Playas Gon’ Play but Probably Shouldn’t
If these posts are interesting to you, please subscribe:
and share!
Also, feel free to follow me on twitter: @azakmay
A strange game. The only winning strategy is not to play. It turns out that sometimes the optimal strategy is not to participate.
I came across such a game when scrolling Twitter a week ago:
For the unfamiliar, on-chain game just means a blockchain game controlled by no one. For this one, users attempt to choose the minority response between two options, and the pot is automatically distributed.
This seemed like an interesting idea because the poll came out way more lopsided than one would anticipate with random guessing:
One would expect this to be much closer to a coin flip (i.e., 50 / 50), but people are funny and irrational, so of course, it is lopsided as everyone overthinks this simple guessing game. I imagine we all did something like this:
Me: I’ll just pick one,
Still Me: No, I should choose B since I bet most people chose A!
Me, after voting: Ahh, shit.
But let’s go back to Dan’s tweet and think about what he is saying in relation to the poll’s outcome. Everyone who voted for A would win some money from the players who voted for B. If there were 1000 players, betting $5 each, the pot for A would be what B lost: 550 * 5 = $2,750. Meaning that each person that voted for A would’ve won $6.18 ($2,750 ÷ 445) – more than doubling their money! Even in games that seem random like this, there are optimal strategies, and we can use game theory to think about them.
The Optimal Strategy
I wrote some quick functions in Python to help visualize this payout structure, assuming a bet size of $5 and 100 bets total.
As expected, the payout quickly decreases as the number of individuals in the minority grows until it reaches the Nash Equilibrium of 0 (i.e., the point at which no one is better off switching their strategy). Knowing what we do, is there an optimal strategy for the game? One might jump out: bet both sides, and you at worst break even in the event of a tie. Dan and many replies quickly realize this outcome.
However, in my opinion, this isn’t a complete picture of the optimal strategy. Even for someone to implement this strategy, a couple of assumptions must be true:
On-chain transactions are free
Time is free - we will get rid of this assumption shortly.
I think both assumptions are incorrect. First, on-chain transactions have costs (we all remember ConsitutionDAO!), and this game has two transactions: sending the money and having the money sent back. Second, there is always opportunity cost with time.
We’ve now introduced two additional costs that are associated with the game. To make the game worth playing, we must overcome these extra costs. We must ask, is the optimal strategy even to play the game? If we assume that we bet on both sides and all players realize this, you will always win $0 minus the transaction costs and time to play. This seems like a losing endeavor, and we might conclude, “A strange game. The only winning move is not to play”
The New Optimal Strategy
Based on what we’ve shown above, the optimal strategy seems to be to walk away. Although, there is one potential problem with this strategy. It assumes that all players act rationally, and that might be an exploitable flaw since it relies on a couple of assumptions itself:
1. Everyone will recognize they should vote on both sides.
2. Humans are rational 🤔🤔.
We are now left with these two new assumptions to overcome the additional costs. Let’s focus on time first. There might not be monetizable opportunity costs associated with the time, the game might be fun and add utility, or we can assume the time cost is negligible because software allows us to build a bot that votes both sides every time. Either way, we will just ignore the time component. We are now able to focus on the transaction costs and are left with the simple scenario:
We need more irrational humans than the cost of transactions
Based on running some different simulations, we can get a sense of how many irrational humans we need to keep playing this game such that we make greater than $0. Assuming that there are 100 bets placed at $5 a bet, here is a table of how many irrational humans we need based on different transaction costs - if we still stick to the best strategy of betting on both sides:
As transaction costs approach $5, we need more irrational players to make the game worthwhile. If the transaction costs are independent of the betting amount (i.e., transaction costs are constant), we need fewer irrational players as the amount per bet increases. For example, if the bet size increased to $10 a pick at a transaction cost of $1.00, we only need three foolish players now.
Conclusion
In the economy and normal markets, there are almost always irrational actors. Keynes coined the term animal spirits in The General Theory of Employment, Interest and Money to describe the instincts, proclivities and emotions that ostensibly influence and guide human behavior, which is basically what we need in this game to make playing rational– irrationality to make something rational! Recognizing the existence of these irrational actors is an essential part of investing, whether that be in crypto, equities, or anything. And if you’re playing a game, identifying strategies, and making reasonable assumptions about the behavior of other players is a must. Even the simplest of games can be much more complex than they appear.
Title inspired by this classic: [Song Link]