Stochastic stability is applied to the problem of exchange.
We analyze th stochastic stability of two dynamic trading processes in a simple housing market. In both models traders meet in pairs at random and exchang their houses when trade is mutually beneficial, but occasionally they make mistakes. The models differ in the probability of mistakes. When all mistakes are equally likely, the set of stochastically stable allocations contains th set of efficient allocations. When mor serious mistakes ar less likely, the stochastically stable states are those allocations, always efficient, with the lowest envy-level.