Wednesday, March 28, 2012

The Joker Effect, Batman, and Game Theory.

The Joker, as envisioned by Doug Mahnke.  Source.

So,

I am not entirely certain how many times I will ever say this, but I stumbled across a truly fascinating paper in the Journal of Theoretical Biology (thanks, Reddit!) recently, and would like to share the results as best I can.  Not being a theoretical biologist or an avid practitioner of game theory, my understanding may be somewhat limited, but it is exciting nonetheless.

To begin, I will explain game theory as best I can (having background in neither biology nor economics, and having been awake for 23 hours at this point).  Game theory was originally envisioned as a tool for economics.  This predictive mechanism assumes that complicated, real-world situations may be reduced to a "game", a situation with clear rules and rewards.  I have heard through my travels, conversation and the Colbert Report that game theory has been used to predict elections, the collapse of the Soviet Union and various other seemingly unpredictable events.  In an interesting twist, it became clear to scientists that not only could the theory be used for economics, but [bizarrely] seemed to fit biological systems perhaps better than those for which it was designed.

In order to effectively model biological systems and how populations could grow and change over time, evolutionary game theory was developed.  In this system:

1.  A population is considered.
2.  The individuals' strategies are evaluated according to the "rules" of the game.  These individuals are then assigned a fitness (this fitness function is not unlike that present in genetic algorithms).
3.  The fitness of the individuals are considered, and the population increases by one, the new individual likely being a member of the fittest group.  An individual could also change strategies, rather than adding another.
4.  This new population goes back to step 1.

Thus, successful "players" will become increasingly significant in terms of the population, and less successful players will be overtaken.  The paper by Arenas et al. [J. Theor. Bio., 279 (2011) 113-119] utilises this in order to evaluate the performance of individuals in the game.

The game considered is known as a public good game.  There exists a value for the public good, and there are at least two player types in these games.  Cooperators contribute to the public good at some cost to themselves, while defectors are free-riders.  They consume public good while contributing nothing.  You could think of them as taxpayers and non-taxpayers.  With only these two players, defectors often overtake cooperators, a straightforward result since the defectors are not at all burdened. However, the real world, and most real systems are not this simple.  It is assumed that this is due to the presence of other players.

Batman, the ultimate cooperator. Source.
Here, we introduce the Joker.  Where we may consider the Batman to be the ultimate cooperator (great contributions to the public good at tremendous self-cost), and corrupt officials/organized criminals to be defectors, we may introduce a character which introduces new and interesting dynamics.  The Joker, as in his universe, does not personally consume public good, nor does he contribute to it.  However, he destroys large chunks of public good because some men want to watch the world burn.  The introduction of a Joker character over the course of a full simulation can lead to one of two ultimate scenarios.  In the event that Jokers are wildly successful and/or effective, they will overtake the simulation leaving only chaos and anarchy in their wake.  Since this does not appear to happen (either in the Batman universe, or ours), it would appear the scenarios leading to this eventuality are based upon poor assumptions.
The alternative result is that which would more closely mirror reality.  Here, it is assumed that Jokers will never fully overtake cooperators.  This is due to the fact that cooperators thrive off the public good they produce, ensuring at least a small population of them at any given time.  Let me attempt to describe what would happen to a cooperator-defector game with the introduction of a Joker.

1.  As stated above, defectors outnumber cooperators.  This drain on the public good is ultimately detrimental to all parties.
2.  The Joker is introduced.  The threat to the public good makes defectors ultimately unsustainable, and their population share crashes.
3.  A small group of cooperators survives, doing very well on an individual basis (i.e. high fitness), this leads to expansion of their population share.
4. The increase in cooperators leads to an increase in public good, which allows for defectors to emerge from the woodwork, and begin to claim population share at the expense of cooperators.
5.  Repeat.

This scenario ultimately avoids the cooperators being crushed/exploited by the defectors.  In the end, cooperators do much better than they would without a Joker.  As an interesting note, this scenario has been documented in nature.  In the presence of predators, cooperation is actively encouraged where it would not exist otherwise.  Picture a flock of smaller birds chasing away a raptor, even where they would not cooperate otherwise.  Even in humans, it seems that only through the presence of destructive agents (common enemies, perhaps) that we can disregard our differences and get along.

I shall now leave the question that was ultimately posed by the paper.  Who is the true saviour of Gotham City?  Is it Batman, or the Joker?

NM

P.S.  Please point out any grammar/spelling/logic errors.  Proof reading takes time and effort, and I'm going to bed.
P.P.S Edited 2012/07/28, finally gave it a once over.  Also, if I ever become a supervillian, I'll model myself after the Joker.  You know, for the greater good.
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