Cryptocurrency + an Old War Strategy Might Solve FOMO-3D, the New $12m Ponzi-esque.
Note: This article proposes that smart contracts can enable an effective commitment strategy, Click here for my previous article explaining the game theory of Fomo-3D. Fomo-3D itself ended with a combination of sophisticated “blockstuffing” and commitment strategies.
In 1519, Spanish conquistador Hernan Cortes landed his ships in Mexico looking for gold. As he attempted to push inland and battle the Aztec Empire, he feared that his men would break rank and retreat, boarding the ships back to Cuba. He knew he’d win if his soldiers fought. But if they retreated… he might be dead.
Cortes was a brutal man and he devised a brutal strategy: he sank all of his own ships so nobody could retreat. He escalated the conflict to win or die. And so his men, now lacking the option to retreat, had no choice but to fight to the death. And fight they did — his commitment strategy was so successful that “Cortes the Killer” remains (in)famous to this day.¹
Fomo-3D, the popular new Ethereum Dapp, is just such a battle. But instead of Aztec gold you’re battling for 25,000 Ethereum or so. It’s a game written on the blockchain and, assuming that all of the contract code gets fully verified, it might well provide the test case for a very unique feature of smart contracts. That is to say, programmable cryptocurrency seems to offer exactly the same solution to the dilemma that Cortes successfully used.
And this solution might be much cheaper than sunken ships…
I’m going to try to convince you of two things in this article:
- In theory, Fomo-3D’s $12 million jackpot can be won for $1 thanks to a unique feature of smart contracts.
- You should probably not try to do this unless you command a lot of wealth and have thought very hard about the risks.
If the first point is true, it would be an incredible demonstration of Crypto providing new tech in game theory. The second point is always good advice when millions of dollars are at stake, but I suspect that it’s especially true in Fomo-3D’s case. Anyway, let’s dive in.
Playing Cortes in Fomo-3D
In Fomo-3D, individuals buy “keys” to give them a chance at the jackpot. You can think of it like inexpensive bids for the jackpot — they’re “cheap” but they only win if someone else doesn’t buy a key after you. You should only buy if you think there’s a decent chance that nobody will buy a key after you — otherwise you’re sure to lose. And why would anyone buy a key after you? Only if they thought there was a good chance that nobody would buy after them.
This brings us directly to our simple solution:
Fund a smart contract that can only buy current-round F3D keys and burns the remainder unless you win the jackpot. Then tell everyone in the whole world about this contract.
That may sound crazy — it kind of is crazy — but there’s a logic to it. In effect, the way it works is by raising the price of a key for everyone else in the game. Since the contract ensures that anyone else would have to buy a huge number of totally useless keys, this raises to price of a useful key enormously. The useless keys they’d buy are the ones that our contract has guaranteed that we will beat. As a result: Actual Key Price = Useless Keys + Useful Key.
How much should a key cost?
So we found that the Cortes strategy works here by effectively *raising the price* of a key enormously for everyone else. So how expensive do these new keys have to be? They’d need to cost more than anyone could expect to get for the prize.
By definition nobody can expect more from the jackpot than is in the jackpot.² And that’s playing it pretty safe — even for the most “irrationally exuberant” people, setting the new key price to be higher than the prize itself should be sufficient. I’m going to show this using emoji math (but I’ll describe it in words later):
In step one we find someone who thinks that buying a key is worth it — that is, they have an “expected value” for the prize that makes buying a key worthwhile. But then — after the “However” in the picture above— we set the price of a key high enough that nobody would find it valuable. By picking the price equal to the prize itself, it should theoretically guarantee that nobody should buy a single key.
How much would this contract cost?
We talked about the Cortes strategy being effectively free, but weirdly enough, that’s actually under-selling it. It should guarantee the entire jackpot for the realized cost of a single key. It probably won’t in practice, but it “should”.
The trick is that the smart commitment contract can refund your money if you win. This would be like Cortes un-sinking his ships if and only if he won. If he does this then Cortes guarantees the victory and doesn’t lose a single ship.
You could get even more clever here, perhaps writing a bot that auto-bids in F3D at the last second, and paying for it with your large stock of funds. You could — presumably — have the contract award some portion of the remaining funds to the miner who (validly) enters your key purchase last on the registry. You could allow yourself to buy keys for the current round with the funds, and so on. But the core is just a credible, and publicly known, punishment for giving up.
This is what smart contracts seem to make newly possible. It’s actually pretty hard to commit to burning money. Thinking back to the Aztecs, suppose they wanted to play a Cortes strategy, and so they threatened to destroy all of their gold if they retreated. The problem they’d face is how to credibly commit to this. The problem is, once they retreat, they’ve already retreated!
This is what commitment is all about — once things go bad, you don’t want to make it worse. If the Aztecs’ whole plan has failed already, why on earth would they destroy the gold afterward just to prove a point?
But programmable money doesn’t care if you change your mind.
This is not a “blockchain is magic” story.
Or at least, I don’t think it is. What makes the Aztec example really fanciful is that — even if Cuauhtemoc could code in Solidity or Vyper — he would have faced the good old oracle problem. That is, how to define and verify a “Retreat”. That’s very difficult.
But for F3D the oracle problem is a non-issue as far as I can tell: the round will publicly end and it will publicly award a single winner. The enforcer is just the executed code (validated by miners of course, see the FAQ.)
The real challenge, in my opinion, is creating “common knowledge”. If people don’t know you’re committing then you are wasting your money. Remember that everyone could see that Cortes had burned his ships, and everyone knew what it meant. I should probably bold the implication here, just to be safe:
It is an incredibly bad idea to play a Cortes strategy and keep it to yourself, even for a second.
You probably shouldn’t create one anyway (and certainly not based solely on this article.) But as soon as someone creates one, they should tell the world, shout it from the rooftops, etc. That’s because if two people create commitment contracts in a game like this then it’s an absolute disaster for both of them. They will just reset the game, with neither of them winning. For more on this, see the FAQ at the end.
Wrapping up
The Cortes strategy is a “Commitment Strategy”. And playing Cortes really does require commitment, in “for richer and for poorer, in sickness and in health” sense. The game theory jargon for this is something like “ex post incentive compatibility”, but not to worry.
The question of how humans commit IRL is fascinating, of course. Humans have the capacity to act so strategically and override their commitments, and yet we do commit.⁴ But the question of how smart contracts can commit is much less hard. It’s annoying that literally nobody can help you when you lose access to your crypto wallet, but that’s precisely what makes smart contracts so useful for commitment. They aren’t smart at all.
As far as I can figure (and I have been emboldened by speaking with thinkers like Cathy Barrera,) this is pretty new tech in the game theory world.
If it uniquely enables someone to guarantee themselves (or a charity) a huge jackpot, that would be pretty cool demo.
(FAQ Below)
Thanks to Jake Brukhman and ryan youngjoon yi for discussions around this article. Thanks to Yannick Roux for advice on making the piece more readable. Many thanks to a bunch of economists and professors (BK, AP, BN, SM, RA, GW, FE, OH, VS, and others). I own no F3D or associated tokens (and have no affiliation with Team Just.) All mistakes are mine and mine alone.
FAQ
I’ll now turn to answering some common questions and objections. But first let me note yet again that, even if my argument is right, anybody actually trying to *implement* this strategy needs to think very carefully.
Can you really write a smart contract like that?
The real smart contract magic should be in the ex post incentive compatible commitment itself. Apart from miner collusion worries, this is not — in my opinion — an especially technical problem. In terms of the game theory, a contract that straightforwardly imposed a huge cost on you unless you played and won F3D would be sufficient. Clearly the contract I described can be improved upon, but I won’t get into more details here.
Is there an optimal response to the commitment contract other than bowing out?
Considering only this round — and treating agents as broadly rational — then no, I don’t believe that there is. One major reason is that if someone else set a new commitment contract slightly higher than the current one, all that would do is reset the game. The result would be something like what Vitalik Buterin called “Revolution: Hamlet Edition”, where Killing the King doesn’t really let you become King (because, as he notes, the norm against killing Kings goes away so being the King wouldn’t be so great anymore.)
Similarly, if there’s one way to actually win this game (via a commitment contract), why spend enormous amounts trying to defeat it? Unless you had some special affinity for the game itself, the only advantage you’d gain is the ability to implement the same strategy anew. And it would seem that you’ve just weakened that strategy, at least in people’s perception.
But that’s kind of a “norms-based” argument. Maybe it’s unconvincing. Well I should confess something to you, down here in the basement of this FAQ: I am pretty confident that — conditional on the commitment contract being effective in F3D — there are sound technical reasons why the first person with a large commitment contract should win. I can think of at least three reasons for this and a solid, technical team (in my opinion) will find them too. Here’s the hash of one:
c8a4efb06a4e6b5761c5ad3ff9fa5b4bab2ec8f7ea6d52531118e49a4eb90add4e0477bd00e39251c7131031385955bf1b9aae2d2b6a1c7ca956fbfeafdd4d7c
What about the dividends?
Since this is a zero sum game, I can’t see how dividends add anything interesting. If someone buys a new dividend despite a commitment contract, it looks to me like they’re buying a dividend in the purchase of one key. Not too exciting. If they expect more keys to be purchased regardless then they are just buying a dividend in human irrationality. There are plenty of dividends in human irrationality already, so not sure what’d be unique here.
That said, I may be missing something here. It is conceivable that if, say, two players in a war of attrition game hold an equal 50% of all available dividends apiece this could complicate things slightly (on the back of my envelope it would seem to turn a “strictly dominates” into a “weakly dominates”.)
There could be something else I’m missing. Remember — this is not a fully-considered academic article! I am writing this up the same week I first heard about Fomo-3D.
What about the proportional rewards?
The fact that you can choose “teams” in F3D, and that only a portion of your rewards go the pool itself doesn’t seem to change the structure of the game. F3D is what’s called a “zero sum” game, because it doesn’t create wealth. As a result, the additional features don’t seem to affect the equilbria of the game or the “coordination game” nature of the coded game. In terms of affecting the structure and play of the game itself, I haven’t seen a feature that makes a tangible difference. I’ve looked and asked for examples widely, and haven’t gotten any responses, but I could be wrong about this.
How does the possibility of miner collusion affect this?
I can’t say, other than noting that I can’t see a reason why it would be a special problem for this strategy. It could certainly be a concern though.
If this article’s analysis gets proven wrong, what’s your best guess as to how?
I wish more people would answer this question at the end of their arguments! I mean, the obvious reason is that you don’t want to help anyone own you. But still.
Anyway, I’ve been discussing the commitment contract idea enough by now to suspect that if I’m wrong, I’m wrong in an interesting or non-obvious way. So I’m going to go big here and guess that, if I’m wrong, it’s because something about the structure of the game (or even proof of work itself) has already created an inherent commitment contract. This would be an interesting way to be wrong, because it would seem to suggest that we lack common knowledge about a thing that someone would should really like to produce common knowledge about.
It’s also possible that I’m mischaracterizing the nature of the F3D game itself. I don’t think this is true (and literally nobody has suggested this, including in my discussion with the F3D devs) but you never know.
[1]Shockingly, this is not an apocryphal story. I’m not sure where I first learned about it — I used it as an example when helping teach a behavioral strategy class years ago — but a likely source is Barry Nalebuff and Avinash Dixit’s Thinking Strategically.
[2] There are always larger games that this game could be embedded in (status competition, for instance). So, in the Cortes example, if you thought “what about the dishonor of retreating?” you’re right, in a sense. In the math section, if you’re thinking “What if E[Prize] is actually greater than Prize?” Well, you’re definitely wrong, but the point you’re probably making — that payoffs are actually E[Prize]+E[Pride] or something, is correct.
Those are the sorts of meta-games that we’re making explicit in our commitment contract. But, crucially, they need to be very carefully considered when constructing a commitment strategy. Especially if they’re not explicit.
[3] Or more specifically, it acts according to a game broader than what’s being formalized. This is what I took to be Vlad Zamfir’s point about addressing the end-to-end utility function in smart contracts.
[4] Technically, the price of keys rises very slightly over time. Based on my math this shouldn’t matter.
[5] If you want to pursue this further I’d recommend the work of Thomas Schelling, Elinor Ostrom, and Robert Frank.
