AbstractWe consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold $$\Omega $$
Ω
of unit area. It is known that the average cost scales as $$E_{\Omega }(N)\sim {1}/{2\pi }\ln N$$
E
Ω
(
N
)
∼
1
/
2
π
ln
N
with a correction that is at most of order $$\sqrt{\ln N\ln \ln N}$$
ln
N
ln
ln
N
. In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $$\Omega $$
Ω
-dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on $$\Omega $$
Ω
. We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.
Efficiency and strategy-proofness in object assignment problems with multi-demand preferences