We consider multiple-type housing markets. To capture the dynamic aspect of trade in such markets, we study a dynamic recontracting process similar to the one introduced by Serrano and Volij (2008). First, we analyze the set of recurrent classes of this process as a (non-empty) solution concept. We show that each core allocation always constitutes a singleton recurrent class and provide examples of non-singleton recurrent classes consisting of blocking-cycles of individually rational allocations. For multiple-type housing markets stochastic stability never serves as a selection device among recurrent classes.
Next, we propose a method to compute the limit invariant distribution of the dynamic recontracting process. Furthermore, we discuss how the limit invariant distribution is influenced by the relative coalitional stability and accessibility of the different stochastically stable allocations. We illustrate our findings with several examples. In particular, we demonstrate that some core allocations are less likely to be final allocations of the dynamic process than cycles composed of non-core allocations.