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.

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!

Evangelism

"Evangelism: How to Share the Gospel Faithfully" (John MacArthur, et al) - This was a really good book.  Different chapters written by different people at Grace Community Church.  The best quote is "work like an Arminian, sleep like a Calvinist".  I also found a new appreciation for short-term missions, which must be viewed as first-most for encouraging long term missionaries.

State of Marriage

An old post from Albert Mohler I found at the bottom of my inbox...

I'm fascinated by the degree to which Postmillenialism dominates Christian thinking.  I would presume Mohler is a Premillenialist of some sort (being Baptist).  At most, amil.

We must understand that, fundamentally, the majority will always reject God ("the wide road").  The founders of America were not strong Christians, but they did operate under the assumption of a Christian worldview - and that the population would continue to hold that view.

We see now, the consequences of such a system; where the population ceases to hold that view.

Why does the State involve itself in marriage?

From a "Christian nation" point of view, it is to encourage the formation of families.  Tax breaks (in the form of tax tables, and benefits like health care) allow for one parent (originally the man) to provide for a family.  Single people complain of unfair treatment, and the "marriage penalty" is born.  Other groups seek State sanctification of what they call marriage - in order to access the benefits.

"There is no major society that exists without marriage, and those rare movements in history that sought to eliminate marriage led to disaster."

While true, we cannot operate from this motive (pragmatism, or even "the ends justify the means").

We are seeing the fallout of where a Christian derived system is reconciled with the majority rejecting Christ.  The question is: can a stable (and God-honoring) system be derived where the majority reject Him?

I don't know, but I don't know if anyone else is even asking the question.

Some are calling for the State to withdraw from involvement in the regulation of marriage - and I must agree (and disagree with Mohler's claim this "would lead to legal, moral, and cultural chaos").  There are standard forms for wills, etc. which are not blessed by the State.  Christian men will continue to provide for their families as best they are able.  Non-Christians will continue as well as they are able.

But this is just removing a vestigial remnant of the Christian worldview.  It does not address replacing and fortifying underlying structure.

End of Capitalism

(continuing my series on economics)

Finally getting around to another article which triggered this whole excursion...

I like his insight.  Marx saw inevitable problems with Capitalism, which made it unsustainable.  Marx then assumed there was a better way, and created Communism (of course, being blind to its own unsustainable problems :)

"Because the truth might just be that the global economy is in historic, generational trouble, plagued by problems the orthodoxy didn't expect, didn't see coming, and doesn't quite know what to do with."

Work Before the Fall

Now that I have laid some groundwork on economics and our current situation, we can examine the Biblical points on work and the economy.

There is little known about life before the Fall, but what we have is instructive.

First, we have God's work in Creation:

"And on the seventh day God ended His work which He had made; and He rested on the seventh day from all His work which He had made." (Gen 2:2)

The Hebrew word here is מְלַאכְתֹּ֖ו (mel-aw-kah).  It can be used for ministry, or deputyship in addition to "work".  It is not used for servile work.  It is used again in verse 3 (repeated reference to rest from His work).  After that, it does not appear until Exodus.


The work for the man (Adam) is described differently:

"And the Lord God took the man, and put him into the garden of Eden to dress it and to keep it." (Gen 2:15)

The word dress here (עָבְדָ֖)(aw-bad) is usually translated "serve" (also in the context of work).  In fact, in 290 uses, it is translated "serve" 227.  It is translated "dress" only twice (Deut 28:39 being the other one).  Usually "dress" comes from a different word, meaning "do".

("Keep" here means "guard", which is the subject for another day)

Finally, at the Fall:

"In the sweat of thy face shalt thou eat bread, till thou return unto the ground" (Gen 3:19)

So we see a difference in the work of God, and the work of man (not surprising).  The man's work, even before the Fall, is servile (in service to God) - possibly even hard.

At the Fall, we see man's work changed.  Now it is literally "sweat" (zay-aw) to get bread.  This might refer to conditions changing to cause sweat when working (perhaps due to a change in diet - garden vs. bread), but seems to more refer to "frustration".  Before, the work was rewarding and pleasant - now it is tedious and often spoiled.


Man's work was created on day 6 - before God rested, saying everything is good.  The Fall has brought frustration and sweat.

Next Review

There is a new biography of William Tyndale coming out.  It should arrive in a week or so, and will probably take a few weeks to read...  Looking forward to it!