Abstract
In this paper we extend the notion of Shapley value to the stochastic cooperative games. We give the definition of marginal vector to the stochastic cooperative games and we define the Shapley value for this game. Furthermore, we discuss the axioms of the Shapley value and give the proofs of these axioms.
Highlights
The Shapley Value for Stochastic Cooperative GameYing Ma(Corresponding author) Department of Science, Yanshan University 438 west of He Bei Avenue, Qin Huangdao 066004, China
The payoffs of a coalition in cooperative games are assumed to be known with certainty
Stochastic cooperative games Let us first recall some of the definitions concerning stochastic cooperative games as introduced by Suijs et al (1999)
Summary
Ying Ma(Corresponding author) Department of Science, Yanshan University 438 west of He Bei Avenue, Qin Huangdao 066004, China. The research is financed by the foundation for the edbiz of He Bei province of China(2004468)and the foundation for the natural science of He Bei province of China(A2005000301) Abstract In this paper we extend the notion of Shapley value to the stochastic cooperative games. We give the definition of marginal vector to the stochastic cooperative games and we define the Shapley value for this game. We discuss the axioms of the Shapley value and give the proofs of these axioms.
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