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Evolutionary solutions [May. 9th, 2006|01:58 am]
Arvind Narayanan
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It is often surprising how a variety of normal human behavior corresponds to deep statements in game theory, and humans have evolved to adopt social strategies without the slightest clue of what they mean or why they work. (In a sense, the same can be said of other animals, except they cannot even articulate what their strategies are.) For instance, I just realized that the statement "fool me once, shame on you; fool me twice, shame on me" is actually the well known "co-operate then reciprocate" solution to the Iterated prisoner's dilemma. Proving the correspondence is interesting and left as an exercise to the reader.

From: centerforward
2006-05-09 01:25 am (UTC)
That is an interesting correspondence. Didn't occur to me till I read this. On the other hand, it is still counter intuitive (after a whole course on Game Theory) that you would always defect if you knew the number of iterations.
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[User Picture]From: arvindn
2006-05-09 08:00 am (UTC)
There's a very beautiful reason why it's unintuitive (as a special case, it also explains why the PD itself is unintuitive): in real life, there is always another iteration. To understand this assertion, one must consider the "Environment of Evolutionary Adaptedness". During most of the period that is relevant to our current evolutionary make up, we lived in small tribes of around 100 or so. In such a context, there are no one-time encounters. Therefore, we never evolved a mechanism for subconsious (intuitive) reasoning about finite iteration games.

This last statement requires an explanation. It turns out that we reason about logical propositions by turning them into games in our head. Thus, even if the IPD is presented in an abstract manner, we interpret it in a tribal context. To prove this, Cosmides and Tooby performed a brilliant experiment in which they asked test subjects to evaluate a simple boolean formulas (IIRC, something that would simplify with a single application of De Morgan's laws). Lacking mathematical sophistication, the test subjects mostly failed. When given the same formula, however, with the variable names and relations replaced by "Alice", "cheated on", "Bob" and so on, not only did they succeed, their answers were so instantaneous as to have been necessarily subconscious.

I might have mangled some details of the experiment, but that's essentially it. To me it is one of the best science experiments ever.

Actually, the above explanation also solves the paradox of the Ultimatum game, and it doesn't seem to have been proposed yet. Maybe I should write a paper on it :)
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From: centerforward
2006-05-09 10:46 pm (UTC)
Aah.. from economics to evolution :). May be you could consider the following example too for your paper :)

A mother has 101 gold coins to be split between her two daughters. Each daughter can secretly ask their mother for a certain number of coins and will get them if the sum is <= 101 and get none if the sum is > 101. Here there is no direct "utility" for punishment.

PS: I tried to solve this problem by taking expected utility and all that and arrived at 50.5, 50.5 :))
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[User Picture]From: sunson
2006-05-09 02:48 am (UTC)
Dawkins has nicely explained the 'tit-for-tat' strategy in 'The Blind Watchmaker' (or is it in the 'Selfish Gene'? I don't remember).
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[User Picture]From: forvrkate
2006-05-14 06:22 pm (UTC)
I realized the same thing when considering the TIT FOR TAT strategy for the IPD. Was reading about this topic rather recently in The Moral Animal (Robert Wright, ISBN 0679763996).
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[User Picture]From: arvindn
2006-05-14 06:38 pm (UTC)
That book looks interesting. Thanks! There are 3 books on evolutionary psychology on my amazon shopping cart right now, but I've put off buying them after deciding I'm cheap after all and I'm just going to borrow them from the library. Plus I might actually read them if I borrow them, at least a couple of days before they're due :)

P.S: added you. You write well.
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[User Picture]From: forvrkate
2006-05-14 06:46 pm (UTC)
In that case, I strongly recommend the following three books:

0. The Red Queen: Sex and the Evolution of Human Nature. Matt Ridley. ISBN 0060556579.

1. How We Believe: Science, Skepticism, and the Search for God. Michael Shermer. ISBN 0805074791.

2. How the Mind Works. Steven Pinker. ISBN 0393318486. A solid introduction to the theories of cognitive neuropsychology written for an informed layman. Outdated, and (I've heard) highly contested, but still worthwhile.

(I keep a running list of good books I've read in case anyone asks me for recommendations, or in case I force recommendations on unsuspecting livejournal users.)

(Thanks! I attempt to write well, but you should be warned that there are many times in which I fail rather miserably.)
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[User Picture]From: arvindn
2006-05-14 06:49 pm (UTC)
Awesome. Much appreciated.
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