Simple Sequencing Problems with Interdependent Costs

In this paper we analyze sequencing situations under incomplete information where agents have interdependent costs. We first argue why Vickrey-Clarke-Groves (or VCG) mechanism fails to implement a simple sequencing problem in dominant strategies. Given this impossibility, we try to implement simple sequencing problems in ex-post equilibrium. We show that a simple sequencing problem is implementable if and only if the mechanism is a `generalized VCG mechanism'. We then show that for implementable n agent simple sequencing problems, with polynomial cost function of order (n-2) or less, one can achieve first best implementability. Moreover, for the class of simple sequencing problems with ``sufficiently well behaved'' cost function, this is the only class of first best implementable simple sequencing problems.