Conflict vs. mistake in non-zero-sum games | LessWrong 2.0

Source: Conflict vs. mistake in non-zero-sum games | LessWrong 2.0, by Nisan

Summary: Whether you behave like a mistake theorist or a conflict theorist may depend more on your negotiating position in a non-zero-sum game than on your worldview.

Plot the payoffs in a non-zero-sum two-player game, and you’ll get a set with the Pareto frontier on the top and right. You can describe this set with two parameters: The surplus is how close the outcome is to the Pareto frontier, and the allocation tells you how much the outcome favors player 1 versus player 2.

It’s tempting to decompose the game into two phases: A cooperative phase, where the players coordinate to maximize surplus; and a competitive phase, where the players negotiate how the surplus is allocated.

Of course, in the usual formulation, both phases occur simultaneously. But this suggests a couple of negotiation strategies where you try to make one phase happen before the other:

  1. “Let’s agree to maximize surplus. Once we agree to that, we can talk about allocation.”
  2. “Let’s agree on an allocation. Once we do that, we can talk about maximizing surplus.”

I’m going to provocatively call the first strategy mistake theory, and the second conflict theory.

Now I don’t have a good model of negotiation. But intuitively, it seems that mistake theory is a good strategy if you think you’ll be in a better negotiating position once you move to the Pareto frontier. And conflict theory is a good strategy if you think you’ll be in a worse negotiating position at the Pareto frontier.

If you’re naturally a mistake theorist, this might make conflict theory seem more appealing. Imagine negotiating with a paperclip maximizer over the fate of billions of lives. Mutual cooperation is Pareto efficient, but unappealing. It’s more sensible to threaten defection in order to save a few more human lives, if you can get away with it.

It also makes mistake theory seem unsavory: Apparently mistake theory is about postponing the allocation negotiation until you’re in a comfortable negotiating position. (Or, somewhat better: It’s about tricking the other players into cooperating before they can extract concessions from you.)

This is kind of unfair to mistake theory, which is supposed to be about educating decision-makers on efficient policies and building institutions to enable cooperation. None of that is present in this model.

But I think it describes something important about mistake theory which is usually rounded off to something like “[mistake theorists have] become part of a class that’s more interested in protecting its own privileges than in helping the poor or working for the good of all”.