The Nash Equilibrium, Fomo3d, and Dangerous Game Theory

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Fomo3D was a dangerous game theory that was then applied, obfuscated, and raked in a sh#tton of cold, hard cash.

Users would sign up for https://exitscam.me/ and play the game. Their greed would ensure they always spent more than they lost in an auction that Harvard Business School teaches their pupils – it’s called a ‘War of Attrition.’

When offered the chance to bid on a $20 bill with $1, people will bid on it. The problem is this: the 2nd highest bid also has to pay whenever the winner is chosen. So, when the bid is $19 and the prize is $20, someone will surely bid to make a dollar. Now, when you’re the $18 bid you might lose your $18 if you don’t bid again – paying $20 for $20. If you win, you’re down $0. If you don’t bid, and lose now, you’re down $18.

What’s the person with the $19 bid do?

There’s been documented cases where the bidding reached a walloping $4000 – in a display of sheer ego. The loser was caught up in the ecstasy of playing the game.

That’s exactly what Fomo3D did, except the winnings were divvied up in a very smart way that wasn’t previously available to the general public: using an underlying dividend-paying or burning token (forget which) they cleverly increased the token value or delivered payments for token holders when people played the game.

This caused a huge social effort by token holders – and game players – to spread FOMO about the game around the internet. This would bring in new players and – occasionally – those who would even win or lose by ego, or win or lose because of the sheer thrill of the game.

Learning all of this tonight for the first time, I did a brief Google on ‘dangerous game theory’ and was actually learning about game theory for the first time in my life. Now, this shit is fun. And profitable.

I read about War of Attrition. What a beautiful concept.

The wikipedia article linked to a few other sources: Chicken, another dangerous game theory, has a fancy theory name – but it’s still chicken. When one veers off they lose, when both collide they both lose. We’ll examine opportunities here at a later date, but I also came across another interesting concept.

The prisoner’s dilemma is that two guys are caught for selling drugs, and both are facing 2 years for sure. The feds think they’re both involved in a much more serious crime, and tell Prisoner A that he’ll get 3 years if they both confess – but if he confesses, and Prisoner B doesn’t, he’ll get 1 year and Prisoner B will get 10. Now, if he denies and Prisoner B confesses, then he will get 10 years and Prisoner B will get 1 year.

What the feds don’t mention is the final outcome: if they both deny, they’re both faced with 2 years. This is what’s referred to as the ‘globally optimal solution’ – meaning that if I was able to talk to the other prisoner we might both deny.

What’s in my best interest, as Prisoner 1?

Well, it looks as though no matter what I do – without knowing the other party’s intentions – confessing is my best option. I either face 1 year – which is great – or three years. However, I’m completely avoiding the possibility that I might get 10 years – which is the worst-case scenario. Both of us confessing isn’t the best optimal answer on the board, but it’s what’s best without knowing the other party’s intentions – we call this the Nash Equilibrium, after famous mathematician John Nash. This is applied extensively to playing poker – where it applies just as much.

Nash was also one of the most famous schizophrenics, and the subject of the movie A Beautiful Mind. Want to read more about how people with schizophrenia think? Check out this article I wrote on psychotic thoughts (from first-hand experience!)

Now, if we flip these numbers to their inverse and do some jiggery pokery, we can come up with a profitable business idea for anyone to rake in huge amounts of capital from tokensales and giving people the opportunity to have fun – and potentially win big.

Say my risk is that I might lose all of my 2 Ether deposit on betting in this game. The funds are locked in smart contract. If I go with Option 2, there’s a chance that I could lose my whole balance or there’s a chance I might get 1.7 of my ether back. OK, good enough.

If I choose Option 1, there’s a chance I get 1.3 of my Ether back or – here’s the kicker – I might get 2.3 of my ether back (and ‘win’) should Player 2 choose option 2.

Logic would say that a rational person wants their chance at winning, and will always go with Option 1. Whereas, if both players do, then they both lose. Right?

So far this isn’t very promising as a dangerous game.

However, enter an oraclized call to a random number generator choosing 50/50 either option 1 or option 2, as player 2. Sure, this player would need to put funds up first in order to play – which might come from project funds or from tokenholders putting up the funds against people that lock up Eth in a contract – but check this out, here’s what would happen in Game 1:

Player 1 will always (rationally) choose option 1. The RNG chooses 50/50 options 1 or 2. In green/yellow are the possible outcomes for player 1: they either get 1.3 Ether if they lose, or 2.3 ether if they win. Now, no rational GAMBLER would play these odds – but, keep listening! There’s a 50% chance that the pot wins 0.7 Ether, and a 50% chance it loses 0.3 Ether. Fair enough, so averaging out our winnings that’s 0.2 Ether.

I’m going to take this Ether and add half to the game pot. The other half I’m going to use to give value to my game token – by buy n burn or dividends.

Let’s look what happens in Game 2:

Now we’re talking, we’ve sweetened the pot that the Player has a 50/50 chance of winning – with half the house’s winnings from each game before that reinvested back into the pot. There’s a chance they win – and pot doesn’t increase, no new token burn or dividends happen. There’s half a chance they lose again – and it’s added to the pot and increases the value of the token.

Etc etc tending towards infinity, the potential winnings for playing the game increase ever so much while they’re still losing 1/2 the time playing against the evil supercomputer.

3rd game? More money to be won! Eventually, the gambler’s odds increase enough to be a worthwhile bet no matter what – and the token’s value continues to increase with each average result of the game. This creates a frenzy of people spreading news about the game, drawing more and more people and money into the game.

What does this mean for me, penning this article? Even though I don’t have a smart contract developer or a budget, at least now I own the Intellectual Property on this new evolution of a Dangerous Game Theory smart contract game. If you are a smart contract developer and would like to team up, let me know! If I’ve made any critical errors in my math – it wouldn’t be the first time! Let me know!

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