  To overcome incompatibility issues, kidney patients may swap their donors. In
international kidney exchange programmes (IKEPs), countries merge their
national patient-donor pools. We consider a recently introduced credit system.
In each round, countries are given an initial ``fair'' allocation of the total
number of kidney transplants. This allocation is adjusted by a credit function
yielding a target allocation. The goal is to find a solution that approaches
the target allocation as closely as possible, to ensure long-term stability of
the international pool. As solutions, we use maximum matchings that
lexicographically minimize the country deviations from the target allocation.
We perform, for the first time, a computational study for a {\it large} number
of countries. For the initial allocations we use two easy-to-compute solution
concepts, the benefit value and the contribution value, and four classical but
hard-to-compute concepts, the Shapley value, nucleolus, Banzhaf value and tau
value. By using state-of-the-art software we show that the latter four concepts
are now within reach for IKEPs of up to fifteen countries. Our experiments show
that using lexicographically minimal maximum matchings instead of ones that
only minimize the largest deviation from the target allocation (as previously
done) may make an IKEP up to 54% more balanced.
