Axiomatic and strategic justifications of the connected equal splitting rule in the reordering problem

We consider the “reordering problem”, in which agents need to be reordered from an initial queue to be served in a facility which handles only one agent at a time. Agents differ in their unit waiting costs and the amounts of service time needed to process their jobs. We adopt both axiomatic and strategic approaches to study the connected equal splitting rule. This rule selects an efficient reordering of the initial queue and allocates the cost savings obtained after reordering the positions of any two agents equally among themselves and all agents initially positioned between them. We introduce the property of balanced reduction of agents, which requires that the effect of one agent dropping out of the reordering process on the net utility of another agent should be equal for any two agents when no two agents are allowed to exchange their positions in the initial queue without permission from all the agents between them. As we show, the connected equal splitting rule is the only rule that satisfies efficiency, budget balance, Pareto indifference, and balanced reduction of agents. Furthermore, we introduce an extensive-form game with finite rounds exploiting balanced reduction of agents to strategically implement the rule in a subgame-perfect Nash equilibrium.