The Ultimate Answer To The Question Of: Life, The Universe, And Everything ...
I believe that looking at the way complex systems behave in terms of interaction
strategies can be very revealing.
"Tit for Tat" or "Forced Cooperation"
is a strategy for playing "The Iterated Prisoner's Dilemma"
game. This strategy is optimal.
I believe that this strategy
naturally arises in all sufficiently complex systems. I also believe that such systems always give rise to
a complimentary strategy called, "Opportunistic"
or "Always Default".
To understand the difference between these two strategies look at the following payoff matrix.
| column A | column B
------+-----------+----------
row A | 3,3 | 0,5
------+-----------+----------
row B | 5,0 | 1,1
The opponents are called "row" and "column".
If both row and column pick A then the pay off for both is THREE points each.
If row picks A and column picks B then row gets ZERO points and column gets FIVE.
If row picks B and column picks A then row gets FIVE points and column gets ZERO.
If both row and column pick B then the pay off for both is ONE point each.
Another way of looking at this is to think about the "bag of jewels" and "bag of money" game
(this is another way of casting the Prisoner's Dilemma).
Two players meet in a woods, each leaves a bag behind a tree then makes his way to the
other player's tree. Each player either finds a full bag or an empty bag. The payoff matrix
and this model fit together like this: You leave a full bag and pickup a full bag = A,A
(both players get THREE points). You leave an empty and get an empty bag = B,B (both players get
ONE point). If you leave an empty bag and get a full bag you get FIVE points and your opponent gets
ZERO points (and vice versa).
The maximum return is to leave an empty bag and pick up full one. Here is where the 'Tit-For-Tat' part comes in. You can 'remember' from one round
to the next what that opponent did last.
What is the optimal strategy?
Always leave a full bag unless the player you are up against left you an empty bag then
leave him an empty bag. In other words do whatever your opponent did to you last time and
when in doubt cooperate (or leave a full bag). One reason this
strategy is optimal because it can persist when exposed to itself.
The Opportunistic or
Always Default strategy is: Always leave an empty bag.
One reason this strategy is not optimal is that it can not persist when exposed to itself.
What happens is this: In any sufficiently complex system the 'forced cooperation' strategy will always win out.
The cost of this 'winning' is that the opportunistic strategy can have a 'hay-day'. It can run wild
leaving empty bags all over the place and survive quite well until it starts making repeat encounters
with 'forced cooperation' at which time it will be corrected out of existence.
The reason 'forced cooperation' wins is that it can persist when exposed to
itself and punishes 'opportunistic' which can no persist when exposed to either
itself or forced cooperation if it has interacted with that strategy before.
These two strategies are joined together and they give rise to each other in all sufficiently complex systems. The reason that this is the
case is that forced cooperation works with itself and, for a short while,
opportunistic works even better (as long as it does not encounter forced
cooperation again).
When you think about the immune system, biological evolution, the stock market, how humans interact with each other I think
it all makes quite a bit of sense. A good example is modern agriculture. We grow vast fields of the same type of plant, whether
this be corn, soybeans, or tobacco. What happens is that you always get a 'bloom-of-pests' that attack the great field.
A biological bloom and it's ultimate crash is all tied up in this concept. A bloom can be defined
as an opportunistic strategy taking over in a sea of forced cooperation. In all cases these types of things happen,
the bloom is corrected out of existence because it uses up all the resources or the system evolves and the bloom is incorporated
into the system and it goes back to being cooperative.
What will never occur is a system that stays in the cooperative stage or the opportunistic stage. The cooperative stage
always gives rise to the opportunistic stage and the opportunistic stage always corrects itself out of existence one way or another.
This type of interaction of bloom and response is responsible for the idea of robustness. A system is said to be robust
when it can evolve or correct out of existence opportunistic events. The immune system is very good at this.
Complex systems in general are robust. If they are not then they do not exist for long, because
some opportunistic event will come along and wipe them out. A recent article
in The Atlantic Monthly about what could have happened to the native American population when the Europeans arrived is a good example.
I do not think it is too much of a stretch to characterize the events of 9-11 as an opportunistic event in a cooperative system.
A good question becomes: Does the strategy of preemptive strikes, a reaction to an opportunistic event,
represent an evolution of the system to a more robust one? One thing is clear: Reactions to opportunistic
events always cause change, and opportunistic events always occur. I believe that preemptive behavior does not fit
the forced cooperation strategy, I think that it more closely resembles an opportunistic event. I suppose an argument can be made
that adopting opportunistic behaviors can be thought of as forcing evolution or creating robustness, but the tone of
this discussion is that you need to really think about what you are doing before you do it. It is probably the case that you can
not assign the tags <good> and <bad> when
discussing these strategies.
These types of behaviors, periods of calm punctuated by periods of chaos and upheaval typify all sufficiently complex systems.
I think the ideas of forced cooperation and opportunistic events represent a good explanation of of why these systems behave
the way they do and therefore represent a fundamental part of why the universe works the way it does.
Note: Consciousness as an emergent behavior.
Complexity and Emergent behaviors.
Demographic Prisoner's Delimma.
Stable or Robust? What's The Difference?
Game Theory, Complexity, and Simplicity PART III: Critique and Prospective
Robert Axelrod's Home Page
The Game Of Life.