The Prototypical Negotiation Game

johnswentworth20 Feb 2021 21:33 UTC
97 points
16 comments5 min readLW link1 review

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 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 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.) 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.

johnswentworth20 Feb 2021 21:33 UTC
97 points
16 comments5 min readLW link1 review