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Cooperative Stochastic Games

  • Leon A. Petrosjan
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 8)

Abstract

A cooperative stochastic n-person game on a finite graph tree is considered. The subtree of cooperative trajectories maximizing the sum of expected players’ payoffs is defined, and the solution of the game along the paths of this tree is investigated. The new notion of cooperative payoff distribution procedure (CPDP) is defined, and the time-consistent Shapley value is constructed.

Key words

Stochastic game stage game behavior strategy Shapley value time-consistency 

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References

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    Bellman R., Dynamic Programming, Princeton University Press, Princeton, NJ, 1957.Google Scholar
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    Petrosjan L.A., The Shapley value for differential games, Annals of the International Society of Dynamic Games, 3, 409–419, 1995.MathSciNetGoogle Scholar
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    Shapley L.S., A value for n-person games, Annals of Mathematics Studies, 28, 307–317, 1953.MathSciNetGoogle Scholar
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    Shapley L.S., Stochastic games, Proceedings of the National Academy of U.S.A., 39, 1095–1100, 1953.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • Leon A. Petrosjan
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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