. (eds) Frontiers of Dynamic Games. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-93616-7_7

Download citation

Publish with us

Policies and ethics

Search

Navigation