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.

Thursday, February 9, 2012

Game Theory and Evolution

It's been several years since I read Dawkin's "Selfish Gene" (where I mentioned it is an overview of game theory).

I realized that some people might want a tl;dr version of game theory.  I think I can fit it in one or two (longish) blog posts:

First, I play a lot of games (to the point where I consider myself an amateur game designer).  Game theory has little or nothing to do with actual, fun games.  It also has nothing to do with "gaming" (the self-respecting term for gambling).

Game theory deals with logic puzzles.  Both in finding the optimal solutions for them, and dealing with "populations" (numbers of agents all involved in the puzzle).

A classic example is the "prisoner's dilemma":

Two prisoners each have two choices, (0) remain silent, or (1) squeal on the other prisoner.

This yields four outcomes:
00(Both silent) Each receives a small benefit
01(One squeals) The squealer receives a large benefit, the silent a large penalty
10(As above, roles reversed)
11(Both squeal) Each receives a small penalty

The actual numbers used can vary, and the numbers (and their ratios) will determine the outcome in the later simulations.

The optimal strategy is to remain silent (since both win).  However, if you know the other will be silent, you can "cheat" him and squeal (getting yourself a large bonus).

Now, let's apply that to populations.

Imagine a large population of "silents" (agents who always choose the silent option).  This population is stable, it always generates benefits, which allows it to continue (propagating more silents).

Now add a single "squealer" to the mix.

This squealer will reap large benefits in every transaction, and never have a penalty.

In the next generation, there will be more squealers.

However, the population will never reach all squealers.

This is because when two squealers meet, they are both penalized. The final ratio will depend on the relative values for the four outcomes.

A population of all squealers might disappear (since they are all penalized), depending on the rules of the simulation.

To be continued!