Exploring the connections between sensitivity analysis and cooperative game theory can yield valuable insights into the interpretation and application of sensitivity indices. In cooperative game theory, the Shapley value provides a fair distribution of payoffs among players based on their contributions to the overall outcome. Similarly, in sensitivity analysis, indices like the Shapley effect can be interpreted as measures of input importance, reflecting how much each input contributes to the variability of the output.
By delving deeper into these connections, one can enhance the understanding of how to allocate importance among inputs in a more equitable manner, particularly in scenarios where inputs may have synergistic or antagonistic interactions. This perspective can lead to the development of new sensitivity indices that incorporate notions of fairness and cooperation, potentially improving the interpretability of results in complex models.
Moreover, the framework of cooperative game theory can provide a structured approach to address issues of input dependence and interaction effects, allowing for a more nuanced analysis of how inputs work together to influence the output. This can facilitate the identification of key input combinations that drive model behavior, leading to more informed decision-making in model calibration and uncertainty quantification.
Overall, the interplay between sensitivity analysis and cooperative game theory opens avenues for innovative methodologies that enhance the robustness and applicability of sensitivity analysis in various fields, including environmental modeling, finance, and engineering.