Group for Research in Decision Analysis

G-2016-87

Node-consistent Shapley value for games played over event trees with random terminal time

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We consider a class of dynamic games played over an event tree, with random terminal. We assume that the players wish to jointly optimize their payoffs throughout the whole planning horizon and adopt the Shapley value to share the joint cooperative outcome. We devise a node-consistent decomposition of the Shapley value, which means that in any node of the event tree, the players prefer to stick to cooperation and to continue using implementing the Shapley value rather than switching to non cooperation. For each node and each player, we provide two payment values, one that applies if the game terminates at that node and the other if the game continues. We illustrate our results with an example of pollution control.

, 17 pages