We confront the philosophical literature on fair division problems with axiomatic and game-theoretic work in economics. Firstly, we show that the proportionality method advocated in Curtis (in Analysis 74:417–57, 2014) is not implied by a general principle of fairness, and that the proportional rule cannot be explicated axiomatically from that very principle. Secondly, we suggest that Broome’s (in Proc Aristot Soc 91:87–101, 1990) notion of claims is too restrictive and that game-theoretic approaches can rectify this shortcoming. More generally, we argue that axiomatic and game-theoretic work in economics is an indispensable ingredient of any theorizing about fair division problems and allocative justice.