Position values and fixed-fraction rules for rooted tree cost allocation problems

In this paper, we introduce a new class of cost allocation rules for rooted tree cost allocation problems that is based on the position value (Meessen 1988 and Borm et al. 1992). We further extend this by introducing a class of cost allocation rules that, besides these new position rules, also contains the fixed-fraction rules of Gudmundsson et al. (2024) and the permission values of Gilles et al. (1992), also known as upstream equal sharing rules in Ni and Wang (2007) and Dong et al. (2012). This last rule belongs to this class but is neither a position rule nor a fixed-fraction rule. We provide an axiomatic characterization of the new class of rules, and by additional axioms obtain axiomatizations of subclasses of rules. We argue that the axioms are specifically useful to motivate the application of these rules for smart contracts in, for example, blockchains.