FOMO3D, a blockchain game, has attracted $12 million worth of Ethereum and locked up these pledged assets through a series of complex and exotic rules. A little analysis, however, reveals that these rules are hardly unusual. In fact, it’s a scaled up version of a classic model of behavioral game theory that I taught early in my class at Harvard Business School.
FOMO3D (F3D) is a game that uses a “war of attrition” game that can lead to a lot of ridiculous consequences. Fortunately, many economists and evolutionary biologists have studied variations of the attrition war game in depth. Here are some of the core findings:
- The “winner” is expected to earn $0
- Players lose control and fail miserably
The second part of this article will take a slightly technical look at how smart contracts can solve the game problem of attrition wars. But before we do that, let’s take a look at attrition war games (a game designed by Martin Shubick) in our first HBS professor’s negotiation class.
In his class at Harvard Business School, Professor Max Bazerman auctioned off an ordinary $20 bill to the highest bidder, but with one special stipulation: the second highest bidder also had to pay. What would you do in that situation? Max waved a shiny $20 bill and began bidding for as little as $1. Will you bid on it? Think about the question before you give an answer.
Did you bid on it? Of course I did! Who would pass up the opportunity to make $20 with $1? So everyone bid and entered the second round with the same idea — after all, who would pass up a chance to win $20 with $2?
But the real fun comes at the end: after bidding and bidding, “Who wouldn’t pay $2 to win $20?” To “Who wouldn’t pay $19 to win $20?” . The next logical step is “Who wouldn’t pay $20 for $20?” That’s when you really notice the impact of the subtle premise that the second highest bidder also pays.
Let’s say you bid $19. If the auction is successful, they get $20, making a net profit of $1. But don’t forget your competitor Carl, the second highest bidder. Carl bid $18 before you, and if you win, he still has to pay $18. For Carl, the question becomes whether to gamble or walk away with $18.
So Carl keeps bidding.
The highest price became $20.
Now it’s your turn.
In this situation, would you pay $21 to win $20?
Of course you keep bidding!
If you give up, you lose $19 and walk away with nothing. But if you keep bidding, you stand a chance of getting at least $20 to cover your losses. A weird situation arises: To win the $20, you add $1 to your price per round. Your bid will gradually exceed $20, as will Carl’s, and it becomes a vicious circle. Eventually, one of you will walk to the front of the classroom and bid an incredible price for this $20 bill. Even at Harvard, there are still idiots who lose a lot of money to win that $20. In fact, there are documented cases in which a businessman ended up paying $2,000 for $20 ¹. Here’s a quote from Northwestern University professor J. Keith Murnhigan, who describes the huge auction that took place in a Classroom in Hong Kong:
“[Even after bidding went up to $400] the heat was still there. The other students shouted at the bidder to stop, but even in that commotion, he ignored them. My knees were shaking when the bid reached $700…When they finally stopped at $2,000, the class went crazy and everyone was scared.”
For that $20, the two competing bidders owed the professor a total of $4,000. The so-called “winner” was a CEO who called the tragedy a disaster caused by ego. The loser described how everything was a blur and that his pulse and blood pressure were still not back to normal an hour after the class ended.
Meanwhile, the professor who made a 200-fold profit on $20 said he felt like he had “earned an imported sports car.”
The whole auction process gives a glimpse of the madness of human nature. Onlookers lucky enough not to have participated in the bidding, and to have watched the whole farce, may have naturally felt smug. But let’s be clear, in theory, neither of them got it exactly right. (That’s how weird game theory is.) But that makes sense, because you can’t have consistently positive revenue in this game.
Positive returns are not guaranteed, but people tend to do worse. Bidders overbid, sometimes turning into frenzied situations like the one in this case. People’s reason is overwhelmed by behavioral factors such as loss aversion, inequality aversion, and negative reciprocity. But to investigate the causes behind such an extreme case as $2,000, we might need Rene Girard to imitate the big murder of competition theory. Anyway, utility functions get weird in the field of behavioral game theory.
But let’s go back to FOMO3D for now. In F3D, players buy “keys” to win prizes (currently worth $12 million) that are distributed 24 hours after the purchase. If no one makes another purchase before the 24-hour clock runs out, you win a big prize. However, if a new player buys a key, the game’s countdown will be extended, and the new player who has just made the purchase will get the bonus first.
The core of FOMO3D is essentially a “war of attrition” game similar to a $20 auction ⁵. The whole point of the game is that when someone else buys a new key and adds money to the $12 million prize pool, you “lose.” In response, you can “regain your chance” to compete for the final prize by buying a key again. This is similar to the psychological mechanism we saw at the $20 auction.
It is more accurate to call the dynamic model of F3D games an all-pay auction, in which rewards are constantly generated while the winning trigger condition is always the same:
The built-in model of F3D targets many of the basic modes of human behaviour (this underlying design has not changed regardless of the Solidity code written during implementation).
So how do you win attrition games? The first method is to parameterize the behavioral utility function of competitors in the auction, and then set the mixed auction strategy to make the income expectation of competitors irrelevant to whether they participate in the auction. It doesn’t matter if you don’t understand, you don’t have to play the game and the expected revenue is the same ($0).
Beyond that, we only have a rough idea of the game because we’ve only read the source code. Fortunately, we found that commitment strategies work, and smart contracts are the best way to do it. For example, one could write a publicly visible contract to support an automated betting robot, which would automatically place bets a second before the drawing, and whose bets would act as incentives to both people before and after the bet (since those bets are doomed to failure ⁶).
If a similar strategy were applied to the $20 game above, it would look like this:
Imagine if smart Christina wrote an auto-executing program, funded by a smart contract, that would automatically outbid others until the auction reached $1 million. Christina set the program to start at $1 and publicly destroyed the program and the private key to the contract. What is your best strategy in this situation? Don’t do anything.
When used against F3D, the contract should take into account the characteristics of F3D players and developers, their long-term vision, and the “metagame” lottery function, but the basic idea is the same. But in theory, Christina’s promise would have had the same effect even if she had written the contract so that the balance of the $1 million prize would be returned to her purse if she won.
But even this money-losing strategy may be worth it to some groups. If only it made people aware of the negative externalities that F3D brings to the Ethereum network (and, more broadly, damages the reputation of blockchain) and ended the game, it would be worth the cost to some people or groups.
An alternative to winning, proposed by Justin Drake, is that miners conspire to “win” by packaging only certain deals. This is a smarter approach, but we suspect it will lead to a result that no one wants, which is that it will significantly undermine Ethereum’s credibility and create negative externalities.
In any case, given the success of F3D, it’s reasonable to expect more of these games to hit the market. It would be interesting to see smart contracts as one of those remedies. Further discussion and some slightly more specialized knowledge will be carried out in part 2.
[1] : “A Very Extreme Case of a Dollar Auction”, Murnighan (2002)
[2] : The professor quoted here is true, but in fact the professor donated the money to charity.
[3] : To demonstrate why not bidding is not the optimal strategy, let’s assume that everyone applies this strategy. At this point, obviously, if no one is bidding, you should definitely bid $1 to make $19! Nash equilibrium requires that there is no longer any incentive to break equilibrium in the current state.
But what if you just bid $20? If you do that, you won’t make any profit, but there’s no reason for anyone else to bid. So a direct bid of $20 makes sense in game theory, but a sustained bid of $20 makes no sense. That’s how interesting game theory is.
Mixed strategy equalization, which is making different choices probabilistically so that no matter what your competitors choose, your expected return is zero. It should also be clarified that the second highest bidder in the game does not pay the sum of all bids. Bn), instead paying the second highest bid Max (BI… Bn).
[4] According to Girard’s theory, the $20 becomes more valuable to each of the competitors. Interestingly, in the professor’s case, he was accused of “changing the rules of the game” (requiring students to raise $50 each time they bid more than a certain amount).
[5] : There is no loss of generality in missing some of the intricate details of the game (as far as we know). For example, FOMO3D also has a dividend setting, but this seems to be a secondary trigger. That is, you don’t buy dividends unless you think someone “dumber” will buy them. It’s like the northeastern professor telling the other professors in his office that he’s going to cut their leeks. Dividends are a good design only if Smart Christina can’t write a normal smart contract at all, otherwise you’ll only lose $19.
Thanks to U/QuestionablePolitics on Redditor for reminding us of that.
[6] : The description here is not very precise. In my second article, THERE is a more scientific way to write such smart contracts and what to do about them.
The original link: https://hackernoon.com/fomo3d-and-dangerous-game-theory-97bd5f47ab3b
By Matt Stephenson
Translation & Proofreading: Ann Clint & Min Min