  Introducing the simplest of all No-Signalling Games: the RGB Game where two
verifiers interrogate two provers, Alice and Bob, far enough from each other
that communication between them is too slow to be possible. Each prover may be
independently queried one of three possible colours: Red, Green or Blue. Let
$a$ be the colour announced to Alice and $b$ be announced to Bob. To win the
game they must reply colours $x$ (resp. $y$) such that $a \neq x \neq y \neq
b$. This work focuses on this new game mainly as a pedagogical tool for its
simplicity but also because it triggered us to introduce a new set of
definitions for reductions among multi-party probability distributions and
related {locality classes}. We show that a particular winning strategy for the
RGB Game is equivalent to the PR-Box of Popescu-Rohrlich and thus
No-Signalling. Moreover, we use this example to define No-Signalling in a new
useful way, as the intersection of two natural classes of multi-party
probability distributions called one-way signalling. We exhibit a quantum
strategy able to beat the classical local maximum winning probability of 8/9
shifting it up to 11/12. Optimality of this quantum strategy is demonstrated
using the standard tool of semidefinite programming.
