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The Slot Machine Model: Speculative stickiness, game theory, and analysis of Hex

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Introduction

In my other posts I talked about different models. I mentioned the slot machine model along with the vending machine model. This post is going to focus on the slot machine model and the concept of speculative stickiness which was "coined" (pun intended) by Richard Heart of the Hex project. I looked carefully at the game theory behind the Hex project in this particular economic analysis paper: Hex Economic Analysis Audit and was impressed by a particular part of that paper which I'll be discussing. I also want to note it's impressive that they got an economic audit at all as this needs to be standard for projects from now on and to improve on this I think the audit should be done by multiple independent entities rather than just one (just in case).

About the slot machine model

The slot machine offers the customer who seeks to get rich or make money the opportunity to do so. Slot machines sell "opportunities". Each opportunity has some cost which can be a fixed cost or not, and is paid using casino tokens or whatever acceptable form of payment the slot machine is designed to accept. The slot machine then applies randomization usually with a bias favoring the machine, so that there is some probability known of winning the jackpot greater than 0, and then after some amount of sales then with luck one of the opportunities produces a variable ratio reward.

The science behind the slot machine is the science of behaviorism. The variable reward schedule is the "psychological algorithm" behind the slot machine model. This variable reward schedule is to say that out of X number of attempts the customer has some probability of winning some unfixed amount of rewards. The customer cannot predict how much time or how many tries or opportunities they have to buy in order to get the win. The customer cannot predict how much they will win.

Speculative stickiness for the greater good?

Speculative stickiness is a concept I saw discussed by Richard Heart in his videos but it's really an old concept which he gave a new name. The concept of speculative stickiness is the same mechanism behind Robin Hansen's Futarchy where prediction markets are used for governance. In my opinion it is inevitable that there is going to be betting going on about anything and everything. How can this energy be applied to something useful or even good for society rather than simply betting on fantasy sports?

What allows Futarchy to even work? The speculative stickiness of the system. This same speculative stickiness is behind gambling and when you look at a casino it is also there, but as defined in the Hex ecosystem it is defined by the speculative components available for market participants. For example crypto currencies may have Token Price and Hash rate. Hex has: HEX price, Share price, which directly affects staker profit per share: % of supply staking, Average stake length, Average stake size, stake expiration chart over time, early & late end stake penalties. In this way there are more moving parts involved and more components to speculate on.

Hex funny enough also has "trustless interest" which sounds a lot like the "risk free interest" of Agoras. It isn't yet known if Hex will be able to produce "trustless interest" but from the look of the game theory it seems like they are doing an experiment to find out.

Analysis of Hex and Game Theory

Hex is a project which I perceive as an experiment to test out some novel game theory. In the paper the specific set of goals of the game theory are laid out. Bitcoin for example is designed to appreciate over time but it's not designed to benefit holders more than miners. Bitcoin has to appreciate for mining to be profitable long enough for the network to grow but there is nothing specifically in the Bitcoin game theory to make holding Bitcoin likely to remain profitable.

Hex seems to have been started as a way to fix the problems of Bitcoin and the risk of downward price volatility. The same problem we see in Steem where the price of Steem keeps going down even as more people join. The way the Hex project is attempting to solve this is by deliberately aligning the incentives to reward the long term holders at the expense of the short term holders. In the Hex protocol this game theory mechanism is called "Longer pays better".

Longer pays better is proven in the analysis of the game theory to be true as the optimal strategy to maximize payouts when there are a specific set of parameters. Stakers who unlock early are penalized (unlike in Steem where the original holding period was 2 years and they simply changed the protocol to get out of the agreement). Note: "The fact that longer pays better for a specific set of parameters in no guarantee that this happens for any other choice of parameters.".

So what we can see from economic analysis in the paper is that you can set a goal when designing your networks so that participants if they participate according to the rules then you try to optimize for "longer pays better" for example if that is indeed a goal. Longer pays better essentially rewards those who stake the longest with the biggest rewards, and because staking requires locking up (and burning) tokens, it both reduces the total supply and it creates reward for long term holders while also probably and I stress the word probably, limits downward volatility.

Conclusion

In my opinion lessons will be learned from all attempts to improve up on game theory. These lessons will produce best practices or reproducible results. From this we could then have a foundation to build from for the next generation of projects.

Note: Hex has one risk which to be aware of. There is an origin address. No one knows the purpose of the origin address or the owner of it. The origin address gets paid by:

  • The Origin is paid ½ of all HEX reclaimed by penalties (the other half going to the payout pool)
  • The Origin is paid a copy of all bonus payments (can ask why this is necessary?)
  • Speed claim bonus
  • Referral bonus
  • We Are All Satoshi increments
  • Critical Mass/Virality bonuses

More

In theory since the code is out there eventually someone may be able to fork the project and reduce the payment to the origin address to something more reasonable. I consider these payments to the origin address the equivalent of "bank fees". But since this is just code, anyone can do a snapshot, create a Hex clone, airdrop to all addresses so they are all the exact same balances but swap out the origin and flush address.

What is the flush address? Again we don't know. The flush address could even be a burn address for all I know (clue is in the name?). The point is again anyone can snapshot and airdrop an upgraded improved Hex. So it is the case that Hex can be forked and upgraded.

Keys to understanding how the Hex "Virtual Lending" works:

  • When you stake Hex, the Hex is burned (the circulating supply decreases). So if 90 percent of Hex users are staking this would mean the supply is decreasing by a lot.
  • When accounts "cash out" as you would say if you think of it as a certificate of deposit, it means out of the new Hex generated from inflation, those cashing out get their Hex from that. Hex increases at a limited rate, somewhere around 3% is what I hear.
  • The stakers essentially get rewarded for staking for longer, longer staking means more of the future Hex. The fact that the coins are burned means it's not lending from one to another, but the circulating supply compresses or decompresses according to how many are staking.

So the key innovation of Hex is the ability to dynamically compress the circulating supply creating scarcity for late stakers. This scarcity benefits earlier stakers. The burning of Hex happens when anyone stakes. This means late stakers who FOMO in will burn Hex further which benefits late stakers even more. If many many people mint and stake Hex, then a lot of Hex gets burned.