The European economic integration leads to increasing mobility of factors, thereby threatening the stability of social transfer programs. This article investigates the possibility to achieve by means of voluntary matching grants both the optimal allocation of factors and the optimal level of redistribution in the presence of factor mobility. We use a fiscal competition model a la Wildasin (1991) in which states differ in their technologies and preferences for redistribution. We first investigate a simple process in which the federal authority progressively raises the matching grants to the district choosing the lowest transfer and all districts respond optimally to the resulting change in transfers all around. This process is shown to increase efficiency of both production and redistribution. However, it does not guarantee that all districts gain, nor that an efficient level of redistribution is attained. Assuming complete information among districts, we derive the willingness of each district to match the contribution of other districts and we show that the aggregate willingness to pay for matching rates converges to zero when both the efficient level of redistribution and the efficient allocation of factors are achieved. We then describe an adjustment process for the matching rates that will lead districts to the efficient outcome and guarantee that everyone will gain.