Central matching systems for the allocation of cadaveric kidneys can improve graft survival by improving the matching achieved between donor and recipient. Allocation algorithms, which are used by such systems, implicitly assume that the goal of the system is to maximize the health benefits received by a population in need of transplant procedures. However, participants in the provision of health care delivery may have other goals in mind e.g., the need to care first for their own patients. In this paper, we study how a central matching and exchange system is affected by the explicit incorporation, into the process of organ allocation, of a transplant centre's preference to care for its own recipients. In particular, we address the following issues (i) Compared with a system where no exchange takes place, are there centres that are more likely to benefit from participation in an exchange system based only on allocation of organs according to medical criteria? and (ii) What is the overall impact, as well as the impact on each centre, of incorporating different incentive mechanisms into the allocation algorithm? We have modified a computed simulation model, previously developed by us, to prospectively study the above issues. Five different matching algorithms were defined and compared, ranging from a decentralized system (i.e. no sharing of organs) to a centralized system (i.e. the allocation is determined by the central system regardless where the kidney was procured). The remaining algorithms incorporated different incentive mechanisms in order to encourage centres to participate and contribute organs. The simulation was set to run for a period of six years. We found that even though all centres benefitted from participation (i.e. all attained higher human leukocyte antigen (HLA) tissue match scores), smaller centres benefitted more than did large centres. When we examined the impact of offering explicit incentives to procure more organs, we found a slight increase in the total number of kidneys procured, a difference which was not found to be statistically significant nor sensitive to changes in the magnitude of incentives. The introduction of certain incentives into the system seemed, however, to prevent a potential decline in the number of organs procured (i.e. by avoiding a ‘free rider’ phenomenon). Furthermore, the discrepancy between HLA matching achieved by centres of different sizes was minimized (i.e. equity was increased).