Cutting a Cake Is Not Always a 'Piece of Cake': A Closer Look at the Foundations of Cake-Cutting Through the Lens of Measure Theory

Since the groundbreaking work of Steinhaus (1948), cake-cutting is a metaphor for the so-called fair division problem for a divisible, heterogeneous good, which addresses the problem to split a contested quantity (a'cake') in a fair way among several parties A, B, C,...; each party may have its own idea about the value of the different parts of the cake. While mainly mathematicians and economists were concerned with the study of cake-cutting early on, "in recent years, cake cutting has emerged as a major research topic in artificial intelligence," as Balkanski et al. (2014, p. 567) note. They substantiate their claim by listing ten papers on cake-cutting five of which appeared in AAAI (e.g., Cohler et al. (2011)), three in IJCAI (e.g., Procaccia (2009)), and the remaining two in AAMAS proceedings (e.g., Aumann et al. (2013)). For more than a decade now, AAAI and IJCAI (the two top AI conferences) and AAMAS (the leading venue for research on multiagent systems) have published numerous research papers on fair division and, in particular, on cake-cutting. Balkanski et al. (2014, p. 567) go on to write, "The growing interest in cake cutting, and fair division more broadly, is partly motivated by potential applications in AI, such as industrial procurement, manufacturing and scheduling, and airport traffic management (Chevaleyre et al., 2006).