A linear constraint formulation for spatial and temporal cost imputations in accord with Shapley values

In a previous paper the authors presented a linear programming model of a three-riparian, two-time-period, joint river-basin development scheme by using cooperative game theory. The objective of the model was to develop ‘fair’ and equitable divisions of the benefits and costs of cooperation. In this paper the analysis is extended by including linear constraints which satisfy the well-known Shapley-value imputation scheme.