Wolf Game, But With Dynamic Market-Set Tax

Wolf Game innovated a risk protocol for NFTs, packaging DeFi ideas in an on-the-surface intriguing and accessible game.

https://wolf.game/whitepaper

However, there was neither much of a game nor much interesting game theory, and bugs debilitated what little gameplay there was.

The set of decisions that participants had to make were between: whether to stake, whether to shear sheep or unstake staked sheep, and how much wool to unstake sheep with.

The answers are simple.

Stake your NFTs unless you want to sell them, shear your sheep as you want wool, and if you want to unstake your sheep do so with as little wool as possible (2 days worth).

The reasoning is that staked NFTs are productive and unstaked NFTs aren’t. Shearing sheep is far higher EV than unstaking sheep (0.8nWool versus 0.5nWool). There is a little bit of complexity around the last bit, in that shearing your sheep to get the wool prohibits you from unstaking the sheep for two days - but not terribly interesting.

A very static game that hints at a lot of interesting mechanics.

How could Wolf Game or a new Wolf Game type game be made more dynamic?

Our idea is to have a dynamically set tax and dynamically set probabilities of theft. Instead of tax always at 20% and theft chance always at 50%, imagine tax amounts and theft probabilities that are subject to market forces, with wolves and sheep signalling asks and bids in exchange for protection.

Proposal:

Gameplay could proceed in rounds, with each round lasting 16 hours.

Wolves and sheep signal the amount of tax they’re willing to accept and willing to pay respectively.

Sheep that are willing to pay the median ask, pay that tax to the wolves and are protected.

Sheep that are only willing to pay less tax than the median, pay no tax, and are unprotected. The wolves attempt to steal from the unprotected sheep at the end of each round.

If we stopped here, the sheep could just refuse to ever pay tax, and risk the 20% chance of theft. But…

Sheep that are unprotected are afraid, and only generate 50% as much wool as their base production rate.

And now we have a prisoner’s dilemma among the sheep! As well as a prisoner’s dilemma between the wolves and the sheep!

If wolves ask for too much, sheep can effectively strike, refusing to pay the tax, yielding less wool for both the sheep and the wolves.

Wolves asking and getting 20% tax will get .2 * N wool per period from tax paying sheep, whereas wolves will only steal about .2*.5*N wool per period. Thus, it’s better as a wolf to ask for 20% and get 20*C (C being some coefficient) per day than to ask for 30% and get 10C per day from non-tax paying sheep.*

However, the same applies for sheep. Sheep are better off paying 30% per day than having a 20% risk of theft and a 50% wool production fear handicap. This means that individual sheep are incentivized to cross the picket line and pay the high-ish tax, while the larger group of sheep refuses to pay.

Further,

There’s safety in numbers. As the amount of unprotected sheep increase, the probability of an attempted theft decreases by more than linear.

If there’s far more thieving wolves than there are unprotected sheep, the probability of a theft attempt succeeding is 100%. If there’s far more unprotected sheep than thieving wolves, the probability of theft attempt succeeding is 0%. If all wolves attempt to thieve from all sheep, there’s about a base case 20% chance of a theft attempt succeeding.

Let’s say the wolves ask for 35% tax. The sheep are outraged. They agree in their SheepDAO Discord that they’re not going to pay this tax, and signal accordingly on the blockchain. If they all signal their willingness to only pay up to <35% tax, then there will be about a 20% chance of theft attempts succeeding.

Let’s say that 10% of the sheep decide to signal willingness to pay the tax, because it is higher EV for them to do so. This will cause the unprotected sheep to lose some of their safety-in-numbers effect, increasing the odd of theft attempts succeeding from 20% to 35%.

Ouch. The sheep suffer much hurt and anger from the betrayal, as well as theft and loss of wool, and the wolves feast on the sheep’s lack of unity.

Thus, this prisoners’ dilemma organically incentivizes the formation of DAOs. Vaguely reminiscent of OlympusDAO and its forks’ “3, 3” and “prisoners’ dilemma”-esque (questionable) mechanics… kind of. But, I would argue this is much much more compelling.

I have coded a python script that models how the gameplay would go. I’m working with a team. We’ve had art created. We have a new theme ;). We have engineers writing solidity and the web3 js. We’ve had copy written. Discord community managers. We have our marketing underway. We’re launching rapidly in the next week or so.

We’re looking to make the game as interesting and dynamic as possible. We have other mechanics that will impact the probabilities of theft each round in order to prevent the game from becoming stable and static. We have new characters joining the wolf and sheep factions respectively. But we’ve yet to come up with a good way to round out the core dynamic market-set tax mechanic with a way to instill a prisoners’ dilemma in the wolves.

How can we incentivize wolves to break their ranks and ask for low amounts of tax? How can we only have a fraction of wolves participate in the sheep raids? We’ve gone through quite a few ideas I may list out here later, but none have been as elegant as we’ve liked.

If this is an interesting topic to you, please comment or reach out to me. We would like to find collaborators for this project, for future projects, and we’d like to have people audit our code.

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Welcome to the forum and thank you for posting. This is an interesting post as it is a little different than what SCRF has had so far. I do think there is some potential value here, however, as this seems to align with our mission of connecting academia and industry. From your post, it looks like there are some outstanding questions and potentially embedded assumptions worth unpacking for the betterment of the crypto community. In that spirit, there are a few things that you wrote that I would appreciate some clarification/unpacking of that might get a conversation started.

  1. Is the intention here to look more deeply at game theoretical design in applied situations? Or is this just generally a how can we make a game more interesting and dynamic? I would personally be most interested in that first question.
  2. The coordination elements discussed here, like the SheepDAO, are interesting but also don’t seem to conform to Prisoner’s Dilemma dynamics. My understanding is that the dilemma necessitates no coordination between the prisoners. Perhaps the Prisoner’s Dilemma is insufficiently complex for the design you are after? Is there other work that you know of that might help guide this design? I’ll do some searching as well. But that does also challenge/complicate the assumption that DAOs are organically incentivized.
  3. I’m interested in your use of the term DAO. It seems like you’re discussing backchannel interactions, which to me seems like too low of a threshold to start considering something as a DAO. Granted, DAOs are not particularly well understood yet. There is some good discussion on the forum that you can find using the dao tag and also DAO is defined in the SCRF: Glossary. Based on your understanding, are there other sources or definitions we should be looking at? And a related question would be is an entire organization necessary for the dynamics you are looking to incentivize in this version of Wolf Game?
  4. If both wolves and sheep are dynamic in this version of the game, where is your concern that the game will become stable and stale coming from? Is there a research basis for this? Is system stability the inevitable outcome for a game like this?
  5. I think it would be interesting to see what the incentivizations that you have considered are. You mentioned you might list them out. Are they research-backed or are they a brainstorm of your team? It seems like you want to make sure the wolves compete with each other just as the sheep are somewhat competing among one another. That’s why I’m not sure that Prisoner’s Dilemma is the framework to use here. The coordination of behavior heavily modifies those dynamics. At least, that is my understanding. There is an opportunity in this game to examine that question. Perhaps others might be interested in or aware of how to create mechanics that allow wolves to act independently.

I’m looking forward to some discussion here to see if we can find prior research and frameworks that translates into answered you might have for your specific questions.

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