NotePriority matchings revisited

We consider a pairwise kidney exchange model. Roth et al. (2005) define priority matchings of the model and introduce a mechanism to derive them. In this paper, we re-examine the priority matching. First, we consider a general priority ordering where multiple patients may hold equal priority. We provide a characterization of the priority matchings by using the concept of alternating paths. Using the characterization, we examine the effect of a small change in the priority order on a set of priority matchings. Moreover, we provide an efficient method to find a priority matching.