“Sharing Sequential Values in a Network”

Ruben Juarez, University of Hawaii

Chiu Yu Ko, National University of Singapore

Jingyi Xue, Singapore Management University 

Consider a process where agents bring individual values which might be different at every possible step. A planner is in charge of choosing steps and distributing the aggregate value of the process among agents. This `two-tiered' approach, where the steps and the distribution must be selected simultaneously, has important applications to several old and new problems. For instance, consider a social planner in charge of developing a connected public facility (such as highways, rail-roads or irrigation canals).  The project might be developed in different steps, each of which might benefit the agents in a society differently. The social planner is in charge of choosing the steps and redistributing the benefits of the project among the agents. We provide the first systematic study of this problem using axioms that are appropriate to a wide range of scenarios.  These range from a complete information case (where the planner knows the problem) to an incomplete information case (where the planner might not know the individual values of the agents). We impose new axioms as well as adapt more traditional axioms from other studies. Surprisingly, after a comprehensive analysis, we discovered a step selection rule and distribution function that satisfy every axiom imposed.