There's been a lot of discussion recently about self-custody (#1020261, #1030290). While most Bitcoiners espouse the virtues of self-custody, others have questioned whether there's any real demand for it, and whether self-custody will ever become a mainstream option (#679850).

Yet, something that I've occasionally thought about is that having the option of self-custody can be just as important as actually using it (#783976). How can that be? Today we'll take a look at some game theory to help us answer that question.

We'll start by looking at the Stackelberg Model. This is a model that illustrates how the threat of entry by a potential competitor can be enough to deter a monopolist from the worst anti-consumer behaviors, even if the potential competitor never actually enters the market.

The idea is pretty simple: if the monopolist behaves badly, then this gives more space for a competitor to enter the market, which in the long run hurts the monopolist. But if the monopolist behaves in a more pro-consumer manner, it won't leave any space for a competitor to enter---and thus, it gets to stay as a monopolist, which earns more profit in the long run.

Formally, the game tree looks something like this:

And the path of play looks like this:

What happens is that the monopolist knows that if sets a high prices (anti-consumer), that will invite entry by the competitor. But if it sets a low price (pro-consumer), then the competitor won't enter because it wouldn't be worth the upfront cost.

In the actual path of play, the monopolist sets a low price to deter entry, and the competitor never actually enters the market. What we then observe in real life is that the monopolist behaves somewhat competitively, even though there's no visible competition. We can say that the monopolist's pricing behavior is constrained by the threat of entry, even if entry never actually happens.

The Stackelberg Model shows that even though a company might appear to have a dominant market position (like Amazon in e-commerce) it may not actually have that much room to behave anti-competitively. The threat of competition keeps it honest. Amazon does, in fact, make this argument as to why its dominant market position doesn't actually lead to anti-consumer behavior.

Even though the competitor doesn't actually enter the market in the Stackelberg Model, the option to enter is still very important in shaping the market outcome.

To see this, let's imagine what would happen if there was no possibility for entry by a competitor. The game tree and path of play would end up looking like this:

Without the threat of entry by a competitor, there is no longer a constraint on the monopolist's behavior. It is now free to practice whatever behavior is best for itself without regard to any blowback.

Just like how the threat of entry matters more than actual entry in the Stackelberg Model, we can envision a model in which the option to self-custody matters more than its actual usage.

Imagine a game in which a custodian of funds (a bank, a wallet, etc) can either behave well or behave badly. Bad behavior could include any number of actions, like rug pulling, censoring users, selling data, or having bad security practices.

The custodian chooses good or bad behavior, and then users decide to either use the custodian or to self-custody. Self-custody is less convenient than using the custodian, but users prefer to self-custody if the custodian is going to behave badly. The game tree and path of play looks like this:

In this game, the option to self-custody constrains the custodian's behavior and forces it into good behavior.

What if there was no option to self-custody? Then the game tree and path of play would look like this:

Without the option to self-custody, there is less constraint on the custodian's behavior. Because users have no other options, they are forced to use the custodian, and thus the custodian has no incentive to respect the users' privacy or to resist government requests for censorship.

One detail that I've glossed over so far is that it's not just the option to self-custody that matters, it's also how costly the option is. If self-custody is too costly or too difficult, then the constraining force it has on the behavior of custodians is lessened because the threat of self-custody is not credible.

But the amazing thing about Bitcoin is that it does make the option of self-custody much more viable than any previous form of fiat or commodity money. Physical cash is difficult to secure in large amounts, and commodity money is both difficult to secure and hard to transport, and any form of digital cash which is easy to secure and easy to transport must be managed through a custodian. Bitcoin, on the other hand, is easy to secure, easy to transport, all while maintaining self-custody. You just need a few hours learning curve to learn how to use it.

Yet, a learning curve is still a learning curve, and I'm sure we all know plenty of people for whom a few hours of sustained attention is too much. What does that mean for Bitcoin and the future of self custody?

Personally, I don't think self-custody will ever be mainstream. There are too many people for whom the learning curve is too steep, or who are too irresponsible for self-custody to be a good recommendation. And besides, if most custodians are behaving in a trustworthy manner, there wouldn't be much need for self-custody anyway.

But even if self-custody is not mainstream, the option to self-custody will remain important as a disciplining force on the market. The option of self-custody may be exactly the driving force that's needed to keep custodians honest.

But in order for the option value of self-custody to matter, self-custody needs to be relatively inexpensive and uncomplicated. It doesn't need to be so convenient that everyone uses it, but it needs to be convenient enough that there's a credible threat that people will switch to it if no good custodians are available. It's therefore still important for Bitcoin developers to keep working on self-custodial solutions, even if there is little actualized demand.²

Game theory teaches us that having an option can shape the course of events, even if that option is never actually chosen. Similarly, the option to self-custody can shape the behavior of custodians---even if few people choose to self-custody. However, the impact of an option is strongest when the cost of choosing that option is low. Bitcoin devs should therefore continue working on improving self-custodial solutions.