On the expected payment of mechanisms for task allocation

Abstract

We study a generic task allocation problem called shortest paths: Let G be a directed graph in which the edges are owned by self interested agents. Each edge has an associated cost that is privately known to its owner. Let s and t be two distinguished nodes in G. Given a distribution on the edge costs, the goal is to design a mechanism (protocol) which acquires a cheap s-t path.We first prove that the class of generalized VCG mechanisms has certain monotonicity properties. We exploit this observation to obtain, under an independence assumption, expected payments which are significantly better than the worst case bounds of [4, 8]. We then investigate whether these payments can be improved when there is competition among paths. Surprisingly, we give evidence to the fact that in many cases such competition hardly helps incentive compatible mechanisms. In particular, we show this for the celebrated VCG mechanism. We then construct a novel general protocol combining the advantages of incentive compatible and non-incentive compatible mechanisms. Under reasonable assumptions on the agents we show that the overpayment of our mechanism is very small. Finally, we demonstrate that many task allocation problems can be reduced to shortest paths.