Modeling Hyperstructure Incentives

This doc was an attempt to more rigorously prove to myself that in the context of utility tokens that can also be used for voting, hyperstructures can’t be valuable to own while still being free to use. It’s one thing to say, “that’s a free lunch, free lunches don’t exist”, it’s another to actually consider all the relevant variables and prove that that’s the case.
This doc was my tool to do that over the course of the video linked below, and I finished the video somewhat confident that hyperstructures don’t work in being free and valuable (NOTE: I think all the other properties of hyperstructures are extremely worthy and that hyperstructures are an important concept, my criticism of free-and-valuable is meant as constructive critique to improve the concept and to avoid fooling ourselves). But more important than the conclusion is that this is a first pass at a concrete model of the underlying dynamics. In other words, it’s a way in which I could be wrong.
This doc isn’t super accessible for people who would like to help me be wrong. So if you think that hyperstructures are actually free+valuable and that my arguments are wrong, please tweet @connormcmk or cast @nor at me and I’ll clean up this doc so that it’s more useful.
From a high level, this doc was trying to capture the game theory of the players of a hyperstructure. It considers two player types:
investors in the token
users of the protocol

It then considers two scenarios:
the protocol is charging no fee
the protocol is charging a fee

And it considers the moves of players under each of those scenarios, namely:
if the protocol is charging no fee, investors can buy the token and vote to turn on the fees
if the protocol is charging a fee, users can:
buy enough tokens to turn it off
fork the protocol
just pay the fees

Then it considers the ways in which investors can make money:
charging the fee
divesting of governance tokens by selling to users at an elevated price

Finally, it categorizes the possible outcomes of the game. Since the requirement for a token to be valuable is that someone demands that token (i.e. holds it instead of the market return they could be getting) one of these scenarios must take place, and only one is the valuable and free scenario:
Then we show that we can cannot reach the top left quadrant where it’s both valuable and free because there’s no scenario where both the investor and the user have a selfish incentive to hold.

This does not say, “It’s impossible to have a valuable protocol which has the (reasonable) properties of a hyperstructure (unstoppable, forkable, etc.).” Of course you can. It just says that the token value will be based on the expected fees that you can charge for usage of the protocol, and that the fees you expect to be able to charge are entirely driven by how expensive and difficult it is to successfully set up a fork. It does say that the “threat of the fee” dynamic doesn’t work to create value as per the original post :/

There are some nuances consider:
I made some modeling choices here which I consider to be well justified but I’m happy to be challenged on them. Namely:
users have a maximum number of “turns” they expect to use the protocol
in the model, the protocol can only charge a fixed fee (1 UNI / turn) or no fee, it can’t set its own fee level (e.g. if investors think 1.5 UNI / turn would be a better fee, they can’t switch to that, only 1. I think this doesn’t matter because varying other parameters can get us access to the entire state space)
I didn’t actually prove that the inequalities don’t hold, instead I just set up the variables with sliders and moved them around and at the time of creating this it was perfectly intuitive that there’s no combination of parameters where you can get YES and true ​
But it’s not a rigorous proof. bump me if you think a rigorous proof is required.
Here’s the original video where I talk this through:

while True:
print("Hello world!")

fn run():
print("Hello world!")
return run()

the next sentence is true
the previous sentence is false

UNI: 10,000
RULE: if you have >50% vote for X policy then X policy is enacted
POLICIES: charge a 1 UNI usage fee for using Uniswap, or charge no usage fee
PLAYERS: user1, user2, investor

1 UNI = 1 util
user1.utility = 100 utils
user2.utility = 200 utils
user1.max_turns = 100
user2.max_turns = 100

FORKING: at any point, the users can create a new identical fork of Uniswap, for some cost
MARKET RATES: 1 util per util per turn

Story 1:
there is a 1 UNI usage fee for using Uniswap

Three possible moves:
do nothing: pay the 1 UNI per turn in exchange for 1 util of value
fork the protocol: pay the forking cost and set the new fork to 0 usage fee
change the policy: buy 5,000 UNI tokens, vote to change the policy, sell them

Counterfactual to #3: a return of 5k utils
buy 5k UNI for the turn to change the policy
they could have invested 5k utils (1 UNI = 1 util) and gotten back 10k utils at the end of that turn (1 util per util per turn available on the MARKET)

Under what scenario does it make sense for them to buy 5k UNI? As long as they will enjoy 5k / user*.utility

turns of usage for user 1 makes it worth it
turns of usage for user 2 makes it worth it

this implies that in order for them to choose to change the policy, they must believe that the forking cost is > 5k utils, otherwise they would have done it

turns together to make it worth it

utils “should” be coming from user 1, but they have every reason to freeride

benefit - cost of coordination < cost of implementation: no funding for the public good

Investor Thoughts and Prayers:
the counterfactual is user 2 paying the 5k utils to change the policy
“I just need to find a way to push the price of uni sufficiently high that it would take more than 100 turns for the users to make their money back on the change in policy” % forking costs*
greater than
utils for user 2 it’s not worth it
greater than
utils for user 1 it’s not worth it

greater than
utils per UNI then it is too expensive for it to be worth it for user 1

at this point we could consider how that changes the bargaining landscape with user 2, but we’re going to assume that user 2 is just an ass

investor buys 5000 UNI, and is only willing to sell them for more than 2 utils

investor expects to be generating 1 UNI per turn, which is worth 2 utils, in exchange for locking up 5000 UNI, counterfactual is 1 util per util.
per turn

market rate
(what they could be earning)

user1’.utility =
user1’.max_turns =

user2’.utility =
user2’.max_turns =

we want to get a yes the user will buy the tokens, right now we have a
we want this to be true it’s worth it for the investor, right now we have a:

user holds, investor holds:
user does not hold, investor holds: not free
user holds, investor doesn’t holds: yes, hyperstructures exist
user doesn’t hold, investor doesn’t holds: not valuable

user holds, investor holds:
makes money back on selling inflated price (claim: busted)
makes money back on charging a fee: this is just rent. i.e. not free.

greater than
utils for user 1’ and it’s not worth it to take a turn
greater than
utils for user 2’ and it’s not worth it to take a turn

At the price of
utils per UNI,
is not
worth it for user 1’!
is not
worth it for user 2’!
If the investor bought a controlling stake of
UNI at an average price of
utils per UNI, they have
utils worth of appreciation of their UNI, (for a total of
utils worth of UNI) plus, they’re now earning
utils worth of UNI per user per turn.

How many users do they have?
user(s), for a total earnings of
utils per turn.

The expected value of their users is:
over the lifetime
The counterfactual earnings for that amount of utils over that lifetime is:
utils of missed income

Our job then as the investor is to figure out what hyperstructures will have the kinds of favorable conditions that allow us to make back more than the counterfactual earnings, we can achieve this by:
earning sufficient revenue
selling our shares at their inflated price

Current expected earnings:

It’s currently worth the buy:

Under what conditions can we expect that users will want to buy back these shares from us at the inflated price?
turns of usage for user 1’ makes it worth it.
turns of usage for user 2 makes it worth it

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