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Two-Level Cooperation in Network Games

  • Leon Petrosyan
  • Artem SedakovEmail author
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 277)

Abstract

The problem of allocating a value in hierarchical cooperative structures is important in the game theoretic literature, and it often arises in practice. In this paper, we consider a two-level structure of players communication and propose a procedure allocating the value in two steps: first the value is allocated at the upper level among groups of players, and then each group allocates the designated value among its members. We demonstrate how to allocate the value in two steps using the Shapley value and show the difference with the classical one-step allocation procedure. We then adopt this approach for games with pairwise interactions and provide relations between several definitions of the characteristic function and the corresponding Shapley values.

Keywords

Network Hierarchy Cooperation Two-level allocation Shapley value 

Notes

Acknowledgements

The authors thank reviewers for valuable comments.

References

  1. 1.
    Avrachenkov, K., Elias, J., Martignon, F., Neglia, G., Petrosyan, L.: Cooperative network design: a nash bargaining solution approach. Comput. Netw. 83(4), 265–279 (2015)CrossRefGoogle Scholar
  2. 2.
    Bramoullé, Y., Kranton, R.: Public goods in networks. J. Econ. Theory 135(1), 478–494 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Corbae, D., Duffy, J.: Experiments with network formation. Games Econ. Behav. 64, 81–120 (2008)CrossRefGoogle Scholar
  4. 4.
    Dyer, M., Mohanaraj, V.: Pairwise-interaction games. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6755, pp. 159–170. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22006-7_14CrossRefGoogle Scholar
  5. 5.
    Goyal, S., Vega-Redondo, F.: Network formation and social coordination. Games Econ. Behav. 50, 178–207 (2005)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Iturralde, M., Wei, A., Ali-Yahiya, T., et al.: Resource allocation for real time services in LTE networks: resource allocation using cooperative game theory and virtual token mechanism. Wirel. Pers. Commun. 72, 1415–1435 (2013)CrossRefGoogle Scholar
  7. 7.
    Jackson, M., Watts, A.: On the formation of interaction networks in social coordination games. Games Econ. Behav. 41(2), 265–291 (2002)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Liao, J., Cui, Z., Wang, J., et al.: A coalitional game approach on improving interactions in multiple overlay environments. Comput. Netw. 87, 1–15 (2015)CrossRefGoogle Scholar
  9. 9.
    Madi, N.K.M., Hanapi, Z.B.M., Othman, M., et al.: Two-level QoS-aware frame-based downlink resources allocation for RT/NRT services fairness in LTE networks. Telecommun. Syst. 66, 357–375 (2017)CrossRefGoogle Scholar
  10. 10.
    Molina, Y.P., Prada, R.B., Saavedra, O.R.: Complex losses allocation to generators and loads based on circuit theory and Aumann-Shapley method. IEEE Trans. Power Syst. 25(4), 1928–1936 (2010)CrossRefGoogle Scholar
  11. 11.
    Molina, Y.P., Saavedra, O.R., Amarís, H.: Transmission network cost allocation based on circuit theory and the Aumann-Shapley method. IEEE Trans. Power Syst. 28(4), 4568–4577 (2013)CrossRefGoogle Scholar
  12. 12.
    Petrosyan, L.A., Bulgakova, M.A., Sedakov, A.A.: Time-consistent solutions for two-stage network games with pairwise interactions. Mob. Netw. Appl. (2018).  https://doi.org/10.1007/s11036-018-1127-7
  13. 13.
    Petrosyan, L.A., Sedakov, A.A.: The subgame-consistent shapley value for dynamic network games with shock. Dyn. Games Appl. 6(4), 520–537 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Petrosyan, L.A., Sedakov, A.A., Bochkarev, A.O.: Two-stage network games. Autom. Remote Control 77(10), 1855–1866 (2016)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)zbMATHGoogle Scholar
  16. 16.
    Xie, F., Cui, W., Lin, J.: Prisoners dilemma game on adaptive networks under limited foresight. Complexity 18, 38–47 (2013)CrossRefGoogle Scholar

Copyright information

© ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2019

Authors and Affiliations

  1. 1.Saint Petersburg State UniversitySaint PetersburgRussia

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