This paper studies that how an uncertain event can be outlined as an approximate common knowledge. By replacing “know” with “know with certainty α” in standard definitions of common knowledge, approximate common knowledge with some certainty, defined iteratively and mutually, iteratively known and mutually known with some certainty, are explored. Examples are constructed to show that an event which is not common knowledge can be analyzed as an approximate common knowledge with some certainty. An application in the principal-agent model is investigated to show that approximate common knowledge based on uncertain measure can be applied to improve the behavior of an economic model.
Wang, Cheng; Tang, Wansheng; and Zhao, Ruiqing, "Approximate Common Knowledge Based on Uncertain Measure" (2009). ICEB 2009 Proceedings (Macau, SAR China). 140.