Sharing sequential values in a network

Herein, we provide the first axiomatic study on path selection and value-sharing in networks. We consider four sets of axioms from different perspectives, including those related to (1) the sequential consistency of value-sharing; (2) the monotonicity of value-sharing with respect to technology improvements; (3) the independence of value-sharing with respect to certain network transformations; and (4) the robust implementation of the efficient path selection when the planner has no information about network configuration. Surprisingly, these four disparate sets of axioms characterize similar classes of solutions, namely selecting an efficient path(s) and assigning to each agent a share of total values that is independent of individual values. Furthermore, we characterize more general solutions that depend on individual values.