  Non-local games are an important part of quantum information processing.
Recently there has been an increased interest in generalizing non-local games
beyond the basic setup by considering games with multiple parties and/or with
large alphabet inputs and outputs. In this paper we consider another
interesting generalization -- games with non-uniform inputs. Here we derive a
tight upper bound for the classical winning probability for a specific family
of non-local games with non-uniform input distribution, known as
$\mathrm{CHSH}_q(p)$ which was introduced recently in the context of
relativistic bit-commitment protocols by [Chakraborty et. al., PRL 115, 250501,
2015].
