In both the movie and the book we see a coalition of some of the players develop where they attack other players as a group. As I considered this, and being aware of game theory, I wondered how such an alliance could be stable, given the powerful incentive all members of the coalition have to kill each other in order to better position themselves to win the game. In fact, I wondered how members of the coalition would even get any sleep, especially given that they slept near each other. This may seem like a strange question but the Prisoner’s dilemma game can show that it isn’t so strange.
Consider the following table:
Don’t Sleep(all) Sleep(all)
Don’t Sleep(1) Tired, Tired Kill, Killed
Sleep(1) Killed, Kill, Rested, Rested
Here subscript “1″ refers to any member of the coalition and subscript “all” refers to all other members of the coalition. Let’s consider matters from any given member’s perspective (the subscript 1 player). What if the other players don’t sleep? If you don’t either, then you will be tired and, perhaps, more vulnerable to better-rested contestants. But if you sleep while others are awake, any one of them can kill you in your sleep. Presumably, it’s better to be tired than dead so you are under tremendous pressure to stay awake.