"When comic books and economics collide, Ecocomics is Ground Zero. And we have charts."

That's the tagline of this blog of particular nifty and gradually interesting reads. Covering dismal topics blurring the thin fabric between reality and comics, ranging from Superhuman Escort Service (okay, superhuman sex industry); the impact that fictional countries (such as Wakanda, Latveria and Kahndaq) can have on world economy; detailed analysis (complete with charts!) on Batman's Rogue Gallery chances of getting the job done (what Heath Ledger famously said in The Dark Knight, "It's simple. We, uh…kill the Batman."); and attempts to answer the question on who is the richest comic book character!

Some crazy excerpts below...

Now, let's assign the probabilities. I'm going to assume that each Batman rogue has a 2% chance of killing Batman alone (and this is being very, very generous and neglecting the individual skills of each rogue for simplicity). You would then think that adding villains to the scheme would increase the probability of killing Batman by 2% with each new rogue. Except, this ignores the economics law of diminishing returns, which states that as you increase the factors of production, the marginal benefit of those factors decreases. Usually, this applies to outcomes which are continuous (such as production of goods) rather than binary (to kill or not to kill Batman), but we can apply diminishing returns in this case to the probabilities. The theory is that as you add villains, working together will prove more difficult and planning more arduous. Therefore, the probability of getting Batman will increase, but by a marginally smaller amount with each villain added.

Thinking of probability as output, let's assume that in each state,
p = 2*y^0.9, where
p = probability of killing batman and
y = number of villains involved in the scheme.

Hence, we have a diminishing returns function. If there is only one villain involved in the scheme, the probability of killing Batman is 2%.

If there are 2 villains involved in the scheme, the probability becomes:
p = 2*(2)^0.9 = 3.73% (the probability increased by 1.73 percentage points)

If there are three villains involved, then:
p = 2*(3)^0.9 = 5.38% (probability increased by 1.65 percentage points)

And so on and so forth. Now armed with the knowledge of probabilities and utilities, let's conduct an analysis of whether it makes sense for the Joker to team up with Two-Face and the Scarecrow. We must analyze the expected utility of each scenario (teaming up and working alone).

First let's calculate the expected utility of working alone for the Joker. The equation is:
EU = p * (Uk) + (1-p)*(Unk) where
EU = expected utility
p = probability of killing Batman
Uk = utility of killing Batman.
Unk = utility of not killing Batman

We know that for the Joker, the utility of killing Batman alone is 10 and the probability of killing Batman by himself is 0.02. Hence:
EU = 0.02*(10) + (0.98)*0 = 0.2
Hence the expected utility of the Joker killing Batman on his own is 0.2.

Now, we analyze the expected utility of the team-up. We know that the probability of the Joker, Two-Face and the Scarecrow killing Batman is 0.0538. The utility would be 3.33 each. Hence:
EU = 0.0538*(3.33) + (0.9462)*0 = 0.179
Hence the expected utility for the Joker of the trio killing Batman is 0.179.