Towards Generic Low Payment Mechanisms for Task Allocation

We study the problem of procuring a cheap path in a graph in which the edges are owned by selfinterested agents. We focus on basic properties of a class of generalized Vickrey-Clarke mechanisms for the problem. We show that this class of mechanisms satisfies a monotonicity property that can be used to achieve expected payments which, under certain independence assumption, are significantly better than the worst case bounds known for the problem. Next, we investigate whether these payments can be improved when there is competition among paths. Surprisingly, we give evidence to the fact that in many cases of interest such competition hardly helps incentive compatible mechanisms. In particular, we show this for the celebrated Vickrey-Clarke mechanism. We then propose a general method that combines the advantages of incentive compatible and non-incentive compatible mechanisms. Under some natural assumptions on the agents we show that the expected payment of our mechanisms is very small. Finally, we show that a wide range of task allocation problems can be reduced to the problem we study. JEL classifications: C60, C72, D44