Respect Your Assets: Two-Face Doesn't...

Art by Dustin Nguyen from the cover of Streets of Gotham #15, obtained from http://www.dccomics.com/go/?15348

In a recent issue of Batman: Streets of Gotham (issue #15 actually), we see what happens to a crime boss who isn't aware of the resources available to him.

Two-Face has had some trouble maintaining his criminal empire recently. Since Battle for the Cowl, Two-Face has had to face gang wars with both Penguin and Black Mask, as well as the forceful intervention of Batman himself. In Streets of Gotham, Two-Face has also had to deal with the fact that he has an undercover cop in his ranks.

Streets of Gotham #15 shows Two-Face dealing with the ramifications of these events. Most of Two-Faces gang has been murdered or arrested, leaving Two-Face with only two hired thugs supporting him and very little money. This is a dire state of affairs for the crazed crime boss, yet Two-Face refuses to acknowledge the limitations that are placed on him.

When Two-Face continues to expect unreasonable things from his rapidly deteriorating "organization," his last two henchman turn on him. Realizing Two-Face is out of touch with reality, the thugs fill Two-Face with lead rather than continue to risk their own lives for a madman. Naturally, they dump Two-Face into the river and leave him for dead.

Let this be a lesson to all of us. When resources are limited, we need to recognize what we (and the organizations with which we involve ourselves) are capable of. It is important to pay attention to your available assets whether they be property, stock, or murderous henchmen. Don't over-extend yourself (like some recent financial institutions) or you may find yourself floating in a harbor (or bankrupt at the very least).

Food for thought.

share on: del.icio.us digg reditt su

How Does Two-Face Fund His Crime Sprees (Revisited)?

Joker by Brian Azzarello and Lee Bermejo (2008)

Remember when we asked how Two-Face made the money to afford a headquarters, armored cars, henchmen, weapons, ammunition, tools, and all the other useful things he uses in his heists and plots to destroy Batman? Well, Brian Azzarello and Lee Bermejo put forth a bit of an explanation in their recent graphic novel, Joker. Apparently, "Harvey Dent was the rackets in Gotham. From fruit stands to oyster bars, he got a taste. The price of doing business was doing it with him."

This makes sense to the extent that I believe that Two-Face would play the role of Gotham's eminent mobster. If any one of Gotham's "freaks" would be most capable of taking over the Falcone and Maroni businesses, it would be Two-Face. He would have dealings with most of the crooks in the underground and he would skim some off the top for it.

And I imagine that all or most of these businesses involves some drug smuggling, human trafficking, or whatever other shady businesses come to mind when thinking of mobsters. Drug trafficking alone is a lucrative enterprise. According to the U.S. Drug Enforcement Administration, New York City police seized 1,481.1 kgs of cocaine, 279.3 kgs of heroin, 7.1 kgs of methamphetamines, 2,820.7 kgs of marijuana, 79.3 kgs of hasish, 0.6 kgs of MDMA, and 9 meth labs in 2008 alone. In 2007, a man was found guilty of helping to import more than $100 million worth of cocaine into the United States between 1998 and 2003. If Two-Face is at the very top of this game in Gotham City, one of the notoriously corrupt cities in the world, and has his hands in most of these exchanges, I am sure that he is making quite a bit for his villain game.

However, one thing still remains a mystery to me (which I mentioned in the earlier post): Batman. If Two-Face is really running Gotham the way that his predecessor thugs did, then why has Batman not stopped him and seized his assets? While the police in Gotham may be lackadaisical in rooting out these smuggling rings, or simply not have the legal basis or evidence with which to halt these illegal activities, Batman is not bound by such constraints. In fact, that was one of the main issues raised in Batman Begins. The police could not touch Falcone, despite his infractions, but Batman almost immediately was able to stop his smuggling operation and bring him to justice. So why is Two-Face capable of making so much money in Gotham City that he is actually living in a mansion?

Actually, Batman seems to be pretty slow overall in this novel. SPOILER ALERT. It took the entire novel for him to so much as make an appearance to stop the Joker. Before he showed up, the Joker was released from Arkham, skinned a man alive, blew up a building, killed a whole bunch of mobsters, and performed many others lude and violents acts that I will not mention. And Batman didn't even discover it for himself! Two-Face had to actually call him and alert him of what the Joker was up to. What is going on?

Perhaps Two-Face immediately sends his money to offshore bank accounts where Batman cannot touch it. This way in between committing crimes, going to Arkham, and coming out, he has some sort of a reserve from which he can draw funds. Though I'm not quite sure how this would work.

What do you all think? Any theories??

share on: del.icio.us digg reditt su

Uneasy Alliances II: Why Two-Face Loses by Flipping a Coin

Earlier we began a discussion of Harvey Dent and James Gordon's alliance to clean up the streets of Gotham. We concluded that cooperation did make sense in the scenario portrayed by the film The Dark Knight. The cooperation game, or the Stag Hunt game, produced two pure strategy Nash Equilibria -- both players would cooperate or both players would work on their own.

Now, suppose that we take the same situation but introduce randomization. That is, suppose Harvey decides he wants to randomize his actions so that Gordon could not predict what he would do. Note that this is extremely unlikely; people usually intentionally randomize when they are working against another player. But for the sake of argument, suppose that it applies here.

The idea of assigning a certain probability towards an action is known as a mixed strategy. In this game, we can actually find a third, mixed-strategy equilibrium in addition to the two pure strategy ones we had found in the previous post.

So, here is the matrix from last time:

Harvey Dent -->> James Gordon ↓	Cooperate	Don’t Cooperate
Cooperate	(4,4)	(1,3)
Don’t Cooperate	(3,1)	(3,3)

Suppose that Harvey assigns a probability, p, to cooperating and (1-p) to not cooperating. Then we could perform an expected utility calculation to deduce Gordon's optimal strategy.

Recall that Expected Utility (EU) of a given action is equal to the sum of the utility values (U) or outcomes weighted by the probabilities (p) of receiving each. Therefore:

EU = p * U(Cooperate) + (1-p) * U(Don't Cooperate)

Then the expected utility if Gordon cooperates is:
EU(Gordon Cooperates) = p * 4 + (1-p) * 1
=4p + 1 - p
=3p + 1

The expected utility if Gordon does not cooperate is:
EU(Gordon Does Not Cooperate) = p * 3 + (1-p) * 3
= 3p + 3 - 3p
= 3

We know that Gordon will choose whichever action gives yields the greatest expected utility. So setting the two equations equal to each other, we have:

EU(Gordon Cooperates) = EU(Gordon Does Not Cooperate)
3p + 1 = 3
3p = 2
p = 2/3

Therefore, Gordon will cooperate only if the probability that Harvey cooperates is greater than 2/3. Otherwise, he will not cooperate. We can perform the exact same analysis by assigning a probability, q, to Gordon's actions and calculating expected utilities for Harvey. It will yield the same answer, namely that q = 2/3.

So p = q = 2/3 and we have a new, mixed strategy equilibrium where each player chooses to cooperate 2/3 of the time and does not cooperate 1/3 of the time. If Harvey decides to randomize this way, then Gordon cannot benefit by deviating from this strategy alone.

This result is interesting for several reasons. First, each player's expected payoff under mixed strategies is 3. Therefore, the mixed strategy equilibrium outcome is no better than either of the pure strategy ones. Therefore, Dent and Gordon would be just as well off choosing not to cooperate with each other 100% of the time. They would each be strictly better off choosing to cooperate 100% of the time.

Second, I had mentioned before that we were supposing Harvey intentionally randomized his actions, but the truth is that this mixed strategy exists whether he wants to or not. The reason is that these mixed strategies can be interpreted to reflect one individual's beliefs about the other's actions. In other words, Harvey choosing cooperate 2/3 of the time and choosing to work on his own 1/3 of the time can be seen as Gordon's views on what Harvey will do given his uncertainty in the matter. If he believes Harvey will cooperate 2/3 of the time, then he will cooperate 2/3 of the time.

Now suppose that Harvey decides to flip a coin instead. And what's more, suppose that Gordon knows that Harvey will flip a coin. What will Gordon do? And will this be an equilibrium?

If Harvey flips a coin to decide, this means that he will cooperate 50% of the time and work on his own 50% of the time. So, Gordon's expected payoff will be:

EU(Gordon Cooperates) = (1/2 * 4) + (1/2 * 1) = 2.5
EU (Gordon Does Not Cooperate) = (1/2 * 3) + (1/2 * 3) = 3

Therefore, Gordon will derive a larger expected utility from not cooperating and will choose to work on his own all of the time.

This, however, is not an equilibrium. We already know that if Gordon chooses to work alone 100% of the time, then Harvey would be strictly better off by also choosing not to cooperate 100% of the time. By sticking to the coin strategy, Harvey is actually losing some utility.

Of course, there are certain situations where flipping a coin could work. Suppose that Two-Face and the Penguin are facing off against each other by driving their cars towards one another in a bizarre game of chicken. Each can choose to go left or go right. The only thing is that they have to make their decisions at the same time, so nobody gains any utility by turning first. All we know is that each wants to live. So, if they both turn left, they each receive a utility of 10 for being alive. If they each turn right, they will also receive a utility of 10. If one turns left and the other turns right, both will die in the car crash and receive a utility 0f 0. The matrix then looks like this:

Two Face -->> Penguin ↓	Left	Right
Left	(10,10)	(0,0)
Right	(0,0)	(10,10)

Here if we perform the same utility calculations as above, assigning a probability of p to Two-Face turning left, we will arrive at p=1/2. Therefore, if Two-Face chooses to flip a coin intentionally, the Penguin should do the same and this would be a mixed-strategy Nash equilibrium.

Now, this sort of situation does not happen often. And this is why Two-Face's gimmick of flipping a coin to make every decision is usually a costly one. First of all, he gives away his strategy, making it easy for his opponents to predict their best actions. Second, it is not always the case that choosing one action 50% of the time and another 50% of the time is a mixed-strategy equilibrium, as we saw above. If Two-Face continues to adhere strictly to this strategy, he will be losing in the long-run.

And this is why Batman will always win. He knows his economics.

share on: del.icio.us digg reditt su

Should Batman Villains Betray Each Other? (Analysis using the Prisoner's Dilemma)

(This is the second part of a post that will include some very light and simple algebra and game theoretic concepts. Not to worry--it is pretty crude and easy to follow along with. Also, please note that the assumptions made are rudimentary and based off of my own view of Batman and his villains. I welcome everyone to debate them with me).


We've discussed the decision of whether or not Batman villains should cooperate. Now consider another fun issue: lets suppose some of them do, in fact, work together and somehow manage to capture the Batman. There is now another decision that has to be made by each: whether or not to betray the partner.

Let's talk about Two-Face this time. As discussed in the previous post, the benefits of betrayal are obvious. Two-Face could claim full credit for killing Batman, could win the respect of the Gotham underworld, could elicit fear from the elite, and could potentially acquire some wealth and technology from the Batcave that he would not have to share with, say, Mr. Freeze (I can't think of a conceivable reason for that pair to team up, but I haven't used Mr. Freeze anywhere yet).

This situation is a nice example of the Prisoner's Dilemma. So, let's do a really quick summation of this two-player (Two-Face, Mr. Freeze), two-choice (Cooperate, Betray) game in Batman terms to show that it would actually make sense for the two of them to continue to cooperate, even though neither will. We must again assign some utilities for each player. I have done so, as the following normal-form game matrix represents:

Mr. Freeze -->> Two-Face ↓	Cooperate	Betray
Cooperate	(5,5)	(0,10)
Betray	(10,0)	(3,3)

In this matrix, Two-Face is the player on the left and Mr. Freeze is the player on the top. Each has the choice of either cooperating after capturing Batman or of betraying the other. In each cell, the numbers represent the utilities awarded to the respective players given their choice of action.

If both villains cooperate with one another, they each enjoy a utility of 5 from killing Batman and ruling Gotham (5,5). If Two-Face cooperates but Mr. Freeze betrays, then we will assume that Freeze will eliminate Two-Face, thereby winning all of his utility. In this case, Two-Face would get 0 utility and Mr. Freeze would get a utility of 10 (0,10). If Two-Face betrays but Mr. Freeze cooperates, then the opposite happens: Two-Face gets a utility of 10 and Freeze gets 0 (10,0). If they both betray each other, I'm going to assume that they'll either kill each other (in which case they'd both get 0) or they'll both walk away alive, but each would get less utility than they would have if they had cooperated (obviously they'd prefer not to engage in a near-death battle with one another, so they would lose something). Lets award each a utility of 3 in this situation (3,3).

If this is the scenario, each player would rationally want to betray the other. To see this, we must note that Two-Face and Mr. Freeze are hopelessly self-interested. They only care about their own utilities and not that of the other player. Now assume Mr. Freeze decides to cooperate. So we are restricted to the "cooperate" column of the table above. Looking at Two-Face's utilities in that column, it is clearly a better decision for him to betray, as he would be receiving a utility of 10 as opposed to 5. Let's say Mr. Freeze decides to betray, so we are now in the "betray" column. The best decision for Two-Face is still to betray, as he would receive a utility of 3 instead of 0. Hence regardless of what Mr. Freeze does, Two-Face would still want to betray him. The same is true for Mr. Freeze given Two-Face's actions.

Both players will choose to betray each other and (3,3) is the Nash equilibrium outcome. This means that neither Two-Face nor Mr. Freeze can benefit by deviating from his course of action alone. The dilemma, however, is that there exists an outcome in which both players are strictly better off. If both choose to cooperate, then each receive a utility of 5, which is greater than 3. Thus the outcome (5,5) is the Pareto Optimal point. It is the outcome of the game in which one player deviating would necessarily mean that somebody else is worse off.

So, what we have is a scenario in which Two-Face and Mr. Freeze teamed up and were successful (for some reason). Now it would benefit both of them to continue working together, but neither of them will actually do so. Hence they'll walk away with less than what they could have. As the Prisoner's Dilemma demonstrates, Nash Equilibria are not necessarily Pareto Optima. It's sort of funny to think about, actually. Batman can still claim a small victory even in his death.

share on: del.icio.us digg reditt su

How Does Two-Face Fund His Crime Sprees?

Anyone ever wonder how Two-Face gets funding for his schemes? With other Batman villains, it's not so much of a problem. The Penguin, for instance, runs a "legitimate" restaurant/night club, from which he earns most of the resources he needs to continue funding criminal activity in Gotham City. The Riddler is now a semi-legitimate private detective. Villains like Killer Croc don't need to worry about money, as the extent of his rampage through the city involves roaring and smashing. Then there's Poison Ivy and Harley, who occasionally rob a bank and go on shopping sprees, but spend the majority of their time housed in Akrham Asylum. The Joker is a tricky one, since he always seem to have an army of henchmen, but I attribute this more to the crippling fear throughout the underworld of refusing to partake in any scheme which the Joker might concoct.

That leaves us with Two-Face. Former District Attorney and golden boy of Gotham, Harvey Dent, took a tragic turn towards villainy when Boss Maroni threw acid on his face, shattering him both physically and mentally. Since then, Two-Face has held Gotham at ransom numerous times (though never succeeding thanks to Batman), has hired plenty of henchmen, bought several weapons, hideouts, cars, clothes, etc., and staged elaborate schemes that inevitably involve large sums of money in order to capture Batman. This begs the question: Where does he get this money from?

One might argue that Two-Face has enough saved up from his time as District Attorney, that he hasn't needed an additional source of income. But consider this: surely the government would have seized whatever assets he owned once he escaped from Arkham for the billionth time. Further, his pay as DA of Gotham City was likely meager, considering that public prosecutors do not get paid that much. Take a look at this image, reprinted from Payscale.

Median District Attorney Salary, Updated May 3, 2009, reprinted from Payscale.


Clearly, Harvey was a young gun: he had just been a DA for a few years before his accident. Conservatively, I will say that he served as DA for 1-4 years. That means his average annual salary was approximately $57,000 a year. And this is by 2008 standards. Recall that by modern continuity, his accident occurred in 1996. All of this means that Two-Face cannot possibly have enough money saved up to conduct his elaborate schemes against Gotham City and Batman.

Here's another theory: perhaps Two-Face has all his money from bank robberies or underground drug trafficking, criminal activity, etc. This could be true, but we happen to know that the Batman is pretty good at rooting all of these mechanisms out. And I do not think that Two-Face has pulled off enough successful robberies to sustain him throughout the years.

So what's left? We know he does not launder money through a business as the Penguin does. We can assume he does not have money saved up and that he has not scored big enough through crime to sustain his operations for over a decade. And now post-RIP, Two-Face is in a gang war against the Penguin, requiring even more resources to keep up.

The only theory I have is that perhaps he has a private investor; someone deep in the underworld of Gotham benefits politically or financially from Two-Face's successes. I used to think this person was the Penguin, but being that they are now at war with one another, this is unlikely.

Any thoughts from the readers?

share on: del.icio.us digg reditt su