Richard III is full of little (and not so little) betrayals. This sets the mood for the play: nothing is sacred and no one is safe. Richard betrays his friends and family, and his friends and family betray him. Through it all, there's hardly a moment of surprise or shock, even when Richard orders the executions of his nephews, whom he's supposed to be protecting. Betrayal is an expected part of power politics, and the audience learns to be wary of the motives and intentions of nearly every player. Betrayal is also a contagion that drives everyone to preemptive deceit. Only Richmond, who refuses to betray the state's interests for his own gain, can break the cycle of distrust and exploitation.
Even though Prince Edward is just a little kid, he seems to be one of the only characters in the play who knows that Richard will betray him.
In the realm of power politics, betrayal is to be expected.