First, we have to make certain assumptions. Specifically, we need to assign probabilities of capturing Batman and figure out how much these probabilities increase due to the addition of a new cooperating villain. We also need to assign utility values for the Joker for each scenario. Let’s start with utilities.
For not killing Batman, we can obviously assign the Joker a utility of 0.
For capturing Batman on his own, let’s assign the Joker a utility of 10.
For capturing Batman with the help of x other villains, the utility would be 10/x
The last one is sort of tricky. This means that if the Joker cooperates with one other villain (say Two-Face) and together they manage to kill Batman, then the utility for each would be 5. In effect, this means that the villains “split” the utility of 10.
University Economics would’ve been waaaay more fun if we’d been using Batman.