Add to ORKGWe study decentralized trade processes in general exchange economies and house allocation problems with and without money. The processes are affected by persistent random shocks stemming from agents' maximization of random utility. By imposing structure on the utility noise term --logit distribution--, one is able to calculate exactly the stationary distribution of the perturbed Markov process for any level of noise. We show that the stationary distribution places the largest probability on the maximizers of weighted sums of the agents' (intrinsic) utilities, and this probability tends to 1 as noise vanishes.decentralized trade, exchange economies, housing markets, long-run stochastic stability, logit model, social welfare functions.