Consistency and monotonicity in sequencing problems

We explore the implications of consistency in sequencing problems. We first identify all rules satisfying Pareto indifference, individual rationality, and consistency. Next, we ask whether there is a rule satisfying the three axioms together with either one of two additional own-time monotonicity requirements: an agent should lose (or gain) as a result of changes in his service time. As it turns out, the minimal incentive rule is the only rule satisfying Pareto indifference, individual rationality, consistency, and negative owntime monotonicity. On the other hand, the maximal incentive rule is the only rule satisfying Pareto indifference, individual rationality, consistency, and positive own-time monotonicity. We also investigate the implications of other monotonicity axioms in the context of sequencing problems. Journal of Economic Literature Classification Numbers: D63, D71.