Advertisement

Dynamic Games and Applications

, Volume 6, Issue 4, pp 520–537 | Cite as

The Subgame-Consistent Shapley Value for Dynamic Network Games with Shock

  • Leon Petrosyan
  • Artem Sedakov
Article

Abstract

In the paper, cooperative repeated network games containing network formation stages are studied. After the first network formation stage, a particular player with a given probability may stop influencing other players by removing all her links and receiving zero payoffs. This effect is called “shock.” The effect of shock may appear only once, and the stage number, at which shock appears, is chosen at random. In the cooperative scenario of the game, subgame consistency of the Shapley value, based on a characteristic function, which is constructed in a special way, is investigated. To prevent players from breaking the cooperative agreement, a mechanism of stage payments—so-called imputation distribution procedure—is designed.

Keywords

Discrete-time games  Network formation Cooperation Imputation Subgame consistency 

Mathematics Subject Classification

90B15 91A12 91A20 

Notes

Acknowledgments

We thank three anonymous referees for their comments that have helped in the improvement of the paper. We also thank the audience of the 20th Conference of the International Federation of Operational Research Societies for helpful discussion and suggestions.

References

  1. 1.
    Bala V, Goyal S (2000) A non-cooperative model of network formation. Econometrica 68(5):1181–1231MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Corbae D, Duffy J (2008) Experiments with network formation. Games Econ Behav 64:81–120CrossRefzbMATHGoogle Scholar
  3. 3.
    Dutta B, Van den Nouweland A, Tijs S (1998) Link formation in cooperative situations. Int J Game Theory 27:245–256MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Feri F (2007) Stochastic stability in networks with decay. J Econ Theory 135:442–457MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Galeotti A, Goyal S, Kamphorst J (2006) Network formation with heterogeneous players. Games Econ Behav 54:353–372MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Goyal S, Vega-Redondo F (2005) Network formation and social coordination. Games Econ Behav 50:178–207MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Haller H (2012) Network extension. Math Soc Sci 64:166–172MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Jackson M (2008) Social and economic networks. Princeton University Press, PrincetonzbMATHGoogle Scholar
  9. 9.
    Jackson M, Watts A (2002) On the formation of interaction networks in social coordination games. Games Econ Behav 41(2):265–291MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kuhn HW (1953) Extensive games and the problem of information. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 193–216Google Scholar
  11. 11.
    Petrosjan LA (2006) Cooperative stochastic games. In: Haurie A, Muto S, Petrosjan LA, Raghavan TES (eds) Advances in dynamic games applications to economics, management science, engineering, and environmental management series: annals of the international society of dynamic games. Basel, Birkhäuser, pp 52–59Google Scholar
  12. 12.
    Petrosyan LA (1977) Stability of solutions in differential games with many participants. Vestnik Leningradskogo Universiteta. Ser 1. Mat Mekhanika Astron 19:46–52Google Scholar
  13. 13.
    Petrosyan LA, Sedakov AA, Bochkarev AO (2013) Two-stage network games. Mat Teoriya Igr I Ee Prilozheniya 5(4):84–104Google Scholar
  14. 14.
    Petrosyan LA, Danilov NN (1979) Stability of solutions in non-zero sum differential games with transferable payoffs. Vestnik Leningradskogo Universiteta. Ser 1. Mat Mekhanika Astron 1:52–59MathSciNetGoogle Scholar
  15. 15.
    Shapley LS (1953) A value for \(N\)-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307–317Google Scholar
  16. 16.
    Vega-Redondo F (2007) Complex social networks. Cambridge University Press, New YorkCrossRefzbMATHGoogle Scholar
  17. 17.
    Watts A (2001) A dynamic model of network formation. Games Econ Behav 34:331–341MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Xie F, Cui W, Lin J (2013) Prisoners dilemma game on adaptive networks under limited foresight. Complexity 18:38–47CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Faculty of Applied Mathematics and Control ProcessesSaint Petersburg State UniversitySaint PetersburgRussia

Personalised recommendations