Abstract
The problem of constructing the dynamic Shapley values in a two stage game is studied. During the dynamic game, each stage game can be considered as a minimum cost spanning tree game. From the first stage, the players’ strategy profiles construct the graph in stage games, and the minimum cost spanning tree of the graph is defined by Prim (1957). At the second stage, the graph built by the players will be changed in some possible ways, with several specified probabilities. These probabilities are determined by the strategy profiles of players in the first stage. The meaning of the change is to break several edges on the graph. Then the players’ cooperative behavior is defined. Along the cooperative trajectory, characteristic functions are defined for all coalitions. The IDP (Imputation Distribution Procedure) was used to construct dynamic Shapley Values.
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Yin, L. (2022). Dynamic Shapley Value for Two-Stage Cost Sharing Game. In: Smirnov, N., Golovkina, A. (eds) Stability and Control Processes. SCP 2020. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-87966-2_50
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DOI: https://doi.org/10.1007/978-3-030-87966-2_50
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