Wednesday, 11 June 2014

Game Theory Chimps

So it turns out that in a recent study, chimps did better than humans at finding the optimal strategies for some simple games. The game they used was a matching game. Each player simultaneously chooses left or right. One player gets paid if they choices match, the other if the choices don't match.

Assuming the payouts are all the same, obviously the only possible strategy is to choose one or the other at random with a 50% chance of each. You don't want your opponent to be able to guess what you are doing, but beyond that there is no benefit to left or right.

But when the payouts vary, things are more interesting. Suppose the person going for matches gets paid more for a right-match than a left-match. The optimal strategy changes depending on how much more they get paid for the right-match. It's still random in any event, but it's not 50-50 anymore. For example, the mismatch player gets paid 2 rewards for any mismatch, but the match player gets paid 4 for a right-match and 1 for a left-match.

The analysis gives a sort of counter-intuitive result where the matcher always plays 50-50 and the mismatcher varies their choices based on the different payouts of the matcher. I won't go into the details but when you think it about it, the result shouldn't be all that surprising because the game is about predicting your opponent so it's not completely baffling that your opponent's payouts seem to weigh more into your decision than your own.

Anyway, chimps approximated the optimal strategies better than humans. A big win for chimps, right?

Well you'll notice that once the game is not symmetric, the total payout from the game varies, not just the payout to the individual. If you were playing for actual dollars, then both players choosing right means the total payout to the players is $4, whereas a mismatch results in only $2. Human players weren't as good as chimps at identifying a strategy that paid them the most, but their strategies were better at extracting money from the researchers.

The fact is that if you could collude in advance, the correct strategy changes completely. Both players choose right every time and then split the money after.

The outcome of this research to me is not that chimps are better at solving these problems than humans, it is that they have a different set of assumptions. I've written before about maximizing the total output of a game instead of maximizing your personal output as a strategy that is sometimes better - better even at maximizing your personal output.

The key is assuming that other people are basically on your side. Let's talk about another game. Player A is given $10 and is allowed to give any amount to player B. The amount given to B is then multiplied by three, so if Player A gave $5 then B gets not $5 but $15. Then player B is allowed to give any amount back to A, but gets nothing in return. Game theory says that the strategy is obvious: A gives nothing to B and walks away with $10. Humans seem to almost always give some to B and B almost always gives some back, closer to half than to nothing. If you are playing this game for real with real people the actual ideal strategy for player A is to give all $10. Odds are very good you will walk out with at least the $10 and most times you'll get more.

I'm not going to draw any conclusions using results-based thinking, but I would point out here that the chimps seem to be better at quickly figuring out how to maximize their payment than humans, but it was humans who became the dominant species on the planet to such a degree that we can conduct these experiments on chimps.

Adam Smith's notion that we got where we are because of self-interest may need a second look.

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