Almost budget-balanced mechanisms for allocation of divisible resources

Mechanisms for allocation of one or many goods to a number of agents are proposed in this paper. The goal is to propose mechanisms in a general setting where the goods might be divisible or indivisible. A mechanism in the Groves class that is dominant strategy incentive compatible and almost budget balanced is obtained. In the case of one or more indivisible goods, the proposed mechanisms fall back to the mechanisms proposed independently by Moulin and by Guo & Conitzer. The proposed mechanisms are characterised by a linear redistribution or rebate function included in the payments. The proposed worst case optimal mechanism minimises the worst case ratio of budget surplus to efficient surplus. An optimal-in-expectation mechanism that minimizes the ratio of expected budget surplus to expected efficient surplus is also proposed and compared with the worst case optimal mechanism. Numerical solutions for the coefficients of linear rebate function, worst case efficiency loss, and expected efficiency loss are obtained. An example motivating the extension to the divisible case is resource allocation in the uplink of a wireless communication system. This is briefly discussed.