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Given two measured spaces $(X,\mu)$ 
and $(Y,\nu)$ 
, and a third space Z,given two functions u(x,z) and v(x,z), we study the problem of finding twomaps $s:X\rightarrow Z$ 
and $t:Y\rightarrow Z$ 
such that the images $s(\mu)$ 
and $t(\nu)$ 
coincide, and the integral $\int_{X}u(x,s(x))d\mu-\int_{Y}v(y,t(y))d\nu$ 
is maximal. We give condition on u and v for whichthere is a unique solution.
