Midpoint-width lexicographic equilibria: Existence results for interval-valued equilibrium problems

This paper presents a new solution concept for interval-valued equilibrium problems using an appropriate interval ordering that considers both the central value and the uncertainty inherent in the data. The aim is to define solutions in a way that represents the imprecision frequently encountered in real-world situations. The proposed solution concept is then explained through a motivating example, demonstrating its advantages in handling interval-valued data. Furthermore, the study shows that the introduced interval-valued equilibrium problem can be reduced to a mixed equilibrium problem, for which existence results are established using a proof technique based on a KKM-type argument. A projection-based algorithm is also presented by adapting classical splitting methods for equilibrium problems to the proposed interval-valued equilibrium model. This work provides a rigorous and verifiable framework for addressing interval-valued equilibrium problems.