#thomas schelling

Imagine you had to meet someone in New York City. You couldn’t communicate with them in advance; you only knew that you had to meet them somewhere in the city at some point on a particular day. Where and when would you choose to go, in order to maximize the chances of meeting them?

The economist and game theorist Thomas Schelling posed this question to students. The most common answer given by them was to meet at 12pm by the information desk at Grand Central station. It’s not that 12pm is a particularly useful time to meet, or that Grand Central station is a particularly useful place – you could easily rattle off a list of a hundred other places that are equally suitable. But in trying to pick a point, you’re trying to guess what other people might pick. 12pm feels like a particularly salient time, and Grand Central station feels like a particularly salient place to meet people. It feels like what other people will pick, and so it’s what you should pick.

[...]

These focal points, points around which people can organize and coordinate even without communicating with one another, are called Schelling points after Thomas Schelling. They’re a great example of how human beings can coordinate their actions even without communication, as a result of the mental models they have about other people’s behavior.

Schelling points are a useful tool for thinking about organizations. They help us to think about what people do, and where they go, in the absence of communication.

Imagine you’re working in a professional services business with lots of clients. You want to know what the latest developments are on a particular project. Where do you go? Clearly, you could solve this problem with communication. You’re not in the artificial environment of an academic experiment; you can just go and ask the person who’s leading the project, and they’ll give you an update. But that’s slow, and interrupts them, and means you need to wait on a reply. It also scales very poorly – what if that person is getting ten people asking them for updates every day? Coordination that requires communication is costly, and so it’s still worth exploring solutions that don’t involve communication.

If you have a system that everyone uses, and that provides an obvious and salient summary of projects, then that will become the place people working on projects will post their updates, and it will become the place people wanting to check on those projects will go to check on them. People will use it without having to communicate with one another. You will have created a Schelling point, a way for people to coordinate without communicating.

A big shared drive full of random documents tends to lack Schelling points; a more structured knowledge base is more likely to grow them. A clearly structured and easy-to-navigate website will develop popular Schelling points; a jumbled-up one won’t. Schelling points can be deliberately designed, can be consciously built into tools, and can be strengthened by the consistent use of those tools.

Ultimately, though, Schelling points are effective because of social norms. I know what’s salient to me, and I know what’s salient to you; we share an understanding of the world, and that allows us to converge on something without communication. Nobody designed Grand Central station as a Schelling point; it just is one, as a result of an unknowable emergent process within our collective psyche.

Schelling points, then, are enormously powerful. They allow for people to coordinate without communicating, even in enormously large organizations. They can be designed thoughtfully into processes to make them more effective.

But there’s a danger to them, too. Schelling points can be accidental as well as designed, and they’re also self-strengthening: the more people coordinate around a single point, the more plausible that point is as a choice, and so the more people will coordinate around it, and so on. Schelling points emerge whether we like it or not, and can prove stubbornly hard to displace. We are as much the prisoners of them as we are the designers of them; we’ll likely still be meeting people in Grand Central station for many years to come.

1.

Schelling defines games of strategy as any situation in which each player's best choice of action depends on the actions (he expects) the other player will take (and vice-versa, reflexively). This is in contrast to games of skill and games of chance. "Strategy," then, is the study of conflicting parties' behaviors as they are premised on "the interdependence of the adversaries' decisions and on their expectations about each others' behaviors."

We will call "script" a set of moves, from start to end, across a game. Games of strategy are definitionally marked by their lack of a player-independent & globally optimal ("PIG-optimal") script—that is, a script which will produce the best possible outcome in every game against every possible player.

(Or at the very least, these games of strategy have not had their PIG-optimal strategy discovered yet, so a successful move, or script, is functionally indexical—"indexical" as in, "player and context-dependent.")

When moves are indexical, it means that their efficacy depends on the opponent's future move(s). In "Rock, Paper, Scissors," no single move is PIG-optimal. The efficacy of playing "rock" fully depends on whether the opponent will play rock (resulting in stalemate), paper (defeat), or scissors (victory).

2.

Strategy games span a continuum between cooperative and adversarial.

In games tending toward the cooperative side, it behooves players to be legible, and thus predictable. This is because, if any individual player's best move depends on other players' next move(s), then Pareto optimal aggregate play among all players requires players perfectly anticipating each other (so they are each, individually, able to make the best move dependent on each other). In a cooperative game of Rock, Paper, Scissors where winning consisted of matching moves (e.g. two rocks, two papers, etc), it behooves players to get into a rhythm, to repeat themselves, etc.

This goes some way, I think, toward explaining social customs and conventions, the inculcation of habit. It is a pro-social gesture to be legible, insofar as it allows other players in a social space to optimize around you. This reciprocal self-legibilizing allows for spontaneous organization, where sophisticated behavioral patterns emerge in e.g. conversational turn-taking, team sports, drivers who efficiently and safely manage an intersection with a broken traffic light, etc. Meanwhile, those who are unpredictable or illegible are "creepy," "unsettling," etc...

(Convention—settling on a shared script—is also computationally tractable, whereas assessing other players' next move in order to make your next move, when their move depends on their assessment of your next move, which depends on... is an NP-hard recursive problem. More on this soon.)

In games tending toward the adversarial side, it behooves players to be illegible, and thus unpredictable. This is because, if any individual player's move efficacy depends on his opponent's next move(s), then that player is disadvantaged if his opponent can anticipate, and thus thwart, his choice. For a competent opponent to know that he is about to play "rock" is equivalent to losing. So long as he can be anticipated, he cannot win, because in a game like Rock Paper Scissors, moves are fully indexical in their "quality" or efficacy. There is no "better" or "worse" move in a vacuum; only better or worse moves given an opponent's move.

Another high-level strategy, for adversarial games, is what I'll call "pseudo-legibility." This approach involves setting up an opponent expectation, by intentionally leaking information, or displaying a pattern, during low-stakes rounds of the game. Then, when a high-stakes round approaches, the player "cashes out" by breaking his pattern. Here he has flipped the script: by making himself appear predictable, he has in actuality made his opponent predictable.

For instance, a poker player may feign a tell, and then display that tell several times during small pots. Later in the game, when a large pots (and a good hand) comes around, he can once again display the tell, and lead his opponent to believe he is bluffing. At this point, he can just "take his opponent's money": he can "play" him by ratcheting up the bet and clearing house.

3.

Note that there is in some sense a player-independent optimal strategy for Rock, Paper, Scissors, which is pure randomness. The problem is that pure randomness will secure a lower win percentage against sub-optimal players than a player-dependent strategy would have. Randomness is only "optimal" in that, if one has no idea who his opponent is, it is the optimal strategy. We will call this a player-blind optimal strategy, or PB-optimal. In a one-round game of Rock, Paper, Scissors against an anonymous opponent—or in a multi-round, blindfolded game, where neither player learns their opponent's moves (and by extension, the outcome of the round) until all rounds are over—pure randomness is the most effective strategy.

(This has something to do with "exploitability"—@natural-hazard has written that "Traditional game theory sacrifices any plausible yet uncertain edge you might have for the guarantee that you will never be taken advantage of." But I have yet to integrate this concept of exploitability into my broader understanding.)

One interesting property of PB-optimal strategies is that they are also the optimal strategies when playing against other PB-optimal players. That is, the PB-optimal strategy becomes more and more effective the better the players one is competing against. In a tournament of professional Rock, Paper, Scissors players, winners would be those best at cognitively simulating randomness. In a tournament of amateur Rock, Paper, Scissors players, winners would be those best at reading their opponents, at "playing the player."

(Also, in some meaningful sense, winners would be playing the room: If, thus far in the tournament, you've noticed that players are rock-heavy, you might be inclined to play paper OR, alternatively, hypothesize that, since other players have thus far had outsized success—premium returns—on playing paper, then a preference for scissors may be a successful tactic.)

4.

Playing the player involves what we can call generalized reading. There are conceptual reasons to call it this, but the idea is bone-achingly simple: to play a player—to recognize his patterns and regularities, in order to exploit them—one must interpret the player. Look for clues, watch his face for tells, pay attention to how he responds to certain moves, or what biases or preferences exist in his play. And inevitably, if one plays with patterns, then these patterns are on display—all moves are publicly visible in their entirety by both players. One cannot play "rock" while hiding that one is playing rock. In this sense, information inevitably "leaks" in the process of play.

PB-optimal play, in other words, becomes optimal when player moves do not leak information. Only in the "blinded" version of Rock, Paper, Scissors can one "play rock" while hiding "playing rock."

In a game like Rock, Paper, Scissors, virtually all players are equally competent at selecting and deploying moves, conditioned on knowing what their opponent will play. (Each player knows rock beats scissors, scissors paper, paper rock. And each player is equally physically competent at using a given move; there is no level of skill that bars them from countering rock with paper.) Therefore, success in the game is one-to-one with success at anticipating one's opponent. This makes it an extreme case of strategic indexicality, the property of strategies depending on opponent strategy. But there is always, in games of strategies, an element of indexicality to a given move's efficacy—otherwise it would not be a game of strategy, it would have a PIG-optimal solution.

Randomness is PB-optimal insofar as it prevents the opponent predicting, at a rate higher than 1/3, what move one will play next. Illegibility is chosen deliberately as a descriptive term here: one cannot be "read" by one's opponent, when one plays randomly; there is no pattern to pull out of gameplay. It is ironic, and perhaps deeply important, that the strategy which is optimal when blindfolded is also the strategy which blindfolds (one's opponent.)

Pseudo-legibility, then, is a strategy of generalized writing. Insofar as your opponent is basing his moves on what he predicts you will do, and he is making predictions based on his interpretations of your previous play (including e.g. body language), then it is advantageous to present him with a false reading, a false interpretation. By planting such a false reading in his mind, one can thereby begin predicting his behavior while simultaneously remaining unpredictable oneself.

This occurs in situations of mixed conflict and coordination. When one feels like they have been "led on," or that they operated under a false impression, they feel they have been "played." They believed the Other was presenting—pro-socially and honestly—a certain pattern, and thus presented their own pattern pro-socially and honestly. This makes them manipulable to the Other, while the Other remains un-manipulable to them. (Because the Other's real patterns are unknown.)

5.

Strategy games get weirdly recursive, in their induction patterns, because one is not modeling what "is" but what their opponent believes. Simultaneously, the opponent is modeling what his opponent believes. Thus, one must model what one's opponent believes one believes one's opponent believes... etc. The "level" at which this mutual modeling bottoms out matters quite a bit, insofar as a player who is thinking too many "levels" deep will mis-model his opponent.

In this sense, strategy games share many structural similarities with Keynesian Beauty Contests, the world of fashion, stock bubbles, sexual fitness etc. A female of a species inclined to find those males handsome which other females find handsome is, in some sense, looking for genetics that will produce a sexually desirable offspring, to the extent that the sexual taste of females in her offspring's generation can be modeled via the sexual taste of females in her generation.

Hyperstition is at its most effective in such systems. The difficult part is breaking inertia, giving the meme a kick-start. But once it picks up momentum, this momentum builds via the positive feedback loops of a Matthew Effect. The meme goes "viral." This is known as runaway selection, and it can come at the cost of an organism's non-sexual fitness. That is, in optimizing for some intra-species game, it becomes less optimized for the inter-species game. Which, of course, is the opposite of how these things are "supposed" to work.

I think a lot of the work that human beings are up to is basically about self-representing future states. Schelling talks about what strategy is in The Strategy of Conflict: basically, it’s mutual anticipation. Because your actions (and your future actions) are going to change the environment in which my own decisions and actions exist. That means that if I want to optimize my own future, then I need to anticipate yours.

He calls tacit bargaining a situation where two sides with some conflicting and some mutual interests are playing a variable sum game and they act on the basis of what they think the other party is going to do, which is in turn influenced by what the other party does, and so on recursively. A classic example is Rock-Paper-Scissors:

I played rock last move, so they know I know I’m not going to play rock again, because I lost last turn. So they know not to use paper. They’re going to play either rock or scissors. And then, obviously, if that’s a common pattern, I’m going to think about how you might be thinking that’s the strategy I’ll take, etc.

This is commonplace in everyday strategy games, it’s basically just predictive processing meets theory of mind.

Say person A and person B are walking down the sidewalk in opposite directions, approaching each other on a narrow path. They’re definitely going run into each other soon if they keep walking forward. One strategy is to “perform obliviousness”, as Kenneth Liberman calls it. (We might also think of it as "performing dominance" or expressing a strong preference for non-adjustment.) You basically act as if you don’t know or care I’m there, you’re not changing course. If person A is performing obliviousness, then person B can say “You know what, I know what your path is. Let me just slip to the side and then we’re both fine, we won’t run into each other.” But as soon as you get into the more recursive modeling, e.g. Person A looks at Person B while they’re still thinking and thinks: “Wait, is Person B also performing obliviousness?” and decides to be more reactive, then you end-up in this weird side-to-side shuffle. For instance, you’re ten yards apart, you’re both going back and forth horizontally, getting in each others’ way. It’s in both your interests to get out of each others’s way, but it’s in each of your interest to not move or to move the least. Lot’s of reasons that might be—laziness, energy expenditure minimization, or even status games.

What this comes down to is that Person A, who’s performing obliviousness, is broadcasting a self-representation of a future state. Doing this allows other agents to organize around them, to coordinate more effectively.

A similar example is playing “Chicken”. Let’s say you’re driving towards another car, betting on who’s going to turn away first. If you throw your steering wheel out the window or spray paint over your windshield in advance, there is no way to steer or react in time, respectively. You’ve self-bound to a course of action. Your opponent no longer has a choice, if they don’t turn away, the two cars will crash. You know that your opponent is a rational agent, or at least rational enough to want to live. So you’ve won. Your opponent has to get out of the way, because they know for a fact that you won’t. It’s better for them to lose face then run into you and die. You’ve established a single Schelling point, a single outcome the system will coordinate to if no further communication or changes can take place.

I create this self-representation, I broadcast it, and then we optimize around a shared future reality that I’ve created. Problems emerge because humans can represent one way and act another way. There’s nothing inherently binding about language. I think that’s really interesting—it’s what optikratics and self-deception is all about.

When you throw your steering wheel out the window, you’ve self-bound. There’s a physical limitation on what you can do now. If the other person driving towards you can see that self-binding of futures then they know you just can’t make another decision, even if it would rational, even if it would be better for you to get out of the way at the very last second. You can’t make the decision anymore. You’ve said: I win or bust.

You’re essentially making a tradeoff: I’m going to sacrifice some still good, but not quite optimal futures, like veering away first in the game of Chicken. I’m going to throw my steering wheel out the window and sacrifice these not-bad futures, for the most optimal future: the one where I win and don’t die. You can put all your eggs in one basket, put all your resources into achieving the optimal outcome. But problems emerge: you can represent things one way, but act in another. Consider the theatrical effect of throwing out a dummy steering wheel and making sure the real one wasn’t visible through a heavily tinted windshield.

Schelling talks about how different it would be if you had a society where you could linguistically invoke an oath, e.g. to God. Imagine a society full of perfectly rational, hell-fearing individuals. Invoking an oath to God is perfectly binding because nothing is worse than an eternity of damnation. In such a society there’d be no such thing as boring. I’d say “I swear to God, I won’t pay more than $16k for this car.” Now the salesman can take it or leave it. Normally, there’s a whole range. Let’s say the car costs the salesman $12k wholesale. Let’s say it’s worth $20k to me. So any sale between $12k and $20k is going to be mutually beneficial—kind of like getting out of the way in Chicken. It’s a positive sum game, so it’s better to negotiate than stalemate. A stalemate here would mean the seller doesn’t make any money and I don’t get a car.

Schelling talks about how conflict is not just about conflicting interests, they have a whole base of mutual interests and then some conflicting interests. Other than wars of total annihilation, there’s no such thing as pure conflict. In this case it’s clear: the seller wants money and the buyer (me), wants a car. For anything between $12k and $20k there’s mutual interest, but the settling point of the negotiation has a lot to do with bargaining power. If one party considers the other rational, then they have to somehow convince the other party that they won’t go lower or higher. If the seller thinks they’re dealing with a rational buyer, who’s interest it is to buy at $12k, then the seller has to somehow convince the buyer that he won’t go that low. The buyer has to show that he won’t buy at $20k even though it’s still in his interests, in order to get the best deal possible. In essence, you’re approximating the swear-on-God technology that would allow you demonstrate you won’t buy at a given price.

This makes me think about Blockchain, because Blockchain smart contracts are a form of self-binding. Without Blockchain, though, I can still go to a 3rd-party and say “Hey, if I pay more than $16k for the car, then I’m going to owe you $10k.” and sign a formal legal document to this effect. You bring a copy of your little legal agreement to the car seller, with the proper documentation to confirm its legal authority. Now the seller has to basically take $16k or leave it. (Note that we’re assuming there aren’t any other buyers in this ideal situation.) Basically, the seller is going to take the $16k unless he’s got more than $16k worth of spite, because he has perfect evidence that you’re not going to go higher than that. (If he’s got more than $16k worth of spite he’ll tell you to fuck-off with your fancy third-party leveraging strategies.)

I think a lot of human behavior comes down to this self-legibilizing process. The way you dress, the way you behave, the patterns of conversation you engage in all assert this. We think of manipulation as distorting someone’s priors so they’ll act a certain way. You could also distort their values, but values are harder to budge than priors in general. Values often exist independent of facts and are usually ingrained. It’s much easier to say “You thought these guys were the good guys, but they screwed you over, and I’m going to exploit your already-existing belief in Justice.” The general background notion of justice we often lay-claim to is likely just biological priors that were selected for certain kinds of cooperation.

A lot of manipulation happens by distorting someone’s impression of you. An impression is just a sense of how someone is going to behave. If you have a sense of how someone else is going to behave, then you can say, “You know what, I can behave this way, which has consequence X for the other party, because I know they’re not going to get too mad at me. Or they’re not going to burn the bridge. Or they’re going to be fair about it if I present them with this problem.” For example, if you know how mad a landlord will get with you for a breaking a certain rule, that influences if (or how often) you might choose to break it.

We constantly want to do things that rely on predicting the behaviors of others. I want to know that you’re going to wire me back this money, because you really are an exotic prince who just happens to be in a really bad situation. That’s a dramatic example, but the world is full of examples where manipulation matters: our sidewalk example from earlier, negotiating salaries, or even micro-behaviors like doing the dishes. You do the dishes because you think it’ll strain the relationship between you and your roommate if you don’t. If your roommate gets upset regularly then their actions create a model in your head of how they’re going to act that can be strategically deployed. Knowing that in the future your roommate is going to get mad if you don’t do the dishes means it’s now in your interest to do the dishes, or that you can use them as payback if revenge is what you’re after.

U.S. Navy/Michael Williams Thomas Schelling, an influential figure in economics and strategic theory, made groundbreaking contributions to the understanding of conflict and bargaining in the 20th century. Born in 1921, Schelling was a Nobel laureate economist whose work spanned several areas of strategic thinking, particularly in the domains of nuclear deterrence and conflict resolution. His…

... it’s the logic of Chicken. But the eventual result may be something no sane person wants: a car crash. In May’s recent speech, she set out her willingness to risk such a crash by saying she might walk away without a deal. That does make some sense: it’s how you act if you want to win a game of Chicken. But there are games of Chicken that nobody wins.

That leads to a second insight from Schelling: the difference between deterrence and what he called “compellence”. Deterrence dissuades action, but compellence means persuading or threatening someone so that they do act. In his 1984 book Choice and Consequence Schelling pointed out that deterrence is easier. A deterred person does nothing, so need not admit that the deterrence worked, but a compelled person must visibly acquiesce.