The Subgame-Consistent Shapley Value for Dynamic Network Games with Shock
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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.
KeywordsDiscrete-time games Network formation Cooperation Imputation Subgame consistency
Mathematics Subject Classification90B15 91A12 91A20
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.
- 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.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.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.Petrosyan LA, Sedakov AA, Bochkarev AO (2013) Two-stage network games. Mat Teoriya Igr I Ee Prilozheniya 5(4):84–104Google Scholar
- 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