  In a housing market of Shapley and Scarf, each agent is endowed with one
indivisible object and has preferences over all objects. An allocation of the
objects is in the (strong) core if there exists no (weakly) blocking coalition.
In this paper we show that in the case of strict preferences the unique strong
core allocation (or competitive allocation) respects improvement: if an agent's
object becomes more attractive for some other agents, then the agent's
allotment in the unique strong core allocation weakly improves. We obtain a
general result in case of ties in the preferences and provide new integer
programming formulations for computing (strong) core and competitive
allocations. Finally, we conduct computer simulations to compare the
game-theoretical solutions with maximum size and maximum weight exchanges for
markets that resemble the pools of kidney exchange programmes.
