What would happen if the Joker studied macroeconomics to decide whether to team up with Two-Face or go it alone? An economist known only as ShadowBanker has posted an analysis of the merits and drawbacks of supervillain team-ups, with charts.
Apparently, the Joker would have to be crazy to team up with other Bat-adversaries, as he regularly does in the comics, especially those written by Jeph Loeb. After all, the Joker's satisfaction in defeating Batman goes down the more people are involved, because he derives maximum satisfaction from disposing of Bats himself. (Assuming the Joker actually wants to kill Batman, which isn't really his goal anyway.) Of course, the Joker's chances of defeating Batman go up if he collaborates with other villains — but then the law of diminishing returns kicks in, so each extra villain you add to the scenario only increases the Joker's effectiveness by a small percentage.
In a second blog post, ShadowBanker (who appears to be smarter than a lot of non-shadow bankers) examines a scenario where two or more Bat-villains team up and actually succeed in defeating Batman. Is it in their interest to betray each other? Answering this question requires game theory, the prisoner's dilemma, and a chart showing how Mr. Freeze and Two-Face can maximize their utility. (Short answer: each villain comes out on top if he betrays the other... but not if they both betray each other.)
If only Gotham City's nastiest actually thought about the prisoner's dilemma before they decided to work with Hush or Black Mask. Someone needs to toss Brad DeLong into a vat of chemicals so he can smarten those rogues up.