From cooperative play to multi-critical decision: The Shapley Index and the Choquet Integral in comparison

This study explores the integration of Shapley’s Index and Choquet’s Integral as a hybrid approach to improve the Analytic Hierarchy Process (AHP). While AHP provides a structured methodology for multi-criteria decision-making, it suffers from limitations related to subjectivity in the determination of weights. The Shapley Index, derived from game theory, introduces a rigorous analysis of the marginal contributions of criteria, while the Choquet Integral considers non-additive interactions between criteria. By combining these methodologies, the proposed model allows for the representation of synergies and trade-offs between criteria, improving the reliability and accuracy of decision-making. Applying the model to a case study, the article compares the results obtained with the two approaches, highlighting the contexts in which each method excels. This analysis provides a basis for future applications in critical areas such as strategic planning, risk management and energy sustainability.