A Resolution Under Interval Uncertainty

Traditional transferable utility (TU) games assume precise real-valued utilities for coalition outcomes, but real-world situations often involve uncertainty or imprecision. Interval TU games extend the classical framework by representing utilities and payoffs as closed intervals, leveraging interval arithmetic to address inherent ambiguities in data. This paper reviews the theoretical foundations of interval TU games and explores allocating solutions under uncertainty. Central to this study is the adaptation of consistency, a fundamental property in game-theoretical resolutions, to the interval framework. Drawing on concepts such as the pseudo equal allocations of non-separable costs and the pseudo weighted allocations of non-separable costs, we characterize these allocation resolutions through a specific reduction and related consistency. By bridging classical TU games with interval generalizations, this study offers a robust foundation for analyzing allocations under uncertainty and outlines avenues for future research in theoretical and applied game theory.