@article{Ma2025, 
author = {Xiaojue Ma and Chang Zhou and Lifeng Li and Jianke Zhang},
title = {Admissible interval-valued monotone comparative statics methods applied in games with strategic complements},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {2},
pages = {3160-3179},
keywords = {admissible orders, monotone comparative statics, interval-valued quasisupermodular function, interval-valued single crossing property, interval games with strategic complements},
url = {https://www.sciopen.com/article/10.3934/math.2025146},
doi = {10.3934/math.2025146},
abstract = {In many theories and applications with uncertainty, using intervals to characterize uncertainty is simple and operable. It is crucial to choose a proper order for an interval method. In general, a total order is superior to a partial order for those applications in which we have to make a final decision. Motivated by this idea, we generalized interval-valued monotone comparative statics (MCS) with a partial order to interval-valued MCS with a total order, to be more precise, with an admissible order. The generalization was not trival. We obtained a necessary and sufficient condition for MCS by a series of new concepts such as an interval-valued quasi-super-modular function and an interval-valued single crossing property with an admissible order. The same condition was only sufficient in the existing literature. Furthermore, we illustrated the efficiency of the interval-valued MCS with the lexicographical orders and XY-order, which are well-known admissible orders. Finally, we applied our results in interval games with strategic complements to get the monotonity of the best response correspondence for player    i.}
}