The Prototypical Negotiation Game

post by johnswentworth · 2021-02-20T21:33:34.195Z · LW · GW · 13 comments

Contents

  The Game
  Powerless Underlings: Intentionally Destroying Communication Channels
  Moving The Schelling Point
None
13 comments

Suppose you want to meet up with someone in New York City. You did not arrange a time and place beforehand, and have no way to communicate. Where and when do you go to maximize your chances of meeting? Empirically, the most popular answer is the Empire State Building, at noon. (Does that change your answer?)

This is the explanation of Schelling points [LW · GW] which I hear most often: there are games where the main goal is for everyone to coordinate on the same answer, but it doesn’t really matter which answer. So, we look for points with some symbolic significance - “Schelling points”.

The message of this post is that this is not the prototypical form of a Schelling-style coordination game which actually comes up most often in the real world. In practice, Schelling points come up when coordinating on the same answer is the most important thing for each player, but they still have different preferences for which answer is chosen. This leads to negotiation - indeed, we could call this the defining property of a negotiation problem. (Abram’s Most Prisoner’s Dilemmas Are Stag Hunts, Most Stag Hunts Are Schelling Problems [LW · GW] says something similar, although the emphasis will be different here.)

The Game

As before, you and a friend want to meet up in New York City. This time you do have a communication channel: you each have a cell phone and the other’s number. BUT you’re both lazy and don’t want to move very far from wherever you happen to be - let’s say you’re at central park zoo and your friend is in chinatown. Successfully meeting up is still far more important than the location chosen, but given a successful meetup, you both disagree on preferred location.

Source. Chinatown is near the bottom, central park zoo is in the lower right of the big park in the center, and the Empire State Building is in the Garment District between the two.

Here’s a few ways this could play out.

Story 1: you and your friend agree to meet at the midpoint of your locations. But in a fit of laziness-inspired brilliance, you lie and claim to be at the far end of central park, rather than the zoo. As a result, the supposed “midpoint” is much closer to you.

Story 2: Same as the previous story, but your friend also lies about their location.

Story 3: Same as previous story, but each of you correctly anticipates that the other will lie and does not believe anything they say. You will both ignore whatever the other says. And so, despite being able to talk to each other, you are effectively unable to communicate. Suddenly, Schelling points like “the Empire State building at noon” become relevant again. It’s relevant precisely because it’s trustworthy - if you both know in advance that the Empire State Building at noon is the natural meetup point, then there’s no room to lie about it.

This is the sort of game where Schelling points typically become relevant in the real world. It’s a negotiation game: both players care more about reaching an agreement than about which specific agreement is reached. But they still have different preferences about which possible agreement is reached, so there’s competition over it. The relevance of Schelling points comes in, not from a lack of communication channels, but from a lack of trust. If nobody believes what the others say, then we can only coordinate on “natural” agreements in which there’s no degrees of freedom which could be shifted by strategically lying.

Let’s look at a couple other ways this could play out.

Powerless Underlings: Intentionally Destroying Communication Channels

Suppose a merchant is selling an “I ❤ NY” t-shirt, and you want to buy it. The maximum price you’d be willing to pay is higher than the minimum price they’d be willing to accept, but you still generally prefer a lower price and they generally prefer a higher price. It’s a prototypical negotiation game: you both care most about reaching an agreement on the price, but you have different preferences about which price is agreed upon.

So, you haggle. The prototypical negotiation game leads to a prototypical negotiation. Round-number prices likely serve as Schelling points, but there are other moves one can make as well.

One of the most common moves in this kind of game is to intentionally destroy a communication channel.

In our “meet up in NYC” example from earlier, you could text your friend “phone dying, meet at central park zoo” and then turn off your phone. You’ve declared a meetup point, and destroyed their ability to negotiate it by destroying the communication channel.

The analogous move for a t-shirt merchant is to hire an underling to run the store. The underlying has no power to negotiate prices - indeed, that’s exactly the point. If someone tries to haggle, they say “sorry but I’m not allowed to change the prices”. If someone asks to speak to the owner, they say “sorry but the owner won’t be here until this evening”, or better yet “sorry but I’ve never even met the owner, this is a huge national chain”.

Of course, the trade-off of this strategy is that the merchant will miss the opportunity to sell a t-shirt to someone who’s willing to pay just a bit less than the merchant’s listed price. No haggling means few opportunities for price discrimination. But as long as customers aren’t too price-sensitive, the underling is a useful strategy.

… and that’s why you can’t haggle with store clerks. In another world, where offering different prices to different customers is more profitable than always charging a high price (and sometimes missing out on sales), maybe store clerks would haggle and get paid based on how high a price they can get, much like car salesmen.

Moving The Schelling Point

Imagine that the “meetup in NYC” game happened a lot more often, between a lot more people. People from one end of the city were constantly meeting up with people from the other end, and a negotiation game played out every time. Then there’d be a lot of incentive to move the Schelling point.

Physically moving the Empire State building would be one way to do this, in principle, though very difficult. (In other games, physically moving an existing Schelling point is more plausible - see e.g. Parable Of The Dammed [LW · GW].)  Alternatively, a bunch of people could fund construction of an even taller building closer to their end of the city. In an extreme case, we could get a runaway arms race of people from both ends of the city building ever-taller buildings closer to their end.

Another strategy would be to put up a billboard saying “Meet up here!”, and run advertisements for the new meetup point, and have everyone on your end of the city put up social media posts about how Everyone Should Meet At The Meetup Billboard Or They Are Terrible.

… which brings us to norms and culture wars.

Norms are a many-player negotiation problem. Disagreements over norms are unpleasant for everyone involved: you violate something I thought was a norm, I punish you for it, you respond with righteous indignation at this unfair punishment for violating something you did not think was a norm, punish me back, quite possibly the whole thing escalates… unpleasant for everyone. Most people most of the time want to agree on norms, whatever they happen to be, and move on with their lives. But we still have different preferences over what the norms should be. For instance, what things should or should not be considered “acceptable” to say in public (i.e. what speech will or will not be punished, or which punishments will or will not themselves be punished)?

The resulting norms are Schelling points: people follow the norms which everyone else follows. And they can be moved around the same way one normally moves around Schelling points.

… so when you see someone posting on social media about how People Who Don’t Follow Norm X Are Terrible, that is actually a substantive move in the game. It’s just like running an ad for a particular meetup point. And of course, people who want some other norms to be the Schelling point will run opposing ads, and sometimes the whole thing will turn into an arms race.

13 comments

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comment by Raemon · 2021-02-20T22:29:26.134Z · LW(p) · GW(p)

I first feel motivated to make completely pedantic points on the examples. (I'll hopefully have something substantive to say about the actual implications later)

On "the most popular answer is Empire State Building", I've heard a few people say this and it's different from what Thomas Schelling says in Strategy of Conflict (most people said "The information booth at grand central station"). Curious if there was a particular followup study with a different answer.

Also, I think the Empire State Building is actually a tempting but demonstrably wrong answer. People who attempt to do this will regret having done so, and wish they and their partner had chosen the Grand Central Information booth. This is because the Empire State Building is big, it's actually pretty hard to find each other in it. You can go to the top level observation deck where your attention is focused a bit better, but a) it costs something like $30, b) I'm not even sure if you can get there on a given day without buying tickets in advance. (I know that to get to the Statue of Liberty you have to reserve a spot weeks or months in advance)

By contrast, Grand Central station's information booth is not only very iconic, and a narrow spot where it's very easy to find other people, but New York City is quite literally designed to get you there. Whether you're in some random place in Manhattan, or the Bronx, or even upstate New York, there's a lot of infrastructure that make it really easy to get to the information booth.

(Penn Station is an option that you should consider, because there's also a lot of infrastructure pointed there. But Penn Station is huge, and has at least two areas that you might consider the precise schelling point. I've seen people literally try to coordinate on meeting up at Penn Station with communication allowed, and fail, because they had different guesses about where the Schelling Point was. Times Square is another obvious choice and I think it's better than Penn Station but still much worse than Grand Central at focusing all of your attention to a single spot.)

If you don't live in NYC and don't know about all the transportation infrastructure, you might end up having to pick Empire State Building because you don't know any better. But, while you're traveling there, there's a good chance you'll bump into the Grand Central information booth, and I think it might even be possible and advisable to figure out that that's the real Schelling Point and switch strategy. (BUT! If you arrive at NYC by bus, you'd end up at Penn Station, and you might also be tempted to notice one of the Big Boards at Penn as a plausible schelling point and switch strategy, and you'd be wrong. I think the Grand Central Booth is visibly more Schelling than the Big Boards at Penn but I don't trust my original seeing on it)

(If you live in NYC, and are having to play this game with someone who's never been to NYC,  and if it turns out that yes empirically most outsiders say "Empire State Building", I'm not sure)

...

Meanwhile, even more pedantically, but there are now multiple buildings taller than the Empire State building which clearly didn't become the new schelling point, so that strategy empirically* doesn't actually work.

*I just now notice and wonder that Empire and empiric sure look like similar words and am wondering what's up with that.

Replies from: gjm, Zvi, johnswentworth
comment by gjm · 2021-02-21T00:52:04.342Z · LW(p) · GW(p)

I think "empire" and "empirical" have less to do with one another than one would guess, but ultimately there is (probably) a connection.

"empire" and "emperor" of course comes from Latin "imperium" and "imperator", from "imperare" to command. (Harry Potter fans may wish to know that the first person singular indicative active form is "impero", not "imperio" :-).)

"empirical" comes from Greek "empeiria" meaning "experience".

So I guess the question is whether "imperare" is related to "empeiria" somehow. Well, yes and no. It appears that "imperare" is from "in" (preposition) + "parare" (to prepare), whereas "empeiria" is from "en" (preposition) + "peira" (a trial or attempt). Greek "en" is the equivalent of Latin "in", so the initial bits are indeed the same.

But what about "parare" and "peira"? Those are words with quite different meanings. But they are both thought to come from PIE *per-, which has a number of meanings (note: all this stuff is conjecture, but not my conjecture). Oldest seems to be something like "first" or "front" -- we get "first" from this, and "pre-", and all sorts of other things. That seems to have given rise to "go through", "carry forth", etc., which is where "paro" comes from. And that seems to have given rise to "try", "dare", "risk", etc., which is where "peira" comes from.

So the (partly conjectural) tree looks like this. Conjectured bits are in square brackets.

  • [PIE *per-, meaning things like "first" and "front"]
    • [PIE *per-, meaning things like "bring out"]
      • Latin paro, meaning "prepare"
        • Latin impero, meaning "command"
          • Latin imperium and imperator
            • English empire and emperor
      • [PIE *per-, meaning things like "try"]
        • Greek peira, meaning "trial" and "attempt"
          • Greek empeiria, meaning "experience"
            • Greek empeirikos, meaning "empirical"
              • English empirical

If you believe the PIE reconstructions then there is a common origin. But as far as actually known words goes, the oldest we've got is "paro", prepare, and "peira", attempt, and it's not obvious prima facie that those are actually related.

comment by Zvi · 2021-02-23T20:38:47.319Z · LW(p) · GW(p)

The Shilling Point in NYC is, as I have always understood it, indeed the clock (aka the information booth) at Grand Central. It's a much, much better choice than the ESB, and also what I expect others to expect here. Epistemic Status is "This Is Known" and this extends to the degree that I will literally say "Meet at the Schilling Point" when I want to indicate that's where we are meeting, which is not that uncommon as it often makes a lot of sense, and the majority of the time no one asks where I meant by that.

(Yes, Penn Station's train times display and Times Square itself are in theory possible but can confirm that they're both objectively terrible, and worse at the job we're proposing.)

Agreed that in theory ESB is on the board but I would be pretty shocked if someone actually went there.

Replies from: Raemon
comment by Raemon · 2021-02-23T20:44:50.058Z · LW(p) · GW(p)

The Shilling Point in NYC

This not the first time you've spelled "Schelling Point" "Schilling point" and I'm curious if that's some kind of on-purpose thing or just a misspelling you happen to do by accident a lot?

comment by johnswentworth · 2021-02-20T23:04:14.060Z · LW(p) · GW(p)

The "Schelling points depend on who you're playing with" essay is a different essay than this one, and Grand Central vs Empire State is an excellent example for that essay.

But this is a particularly interesting point which I will dive into a bit more:

... there are now multiple buildings taller than the Empire State building which clearly didn't become the new schelling point, so that strategy empirically* doesn't actually work.

The key point here is that most people who aren't from the New York area probably don't know that it isn't the tallest building any more. And for Schelling point purposes, people knowing is all that matters. Just building a new tallest building isn't enough, one also has to spread the word that there's a new tallest building. Run ads, post on social media, all that jazz.

On the other hand, if one has to run ads and post on social media and all that jazz anyway, then the "Meet up here!" billboard starts to look like a more attractive option. Tallest building location doesn't become relevant until there's multiple competing billboards with competing ads, so nobody trusts the billboards anymore.

Replies from: Raemon
comment by Raemon · 2021-02-21T00:47:06.296Z · LW(p) · GW(p)

I feel like people knew the Twin Towers were taller? And probably also that the Freedom Tower is taller? The latter certainly had a lot of publicity (for reasons that are probably at least somewhat related to the points in this post, albeit a few abstractions removed)

Replies from: Yoav Ravid, Raemon
comment by Yoav Ravid · 2021-02-21T06:48:53.438Z · LW(p) · GW(p)

As a foreigner i have a vague hunch that it's probably no longer the tallest (cause come on, it can't be for that long, right?), but there isn't a different building I'm aware of that i would pick as probably taller.

comment by Raemon · 2021-02-21T00:49:27.555Z · LW(p) · GW(p)

People probably do start paying less attention as more Big Tall buildings are made, because it gets less interesting the more you do it. But I also think the Freedom Tower has basically all the advantages a Schelling point could have in terms and if publicity and narrative cohesion.

comment by Sherrinford · 2021-02-22T10:31:35.674Z · LW(p) · GW(p)

This is a nice post about an interesting topic. I think it may be helpful to mention that several of these points are discussed extensively in economics, polsci and game theory, though sometimes with a different vocabulary. (But maybe it is somehow intentional to not mention that, in order to keep the post shorter?)

  • "Successfully meeting up is still far more important than the location chosen, but given a successful meetup, you both disagree on preferred location." This resembles the BoS game.
  • In the section "Powerless Underlings: Intentionally Destroying Communication Channels", I like the idea of destroying communication channels after leaving a coordination message and find it an original idea. The store-clerk example could benefit from mentioning that there is a large literature on optimal delegation, for instance to a bureaucratic agent. This includes models of delegation as a commitment device, also modeling how much leeway you should leave to the agent you delegate to. Sometimes it makes sense to delegate to agents with preferences different from your own. In the 1980s that was the reason modeled in the literature on conservative central bankers. There are also papers on delegating the authority to bargain for you, I think I have seen that in the context of climate change papers.

Another point is that I think it would be helpful to define what exactly you call "negotiation game" more explicitly. Intuitively, I would say that the original usage of the term "Schelling point" or "focal point" suggests that it should be possible to write it down as a simultaneous-move game, and I don't think that applies to every kind of negotiation (but I am no expert on how the term is used).

Replies from: johnswentworth
comment by johnswentworth · 2021-02-22T16:55:48.286Z · LW(p) · GW(p)

But maybe it is somehow intentional to not mention that, in order to keep the post shorter?

Yup, exactly. I was hoping someone would mention it in the comments, so thank you.

comment by Timothy Johnson (timothy-johnson) · 2021-02-22T10:14:44.303Z · LW(p) · GW(p)

"...and that’s why you can’t haggle with store clerks."

That is the norm, at least in the US. But a friend of mine worked at Macy's, and she said customers would occasionally try to negotiate prices. They were often successful.

A quick search online found that it's possible to haggle at a lot more places than I had realized: 11 Retailers Where You Can Negotiate a Lower Price (wisebread.com).

I consider this somewhat ethically dubious, though. If the clerks are paid hourly, they don't have their own "skin in the game," so there's no way to have a fair negotiation.

comment by Liron · 2021-02-21T20:59:22.655Z · LW(p) · GW(p)

Upvoted for providing an important deepening of the popular understanding of “Schelling point”