A backpacker gets stranded on an island, and rescue is about a week away. Two cannibals live on the island. The cannibals are not friendly to each other, and both regularly attempt to eat the other. Both cannibals would like to eat the backpacker, but as we all know, a big meal makes one tired and defenceless. In the event that one of them eats the backpacker, the other might strike and eat the eater. Hence, if choosing to eat the backpacker, there is a risk of being eaten oneself. If both of them show up to eat the backpacker, they are friendly enough to share and split the backpacker in half. Both cannibals have a less desirable, vegetarian, diet available on the island. Let eating the (entire) backpacker or cannibal give a payoff of 2. A vegetarian diet is worth 1. Being eaten gives a payoff of 0. a) Write down the normal form representation of the game between the two cannibals. b) The backpacker realizes that the cannibals (otherwise) are highly intelligent and rational beings. Should the backpacker worry about being eaten?
A backpacker gets stranded on an island, and rescue is about a week away. Two cannibals
live on the island. The cannibals are not friendly to each other, and both regularly attempt to
eat the other. Both cannibals would like to eat the backpacker, but as we all know, a big meal
makes one tired and defenceless. In the event that one of them eats the backpacker, the other
might strike and eat the eater. Hence, if choosing to eat the backpacker, there is a risk of
being eaten oneself. If both of them show up to eat the backpacker, they are friendly enough
to share and split the backpacker in half. Both cannibals have a less desirable, vegetarian, diet
available on the island.
Let eating the (entire) backpacker or cannibal give a payoff of 2. A vegetarian diet is worth 1.
Being eaten gives a payoff of 0.
a) Write down the normal form representation of the game between the two cannibals.
b) The backpacker realizes that the cannibals (otherwise) are highly intelligent and rational
beings. Should the backpacker worry about being eaten?
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