(This blog is partially a response to/ built on the portion of this essay covering Stag Hunts and White/ Black Knights.)

When we’re making models of the world we want to simplify things as much as possible. But if you simplify things too much your model is no good anymore. “Too much” is relative, of course. Maybe you built a simplified model for Use Case <A> where it functions perfectly, but when you tried using the same model for a new Use Case <B> it breaks catastrophically. Hopefully you recognize the mistake that’s occuring before too much damage is done.

I think something like this is going on when we talk about “cooperate v. defect” or “stag v. rabbit”. These game theoretic models are great for some rough-and-dirty theorizing about social interactions, but once you try applying it to real life situations you’ll find that 90% of your interactions are… somewhere BETWEEN cooperate and defect.

(Yeah, yeah. The world’s not black and white, man. Everything is grey. We should all stop with that dichotomous thinking…. Obviously nothing I’m saying here is new.  Also, I assume were I to study game theory I’d find lots of pre-existing examples of games-with-neutral-options. But whatever they are I’ve never seen them discussed in online discourse, so…. )

You might not explicitly think “Let me apply this overly simplistic model to this complex situation,” but when the simplistic model is just the way that interactions are always discussed then it worms its way into your psyche like Jodan Peterson’s version of Christianity.

Trying to map real-life social interactions onto a bimodal distribution can bite you in the ass. You lower your bar for what counts as “cooperate” when the only other option is “defect”. You get upset at people who are acting neutrally, because if they’re not cooperating, they must be defecting.

In our mental models, if not our game theoretic ones, I propose we actively try to consider a “neutral” category that exists BETWEEN cooperate and defect, stag and rabbit.

Build or Break

Here is a game (that is similar to my mental model for this post) that makes room for a neutral option. Let’s call it “Build or Break” (because Build-Neutral-Break doesn’t scan well).

Let’s say everyone has little buttons they can push that will send some of their utilons to another player. Pressing Build will send another player 4 utilons. Everytime utilons are transferred from one player to another they are doubled. Because of this, getting into build-build spirals is freaking awesome and results in lots of extra utilons all around.

You might try to launch a build-build spiral by initiating a build and sending another player 4 utilons. Because of the doubling mechanism, they recieve 8 utilons. If they press build back then 4 of those utilons are sent back to you, where it converts to 8 utilons for you! Yay winning spiral!

If they press neutral, they send 2 utilons back to you, which converts to 4 utilons to you in the doubling. You don’t LOSE anything in the exchange (except opportunity cost which isn’t built into the utilon cost), but you don’t end up any better off either.

Someone can also choose Break, and choose to keep all the utilons to themselves without sending anything back.

Here are some examples:

Example 1: After the formation of a new shared house, a roommate starts cleaning the bathroom on a regular basis:

Break: Alice leaves the bathroom a mess. Hair shavings, toothpaste blobs, forgotten clothing  and items.

Neutral: Bob makes sure to pick up after himself in the bathroom, but doesn’t help with any further cleaning. (Note that everyone choosing neutral will lead to a very gross bathroom, as gunk/ mildew/ discoloration accumulates over time just with general use)

Build: Carly picks up after herself in the bathroom and ALSO starts keeping the living room clean.

Example 2: Dan moves to a new city and wants to form new/deeper friendships, so he starts hosting parties and outings:

Break: Emily gets obnoxiously drunk, starts a pointless political fight, and conveniently doesn’t have any money to pay for her drinks.

Neutral: Fred RSVPs, and is a generally good guest that is fun to interact with. He brings something to the potluck.

Build: Ginger is a good guest to Dan’s party and ALSO returns his invite for an outing that she’s organizing next week.

In these examples, game partners are returning build bids in ways that are analagous to the initial build. Alice cleans the bathroom, so Carly cleans the living room. Dan invites Ginger to an outing, so Ginger invites Dan to her next outing. Having the responsive build be analagous makes it easy to compare the two actions and see that they are equivalent.

In real life though, people are likely to respond in less analagous ways, partially due to the fact that we all have different comparative advantages. Maybe Carly has an aversion to cleaning, but instead she starts cooking meals for the housemates. Maybe Ginger has social anxiety around organizing outings, but instead offers to help Dan move, or makes him a thoughtful present.

Avoiding White Knighting

One goal many people have is to get into a cooperate-cooperate spirals of various kinds. It’s nice being in a situation where you can count on your friends to cooperate, and know that they know that you will cooperate too. To start off those spirals, we might try initiating Build with someone. “If I Build with you, will you Build back?”

It can be disappointing when someone doesn’t Build back. This can lead to White Knighting. In Duncan’s original conception, White Knights are people who unilaterally choose to cooperate in a stag hunt game, and then GET UPSET when their game partners decide to go hunt rabbit instead. The equivalent person in a Build-Break game is someone who intiates Build with someone and then gets upset when their game partner doesn’t Build back, even though no promises were made to the contrary. The important note here is that White Knighting is NOT pushing Build, or Stag, or Cooperate, but is the fact that you get upset when that isn’t returned, or put people under an obligation they never agreed to. White Knighting is a BAD thing.

I have White Knight tendencies myself, and much of this post is build up to “How I Avoid White Knighting”

1. How to Handle Breakers (Avoid Them)

In the original conception, there were only two options: Stag (cooperate) or Rabbit (defect), and the incentive gradient pointed individuals towards Rabbit pretty strongly until each individual was certain of full group buy-in. Putting in a neutral option allows for a game where people don’t need to defect to play it safe.

If you force people into a bimodal option, then maybe 40% will chose Rabbit. It’s silly to be mad at something that 40% of people do. But when you allow a big neutral space in the middle, then maybe only 5% of people choose Break. Making neutral an option means that you can be more certain that breakers are just assholes and avoid the breakers.

Avoid Breakers. The more interesting case is what to do with the vast majority of people who push neutral.

2. How to Handle Neutrals (It’s Complicated)

Neutrals are our allies and casual friends! An acquaintance pressing neutral is a GOOD thing! They do NOT however make for good intimate/romantic partners or close friends, who should be Builders with you. You do not want to waste your time pressing Build with a bunch of Neutrals, but having them around is A-OK.

It is fine to exist in an environment of Neutrals… FOR A WHILE. Because although Neutrals aren’t tearing you down, you’re also NOT GOING ANYWHERE. Nobody wants to be stuck at zero forever.

3. Change your Mindset About Obligations from Build Initiations

Pressing Build does NOT obligate our game partner to Build back. Instead, think of pressing Build as a gift to your game partner. You are gifting them the option of a Build-Build spiral (or rather a higher probability than baseline of a b-b spiral), and that gift is received no matter what button they push in response.

What you get out of the exchange is information. You have learned what your game partner will do given the option to Build. WHATEVER they push back at you is a gift of knowledge.

4. Acknowledge Sunk Cost Fallacy

Entering into a Build-Build spiral often takes a handful of unreturned Build button-pushes by the initiator. You might have to invite someone to three outings before they start returning the favor. You might have to clean the bathroom twice before your housemates realize it isn’t a one-off, and start reciprocating.

This can lead to some issues with sunk cost fallacy. “I’ve already put in the effort of pushing Build three times… I don’t want to miss out if it turns out that the fourth time is the charm!” This is particularly true when you’re trying to initiate a Build spiral with someone who is pushing high neutral in return for your Builds.

Personal Anecdote Time: A common occurence with me is getting into new relationships with men who push Neutral in return for my Builds. They go along with my plans, and are nice company as long as I continue initiating, but put in no efforts themselves. The second I stop initiating, the relationship is over. (I at least figure this out pretty quickly now, so don’t waste a lot of time)

5. Avoid Mainly Neutral/ Break Environments

Keep an abundance mindset. The world is full of interesting high-trust sub-communities that just want to Build together. Go there. If you find yourself in a group or community that has a high percentage of Neutrals or Breakers, LEAVE. Vote with your feet. You want to avoid Breakers anyways, and while a group of pure neutrals might not be wearing you down, you also aren’t going to get anywhere with them. You’ll be stuck on a hamster wheel where you keep running  but getting nowhere. Find a group that has enough Builders to make it worth your time.

How to Make the Model More Accurate

This model is still a simplification, and as such we can throw lots of circumstances at it that would break it. We can make it more realistic, but that also makes it more complicated. The two biggest ways to make the model more realistic are as follows:

1.  Put in a Slider so you can send a range of utilons

Instead of just being able to send 0, 2, or 4 utilons, imagine a slider where you can send a large range of utilons. For example, most opening bids cost 4, but maybe I want to make a big impression and send 10. Or maybe I’m risk-averse and low on utilons so prefer to test the waters by just sending 1. Having a slider opens up a whole new set of questions. For example, what if you send 6 utilons, but your game partner generally only sends 5 back? It’s still better than the average, and you’re both gaining in the spiral, but it feels unfair. How do we handle that?

One issue that communities often run into is that what FEELS like everyone pushing neutral is actually everyone pushing neutral-minus. For example, let’s say an organizer spent 10 points arranging an event, and 10 people show up and are generally good guests. They all feel like they pushed neutral, but the organizer still ends up getting burned out. It must be that the organizer is not getting as many points back as they spent. How so?

Well, first off there is a diminishing return for extra guests. Let’s say the organizer gets 2 points from the first two guests, 1 point from the next 2 guests, and doesn’t much care about additional guests. On the other side, there is increasing costs for continuing to bear the burden of organizing. Maybe organizing the first event was FUN! The organizer got to try new things and it didn’t really cost much at all. But by the sixth event, the organizer is running out of ideas, no longer getting novelty, and doesn’t see a way out of being the only organizer. Now each additional event is costing them 50 utilons, even though it still looks like a regular 10 utilon event from the outside.

2. Put noise in the black box so it doesn’t always double

The other way we can make this model more accurate, is by putting a lot of noise in the black box that doubles the utilons when they pass from one partner to another. I used doubling because it was a simple model, but reality is way more complex. Here’s an example where the utilons MORE than double when they pass through the black box:

Zack is traveling when he sees a $5 trinket that he knows his partner would love. It takes him 2 minutes to notice and buy it. His partner, Yvonne values the trinket at $1000. It is the exact sort of thing she likes and she would have to search really hard to find something as good. It also reminds her of Zack, and is a physical representation of his affection and knowledge of her preferences.

Here’s an example where the black box actually subtracts utilons:

Xerxes spends 100 hours crocheting Wilma a shawl as a surprise. But it turns out Xerxes doesn’t know Wilma very well, because she never wears shawls, doesn’t like the color, and also doesn’t like feeling obligated to keep it and return the favor. Wilma values the shawl at -20 (that’s NEGATIVE twenty).

So wow, that black box can really fuck you up. One thing you notice is that the better model you have of your game partner, the more knowledge you have of what the black box will output. Zack knew Yvonne would love this trinket. Xerxes didn’t seem to have a good model of Wilma at all.


Many thanks to beta readers: Tilia Bell, Richard Berg, Jacob Falkovich, Mackenzie Lee, Daniel Speyer, Ben Thomas, and Neil Wehneman


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6 comments, sorted by Click to highlight new comments since: Today at 8:16 PM
Pressing Build does NOT obligate our game partner to Build back. Instead, think of pressing Build as a gift to your game partner. You are gifting them the option of a Build-Build spiral (or rather a higher probability than baseline of a b-b spiral), and that gift is received no matter what button they push in response.
What you get out of the exchange is information. You have learned what your game partner will do given the option to Build. WHATEVER they push back at you is a gift of knowledge.

I think this was the bit that was the most concrete new insight for me. (I sort of knew it, but having it crystalized I think will make it easier to have future conversations with people I'm trying to navigate these sorts of relationships with, or who I observe trying to do it for themselves).

I'm glad to be thinking along these lines, but I have a few concerns. First, it's a bit sprawling, and this makes it hard to tell which parts are closer to mathematically sound and which are closer to informed speculation.

I generally am suspicious of any arguments that treats utility as a thing that can be stored and transferred. It's much more compelling a model to talk about resources, and each human has a conversion rate to their utility for marginal changes in that resource. This leads to much better models than random noise, as you can include how much knowledge we have of others' utility functions (and of our own, for that matter).

Also, it talks about white knight and how one feels about an action separately from the utility gained/lost. If you want to include these features, model them as utility - white knights have a lower utility conversion when the resource is less than they expected.

In fact, I glossed over " I have White Knight tendencies myself, and much of this post is build up to “How I Avoid White Knighting” " the first time. If it had been at the top (and maybe in the title), I would have read the post with a different mindset and would likely have gotten different value from it.

I feel bad about usually, mostly, having opinions about how people name things (I'd like to be the sort of person who engages more substantially with posts). Also I probably had the opportunity to say this during and earlier draft and failed to.


...a thing I notice as I attempt to employ this framework is that build and break are nicely Verb-y words, that I can use in a sentence, but neutral is not.

Some random attempts, none of which I like:

  • Participate.
  • Skate by.
  • Go Minimal.
  • Minimum Viable Cooperate.

Oh. "Maintain." (Or "Sustain.")

These were my first ideas as well, albeit in reverse order ;) Having thought a bit more now, I might prefer yet another option -- what about "twirling"? (like "in circles" or "your hair")

Suppose we ran a tournament for agents running a mix of strategies. Let’s say agents started with 100 utilons each, and were randomly allocated to be members of 2 groups (with each group starting off containing 10 agents).

Each round, an agent can spend some of their utilons (0, 2 or 4) as a gift split equally between the other members of the group.

Between rounds, they can stay in their current two groups, or leave one and replace it with a randomly picked group.

Each round after the 10th, there is a 1 in 6 chance of the tournament finishing.

How would the option of neutral (gifting 2) in addition to the build (gifting 4) or break (gifting 0) alter the strategies in such a tournament?

Would it be more relevant in a variant in which groups could vote to kick out breakers (perhaps at a cost), or charge an admission (eg no share in the gifts of others for their first round) for new members?

What if groups could pay to advertise, or part of a person’s track record followed them from group to group? What if the benefits from a gift to a group (eg organising an event) were not divided by the number of members, but scaled better than that?

What is the least complex tournament design in which the addition of the neutral option would cause interestingly new dynamics to emerge?