Imagine Marriott has two brands: Fairfield Inn and Ritz-Carlton. They each have a rewards program which grants one free night for every night stayed.
Now suppose, in a fit of idiocy, the rewards programs are made cross-compatible. So a Ritz-Carlton reward night can be spent at Fairfield Inn and vice versa. Where do you think the rewards will be earned? Where do you think they'll be spent? The "bad" (Fairfield Inn rewards) drove out the "good" (Ritz-Carlton rewards).
I accentuated the number of brands, magnitude of their value difference and rewards program juiciness. This was to bring into relief the resulting effect. In reality, these terms--and the effect--are smaller. Still, Gresham's law applies if one treats rewards nights earned at different hotels as different currencies. They've simply, now, been brought into a currency union.