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Hunger game theory

March 25, 2012

TLDR:  The Hunger Games has an amusing setting, where you’re punished for eating with a small probability of death.  But the characters in the book/movie might have missed on opportunity to make some beneficial contracts.

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No this post is not about food and my hunger, though my friends will tell you I am always thinking about those things (I can’t believe I forgot to mention food as a topic in my first post, by the way.  Given that, it’s quite likely I forgot a number of things which are important to me.)  This post is about The Hunger Games, a movie based on a book of the same title (in turn, based on some Japanese book), which I watched on Thursday, before the midnight premiere (woohoo, I’m special).  In case you were wondering, I thought the movie was pretty good and worth 2 hours of most people’s time, and I got teary at the end…

SPOILER ALERT (not really):  Part of the premise is that there are these poor people who live in districts that are controlled by a rather cruel Capitol, and where taking food for your family causes your children to be put in what is essentially a death lottery. The main part of the movie is the death-ish stuff that happens after the lottery, but this post will focus on the lottery aspect, which I found amusing.  The more food you take, the more times your name gets put into this lottery (I would die with high probability if I lived in such a district… (shoot this post is kinda about my love for food after all (also parentheses overkill for the win!))).  Let’s call this game the “hunger game” (to introduce terminology that is inconsistent with the movie’s/book’s…)

This hunger game of course really far from a zero sum game.  Let’s take the simple model where the number of times your name gets put in is directly proportional to the amount of food you’ve taken, and where the Capitol doesn’t interfere with or care much about this lottery other than running it (so they won’t stop people who are trying to game the game). So if everyone doubles the amount they take, they all still have the same probability of being drawn!

So… it’s pretty natural to expect people to make agreements where they all agree to not shirk from taking food.  Unfortunately, if the contract isn’t enforced well, you expect individuals to still defect, since the contract necessarily enforces consumption at a point where marginal utility for food at this point is negative.

So you could just do something like, flip some coins to decide at the beginning who will die, and then have them take all the food for the district.  But how would you get people to agree on the amount of risk they would take?  Some families are richer and need to take less food than others; some families have hungrier mouths, or more mouths per children.  Less needy families may prefer to opt out if their share of risk is too high, and prefer to take food on their own; needier families may claim to less needy, to bargain for lower risk in the contract.  Since the agreement basically allows everyone to have more than enough food, it’s hard to reveal preferences.  I suspect that in some model, it is impossible for a dominant strategy truthful mechanism to get maximum social welfare (infinite food).  Perhaps a practical implementation would make the coin flips deterministic and pre-emptive.  Like, “Oldest disabled child takes one for the team and get enough food for the district.”  This is unsatisfactory and would probably not work though; obviously the disabled children would want to opt out…

One way to alleviate the problem is some sort of subsidy (hooray cheaper food!).  Whenever somebody eats, everyone else has to give them some small amount of money, to compensate for the risk reduction the eater is providing.  Since micropayments are annoying, and we don’t want things to depend on the order in which food is taken, the amount people owe each other would just be calculated annually right before the lottery.  Unfortunately, this gets more food, but not infinite food, and I don’t know how the details or math works out.  (But hey, a world in which you get paid food to eat food is awesome!  Though if the world is also where a cruel upper class kills people as part of a game, it probably becomes a net loss…)

What do you guys think?

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From → Economics, Media

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