Monday, 3 July 2017

The economics of Survivor

I love the reality show Survivor, and have done so since the very first season. In fact, it's the only reality show I can stomach. Over the past several years, I have even toyed with the idea of writing a book (or at least, a long monograph) on the economics of Survivor, since there are so many economic concepts that can be illustrated using examples from the show - from game theory, to choice under uncertainty, to comparative advantage.

However, it seems like I've been beaten to this idea. In the latest issue of the Journal of Economics Education, Dean Karlan (Yale) wrote an article on the economics of Survivor (ungated earlier version here). Fortunately for my embryonic book plans, Karlan's article only covers three examples: (1) individual decision-making and how pride and honour can be included in an individual's utility and affect their choices; (2) game theory and backward induction; and (3) repeated interactions (also game theory).

The second example is perhaps the most interesting. It relates to the very first season of Survivor, won by Richard Hatch. Karlan writes about the final immunity challenge in the game, which was a test of stamina where the three remaining competitors had to stand on a stump and touch a pole, with the last remaining one winning immunity and getting to choose which of the other two would join them in the final tribal council:
At two and half hours, all three remained. Then, Richard surprised everyone when he voluntarily took his hands off the pole and disqualified himself from immunity. A real puzzle is why it took him so long to drop out (the answer may be simple: dropping out too soon would have made his strategy obvious, and thus less effective).Why was it optimal for him to lose?
Start at the end. There were four possible paths in this game:
(1) Richard wins and votes out Rudy, thus competing against Kelly in the final. Richard and Rudy had a strong alliance, but Richard did not think Rudy would forgive him for breaking it, even at the final stage. Thus, Richard believed that if he won and voted out Rudy, he would lose Rudy’s vote. He wanted to compete against Kelly, but he wanted Kelly to be the one to vote out Rudy.
(2) Richard wins and votes out Kelly, thus competing against Rudy. Richard loses. Everyone knew that if Rudy made it to the end, he would win the game.
(3) Kelly wins. If Kelly wins, she votes out Rudy (because, again, everyone knew that if Rudy made it to the end, he would win the million dollars). Then, Richard and Kelly compete for the million dollars, but here Richard wins Rudy’s vote, whereas in option #1 above Richard would lose Rudy’s vote.
(4) Rudy wins. Then he votes off either one. It does not really matter, because Rudy would win the game.
Basically, Richard had to ask himself: If I win the immunity challenge and vote off Rudy, what are the odds that the final council will make me the winner? Or, if I lose on purpose, what are the odds that Rudy beats Kelly in the immunity challenge, and then wins the game?
Given these options, Richard actually made the right choice. He released voluntarily. Kelly then won the immunity challenge (after four hours, Rudy lost his concentration and accidentally released the pole) and removed Rudy from the game. Thus, the final vote came down to Kelly vs. Richard, with Richard winning by one vote - that of Rudy’s.
There's much more to the economics of Survivor than this one example illustrates (or even all three that Karlan uses in his article). So maybe there is still space for a book?

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