  The Monge-Amp\`{e}re equation arises in the theory of optimal transport. When
more complicated cost functions are involved in the optimal transportation
problem, which are motivated e.g. from economics, the corresponding equation
for the optimal transportation map becomes a Monge-Amp\`{e}re type equation.
Such Monge-Amp\`{e}re type equations are a topic of current research from the
viewpoint of mathematical analysis. From the numerical point of view there is a
lot of current research for the Monge-Amp\`{e}re equation itself and rarely for
the more general Monge-Amp\`{e}re type equation. Introducing the notion of
discrete $Q$-convexity as well as specifically designed barrier functions this
purely theoretical paper extends the very recently studied two-scale method
approximation of the Monge-Amp\`{e}re itself \cite{NochettoNtogkasZhang2018} to
the more general Monge-Amp\`{e}re type equation as it arises e.g. in
\cite{PhillippisFigalli2013} in the context of Sobolev regularity.
