Thursday, February 23, 2012

Game Theory and Evolution - pt 2

(continuing from the last post)

We've analyzed some simple (always choosing the same) populations (all silent, all squealers, mix of both).

Now, let's imagine some more complex strategies.

In a population of all silents, everything is stable.  Everyone is benefiting equally from each transaction.  We introduced a single squealer, and things got bad for all the silents.

Now, imagine some of the silents have "recognition" - either from communication or remembering some trait (either preventatively, or over time).

So, a "recognizer" will squeal against a squealer, and be silent against a fellow silent or recognizer.

Now, the population is more dynamic.  Pure silents will decrease (are "selected against"), while recognizers win all the time.  Squealers lose to recognizers, but win against silents.  If the silents disappear completely, then this will cascade into squealers disappearing completely.

Thus, a long-time stable population of "silents" will become a stable population of "recognizers" (after a fiery period of transition).

That's the "proof" for evolution (at least, as presented in "The Selfish Gene").

There's a number of things to keep in mind:
  1. It assumes an operating ecology (the initial stable population)
  2. It assumes a mechanism for new features
  3. It assumes that because something might happen, that it necessarily did happen
The fourth point is the main one.  In logic:
if (p) then q
q, therefore p

This is an error (or logical fallacy) known as affirming the consequent.

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