Imagine 100 rational tigers and 1 lone sheep stranded on a magical island. The only food source is grass, which the sheep can eat, but the tigers prefer meat—and specifically, they’d love to eat the sheep. However, there’s a catch:

  • If a tiger eats the sheep, it becomes a sheep itself.
  • Only one tiger can eat at any given moment.
  • All tigers are perfectly rational, prioritizing their own survival above all else.
  • If indifferent in outcome, a tiger prefers fewer fellow survivors (more tigers dead).

The question: Will the sheep ever be eaten?

Backward Induction Solution

We solve this through backward induction, analyzing from smaller cases up:

1 Tiger, 1 Sheep

  • The tiger eats the sheep, becomes a sheep.
  • Now alone, no threat. Survival guaranteed.
  • Outcome: Tiger eats the sheep.

2 Tigers, 1 Sheep

  • If a tiger eats the sheep, it becomes a sheep.
  • Left with 1 tiger and 1 sheep.
  • From above, we know the lone tiger will eat the new sheep.
  • Result: The first tiger dies.
  • No rational tiger acts. The sheep survives.

3 Tigers, 1 Sheep

  • If a tiger eats the sheep, it becomes a sheep.
  • Left with 2 tigers, 1 sheep.
  • From above, no one eats.
  • First tiger-turned-sheep survives.
  • A rational tiger sees that eating leads to survival. The sheep is eaten.

4 Tigers, 1 Sheep

  • Eating leads to 3 tigers, 1 sheep.
  • We know from above: a sheep will get eaten in a 3-tiger scenario.
  • So the first tiger who eats will ultimately die.
  • No one eats. The sheep survives.

This alternating pattern continues:

  • Odd number of tigers: One will dare to eat the sheep.
  • Even number of tigers: No tiger will eat—it’s suicidal.

Case of 100 Tigers, 1 Sheep

100 is even. So, no tiger will eat the sheep.

Final Answer

The sheep survives.

Rational tigers recognize that making the first move will ultimately lead to their own death, so none act.

Reference