Peer-to-peer grids aim to build computational grids encompassing thousands of sites. To achieve this scale, such systems cannot rely on trust or off-line negotiations among participants. Moreover, without incentives for donation, there is a danger that free riding will prevail, leading the grid to collapse. Reciprocation-based incentive mechanisms that use no information provided by untrustworthy peers have been proposed to deal with this problem, and marginalize free riders. However, they have only been studied for the case in which a single service is shared. In this paper we study reciprocation-based incentive mechanism for peer-to-peer grids in which multiple services, such as processing power and data transfers, are shared explicitly. We have modeled such a system and established how peers should assess whether it is profitable to exchange services with another peer (under the assumption that the other peer is not a free rider), an issue that is not present in the single service...