Super-Persistent Predator/Playing With

Basic Trope: A predator will continue to chase very elusive prey in spite of other food that's much easier to catch.
 * Straight: Fluffy the Terrible proceeds to chase Alice and Bob across an entire island.
 * Exaggerated: The duo jumps into a rocket ship and fly to the moon. Fluffy gets into another rocket and follows them.
 * Downplayed: Fluffy merely chases them around a house for a bit.
 * Justified: Alice and Bob are much bigger than other prey and would fill Fluffy's belly much more quickly than anything else.
 * Fluffy's Bizarre Alien Biology makes extremely efficient use of his food, so he can afford to invest a lot of energy in wearing out his prey.
 * Monster Is a Mommy, and Bob has kidnapped Fluffy's babies For the Evulz, prompting it to enter Mama Bear mode.
 * Alice and Bob are the only prey available on the island, and Fluffy has to eat too, y'know.
 * Inverted: Alice and Bob keep hunting down Fluffy, despite it running away and not proving to be a major threat.
 * Subverted: Fluffy chases both of them for quite a while, but eventually gives up.
 * Double Subverted: ...then Bob taunts Fluffy, slapping his butt at him and prompting him into starting the chase again.
 * Parodied: Fluffy is watching TV one day, spots Alice and Bob on the 11 o'clock news, and decides to stalk them.
 * Fluffy uses Offscreen Teleportation to appear already at whatever location they've just run to, Droopy-style.
 * Zig-Zagged: Fluffy chases the duo, then stops when it spots much slower prey. It catches the prey and eats it, then continues to chase them after done with its meal. It then gets tired and stops to take a nap... then wakes up half an hour later, dedicated to finding them again.
 * Averted: Fluffy leaves Alice and Bob alone as soon as they leave its territory.
 * Enforced: "We need to give the audience a sense of urgency and the thrill of the ever-lasting chase!"
 * Lampshaded: "What, does this thing think we're a 5-star meal or something?"
 * Invoked: Bob is leading Fluffy into a trap.
 * Defied: "Oh, those two aren't even worth it, I'll just butcher this cow instead or something."
 * Deconstructed:
 * Fluffy keeps chasing Alice and Bob until he dies of starvation/exhaustion, which could have been avoided if he had gone after easier prey. When Alice and Bob come up on Fluffy's corpse, they lament the senseless waste of monster life.
 * Reconstructed: Fluffy's species is quickly dying out, and its habitat is almost completely devoid of prey. They need to pursue any morsel of food they can find, no matter what the cost.
 * Discussed: "Knowing our luck, he's not gonna go away 'til we kill him."
 * Conversed: "Ever notice how predators on TV are stubborn when it comes to food?"