Conflict vs. mistake in non-zero-sum games

Nitpick: I am pretty sure non-zero-sum does not imply a convex Pareto front.

Instead of the lens of negotiation position, one could argue that mistake theorists believe that the Pareto Boundary is convex (which implies that usually maximizing surplus is more important than deciding allocation), while conflict theorists see it as concave (which implies that allocation is the more important factor).

A political example: In March 2020, San Francisco voters approved Proposition E, which limited the amount of new office space that can be built proportionally to the amount of new affordable housing.

This was appealing to voters on Team Affordable Housing who wanted to incentivize Team Office Space to help them build affordable housing.

("Team Affordable Housing" and "Team Office Space" aren't accurate descriptions of the relevant political factions, but they're close enough for this example.)

Team Office Space was able to use the simple mistake-theory argument that fewer limits on building stuff would allow us to have more stuff, which is good.

Team Affordable Housing knew it could build a little affordable housing on its own, but believed it could get more by locking in a favorable allocation early on with the Proposition.

Dear Nisan,

I just found your post via a search engine. I wanted to quickly follow up on your last paragraph, as I have designed and recently published an equilibrium concept that extends superrationality to non-symmetric games (also non-zero-sum). Counterfactuals are at the core of the reasoning (making it non-Nashian in essence), and outcomes are always unique and Pareto-optimal.

I thought that this might be of interest to you? If so, here are the links:

https://www.sciencedirect.com/science/article/abs/pii/S0022249620300183

(public version of the accepted manuscript on https://arxiv.org/abs/1712.05723 )

With colleagues of mine, we also previously published a similar equilibrium concept for games in extensive form (trees). Likewise, it is always unique and Pareto-optimal, but it also always exists. In the extensive form, there is the additional issue of Grandfather's paradoxes and preemption.

https://arxiv.org/abs/1409.6172

And more recently, I found a way to generalize it to any positions in Minkowski spacetime (subsuming all of the above):

https://arxiv.org/abs/1905.04196

Kind regards and have a nice day,

Ghislain

Nice deduction about the relationship between this and conflict vs mistake theory! Similar and complementary to this post is the one I wrote on Moloch and the Pareto optimal frontier [EA · GW].

I liked this article. It presents a novel view on mistake theory vs conflict theory, and a novel view on bargaining.

However, I found the definitions and arguments a bit confusing/inadequate.

Your definitions:

"Let's agree to maximize surplus. Once we agree to that, we can talk about allocation."

"Let's agree on an allocation. Once we do that, we can talk about maximizing surplus."

The wording of the options was quite confusing to me, because it's not immediately clear what "doing something first" and "doing some other thing second" really means.

For example, the original Nash bargaining game works like this:

1. First, everyone simultaneously names their threats. This determines the BATNA (best alternative to negotiated agreement), usually drawn as the origin of the diagram. (Your story assumes a fixed origin is given, in order to make "allocation" and "surplus" well-defined. So you are not addressing this step in the bargaining process. This is a common simplification; EG, the Nash bargaining solution also does not address how the BATNA is chosen.)
2. Second, everyone simultaneously makes demands, IE they state what minimal utility they want in order to accept a deal.
3. If everyone's demands are mutually compatible, everyone gets the utility they demanded (and no more). Otherwise, negotiations break down and everyone plays their BATNA instead.

In the sequential game, threats are "first" and demands are "second". However, because of backward-induction, this means people usually solve the game by solving the demand strategies first and then selecting threats. Once you know how people are going to make demands (once threats are visible), then you know how to strategize about the first step of play.

And, in fact, analysis of the strategy for the Nash bargaining game has focused on the demands step, almost to the exclusion of the threats step.

So, if we represent bargaining as any sequential game (be it the Nash game above, or some other), then order of play is always the opposite of the order in which we think about things.

So when you say:

"Let's agree to maximize surplus. Once we agree to that, we can talk about allocation."

I came up with two very different interpretations:

• Let's arrange our bargaining rules so that we select surplus quantity first, and then select allocation after that. This way of setting up the rules actually focuses our attention first on how we would choose allocation, given different surplus choices (if we reason about the game by backwards induction), therefore focusing our decision-making on allocation, and making our choice of surplus a more trivial consequence of how we reason about allocation strategies.
• Let's arrange our bargaining rules so that we select allocation first, and only after that, decide on surplus. This way of setting up the rules focuses on maximizing surplus, because hopefully no matter which allocation we choose, we will then be able to agree to maximize surplus. (This is true so long as everyone reasons by backward-induction rather than using UDT.)

The text following these definitions seemed to assume the definitions were already clear, so, didn't provide any immediate help clearing up the intended definitions. I had to get all the way to the end of the article to see the overall argument and then think about which you meant.

Your argument seems mostly consistent with "mistake theory = allocation first", focusing negotiations on good surplus, possibly at the expense of allocation. However, you also say the following, which suggests the exact opposite:

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.)

In the end, I settled on  yet-different interpretation of your definition. A mistake theorist believes: maximizing surplus is the more important of the two concerns. Determining allocation is of secondary importance. And a conflict theorist believes the opposite.

This makes you most straightforwardly correct about what mistake theorists and conflict theorists want. Mistake theorists focus on the common good. Conflict theorists focus on the relative size of their cut of the pie.

A quick implication of my definition is that you'll tend to be a conflict theorist if you think the space of possible outcomes is all relatively close to the pareto frontier. (IE, if you think the game is close to a zero-sum one.) You'll be a mistake theorist if you think there is a wide variation in how close to the pareto frontier different solutions are. (EG, if you think there's a lot to be gained, or a lot to lose, for everyone.)

On my theory, mistake theorists will be happy to discuss allocations first, because this virtually guarantees that afterward everyone will agree on the maximum surplus for the chosen allocation. The unsavory mistake theorists you describe are either making a mistake, or being devious (and therefore, sound like secret conflict theorists, tho really it's not a black and white thing).

On the other hand, your housing example [LW(p) · GW(p)] is an example where there's first a precommitment about allocation, but the picture for agreeing on a high surplus afterward don't seem so good. 

I think this is partly because the backward-induction assumption isn't a very good one for humans, who use UDT-like obstinance at times. It's also worth mentioning that choosing between "surplus first" and "allocation first" bargaining isn't a very rich set of choices. Realistically there can be a lot more going on, such that I guess mistake theorists can end up preferring to try to agree on pareto-efficiency first or trying to sort out allocations first, depending on the complexities of the situation. 

These ordering issues seem very confusing to think about, and it seems better to focus on perceived relative importance of allocation vs surplus, instead.

I like this theory. It seems to roughly map to how the distinction works in practice, too. However: Is it true that mistake theorists feel like they'll be in a better negotiating position later, and conflict theorists don't?

Take, for example, a rich venture capitalist and a poor cashier. If we all cooperate to boost the economy 10x, such that the existing distribution is maintained but everyone is 10x richer in real terms... yeah, I guess that would put the cashier in a worse negotiating position relative to the venture capitalist, because they'd have more stuff and hence less to complain about, and their complaining would be seen more as envy and less as righteous protest.

What about two people, one from an oppressor group and one from an oppressed group, in the social justice sense? E.g. man and woman? If everyone gets 10x richer, then arguably that would put the man in a worse negotiating position relative to the woman, because the standard rationales for e.g. gender roles, discrimination, etc. would seem less reasonable: So what if men's sports make more money and thus pouring money into male salaries is a good investment whereas pouring it into female salaries is a money sink? We are all super rich anyway, you can afford to miss out on some profits. (Contrast this with e.g. a farmer in 1932 arguing that his female workers are less strong than the men, and thus do less work, and thus he's gonna pay them less, so he can keep his farm solvent. When starvation or other economic hardships are close at hand, this argument is more appealing.)

More abstractly, it seems to me that the richer we all are, the more "positional" goods matter, intuitively. When we are all starving, things like discrimination and hate speech seem less pressing, compared to when we all have plenty.

Interesting. Those are the first two examples I thought of, and the first one seems to support your theory and the second one seems to contradict it. Not sure what to make of this. My intuitions might be totally wrong of course.

Curated. This is a very simple and useful conceptual point, and such things deserve clear and well-written explanations. Thanks for writing this one.

The point that the ordering of optimisation and allocation phases is important in negotiation is a good one. But as you say, the phases are more often interleaved: the analogy isn't exact, but I'm reminded of pigs playing game theory

I disagree that this maps to mistake / conflict theory very well. For example, I think that a mistake theorist is often claiming that the allocation effects of some policy are not what you think (e.g. rent controls or minimum wage).

So what happens to mistake theorists once they make it to the Pareto frontier?

I think you would need to define your superrational agent more precisely to know what it should do. Is it a selfish utility-maximizer? Can its definition of utility change under any circumstances? Does it care about absolute or relative gains, or does it have some rule for trading off absolute against relative gains? Do the agents in the negotiation have perfect information about the external situation? Do they know each others' decision logic?

suppoesd - should read supposed

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

I think that's very confusing. The relevant distinctions are not in your essay at all - they're about how much each side value's the other side's desires, and whether they think there IS significant difference in sum based on cooperation, and what kinds of repeated interactions are expected.

Your thesis is very biased toward mistake theory, and makes simply wrong assumptions about most of the conflicts that this applies to.

Indeed, the mistake theory strategy pushes the obviously good plan of making things better off for everyone.

No, mistake theorists push the obviously bad plan of letting the opposition control the narrative and destroy any value that might be left. The outgroup is evil, not negotiating in good faith, and it's an error to give them an inch. Conflict theory is the correct one for this decision.

The reason I'm thinking about this is that I want a theory of non-zero-sum games involving counterfactual reasoning and superrationality. It's not clear to me what superrational agents "should" do in general non-zero-sum games.

Wait, shouldn't you want a decision theory (including non-zero-sum games) that maximizes your goals? It probably will include counterfactual reasoning, but may or may not touch on superrationality. In any case, social categorization of conflict is probably the wrong starting point.