Index Wallets Research Repository

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Index Wallets Research Progress

July

We finished a lot this month.

most theory work is now done (thank you Joel, Raf, Colton, and Philip!)

the

simulation engine⁠

runs and we now have some preliminary results

⁠

the game⁠

is now built, and we have played it with about 50 people

A quick reminder of why we do this: so far, we’ve spent about 60k on theory, simulation, and development of a game. Why do this? Why not just go and build the actual system and try it?

There are two reasons:

This is a much much cheaper way to find out you’re wrong than building an entire company. For just a little bit of investment we get to avoid a ton of wasted work (and money).

We’ve learned innumerable things about the product and system in just 4 months of work which will have real bearing on the business choices we might make if we deem it promising to move forward. For example, we’ve learned about framing language, user interface design, value proposition, network dynamics, exploitation vectors, and initial target markets.

Even if we’ve derisked all those boxes and we believe it’s worth us moving forward, the adoption story rests on what happens if many people adopt the payment method. We’re only capable of credibly telling that story because of the work we do here to see if there’s reason to believe it (and insofar as we do it in good faith).

Theory

Philip and Colton finished their modeling work on index wallets, mostly they studied the adoption dynamics of the system where consumers don’t coordinate. This means that the token is assumed to have a starting market value of 0 and consumers always make the decision that’s immediately best for them (no planning). This is also a single interaction model, meaning the seller isn’t thinking about how they can turn around and pay the next person.

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Joel Miller published this, which is a model that essentially gives vendors the option to enter the market or not, and customers the option to donate or not. Joel argues that, yes, index wallets do uniquely fund public goods, but that free rider problems are still possible. As with Colton and Philip’s models, for the public goods to get funded, a vendor must be the first to increase their valuation, and then customers can reply by donating to the cause. This generally means that vendors must have a private benefit from the public good themselves.

If buyers move first, what is the game theory?

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Raf Kaufmann finished a writeup arguing that index wallets are not viable. In it, he argues that a rational seller will value any token within an index wallet at a devalued price, which will cause prices to be higher to pay them in index payments than regular money, which will cause the market for index payments to crash.

My quick note: What’s unclear here is where the competition model comes in. Clearly, just as the index wallet vendor would like to value every currency as low as possible (because that maximizes their profit) they’d like to price every item as high as possible (because that maximizes their profit). But they are constrained due to competition. However, I don’t see competition models in here.

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Because I wasn’t sure I properly understood Raf’s work, I asked Joel to review Raf’s writeup and he wrote a brief response to it which you can see here:

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An important note: everyone was firewalled from one another’s work while developing their models. So, there was no cross contamination of their results or assumptions (and as you can see, their models are entirely different).

Simulation

Brendan built a

cadCAD based simulation of an economy of people transacting using index wallets⁠

. At this point we have an engine which solves for each of their optimal moves; their moves include changing valuations, and also choosing who to buy from.

Ok, so, starting from the top. The claim about index wallets is that they enable funding of public goods. This is true iff people are capable of selfishly donating to causes, and then socializing the cost of their donation to the rest of the players in the graph. This only happens if players they transact with are willing to increase their valuation of the token above 0. To test this, we make a simulation where players transact with two tokens using index wallets and then allow them to modify their valuations (what Brendan calls the “pricing assessments”) of the tokens in this graph.

The simple story to tell about the model set up is this:

players get to set their own valuations (setting valuations is also the way they set their price)

players get some amount of utility from buying from other players

there is only one product on offer

players are arranged more or less in a grid (many customers per node is hard on the optimization algorithm)

customers always pick the best price

Players update their valuations more or less with this sequence of steps:

1. check each potential customer to see if they'll buy from me

2. if not, see how much utiliity from my best vendor that acquiring this customer would net me

3. increase my valuation for that customer up until the point where it's no longer net profitable for me to acquire them

The big questions we were trying to answer with this were:

do valuations ever grow larger than 0?

does the economy collapse?

what happens to wealth? (does it centralize or not?)

Unfortunately, our research time was cut short because Brendan had to start school, so we don’t yet have visualizations of the actual economy playing out, and we didn’t get the chance to answer those questions to a satisfactory degree. But we do have some charts of the primary results and we have more work coming.

Do Valuations (Price Assessments) grow?

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The first result that we see is that valuations (here called price assessments) do go up. And up and up. In this graph, you can see thot some valuations reached values on the order of 10^13. In fact, rather than worry about tokens immediately becoming devalued (

as Raf did here⁠

), we might worry about them causing hyperdeflation because competition rapidly increases the value of each of the currencies. We can speculate as to why this happens, but the main idea seems to be that there’s a certain amount that the valuation can rise on each turn which is bounded by the cost of goods sold, eventually that valuation propagates through the network, and then that becomes a new baseline for the valuation increase to happen again.

This hyperdeflation result is surprising when we contrast it with Colton and Philip’s work, which seemed to show that adoption of a new currency would tend to be very difficult. Here the simulation seems to show that in the context of a network of players making selfish decisions not only is adoption possible but it can sort of get out of hand.

Now, how realistic is this? Well, there’s a lot of significant dynamics that we’re implementing oversimply:

players have no savings behavior nor time value discounting

product demand is scalar, and purchases are made merely if the price is less than the utility of the product

the graph topology is unrealistic (a grid)

there is only one product to buy and sell

That said, I do still find this to be a fairly compelling result. Even if we were to give players saving behavior, it wouldn’t wipe out their competitive pressures (for the same reasons that a small business owner sets low prices despite also having savings goals). If product demand were some more complex function then it would slightly change the magnitude of purchasing and some purchasing behavior, but it wouldn’t get rid of the presence of competitive pressures. Finally, the simple graph topology is a bit of a problem, in reality there would likely be a few stores that many people bought from. This would change the relative ability for a token to propagate through the graph, and would reduce competitive pressures. So, a next step will be to update the graph topology so as to see if a more typical store system with many customers can create the same dynamics. This can probably be made even more realistic by creating two product classes, “goods” and “labor”, where stores compete to sell products, and non-store players compete to sell labor to the stores.

More realistically, it seems likely that there would be a natural limiting dynamic on the behavior of increasing the value of a currency, whether just due to the cognitive overhead of changing valuations, or due to currency preferences.

Wealth & Economy

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The second result hints at our answer to wealth dynamics and economic stability. Initially, when we plotted this graph we thought that the horizontal lines you see here were evidence that the economy was shuddering to a halt. But, it turns out that what really happened was that the scale of prices became so small that they failed to register on our graph, when looking at an individual player they were still making purchases, just only with tiny fractions of their wallet.

I’m not yet sure how to interpret this result and we’ll have to run more simulations and experiments.

The Game

The key change in the game this month was the addition of the profitability preview at the bottom of the valuations page. We added this because we noticed in previous experiments that players were just randomly changing their valuations around without much clarity as to whether it was helping them.

This change added the ability for players to immediately see both who they were offering a good price to, and how profitable they were if that player accepted the price.

To really understand this, you’ll need a refresher on the scoring rules of the index wallets game. In the game there are three ways for players to earn points:

1 point per ingredient purchased

5 points per recipe completed

2 points per $20 donated to a cause

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Screen Recording 2024-09-04 at 3.07.37 PM.gif

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The key addition to the UI is at the bottom. This chart shows the profitability of a sale if you attract a particular player as a customer.

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Let’s look at Alice as an example:

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What this is trying to say is that with the current valuations you’ve set, the price to Alice will be ⱡ11.0. This is Alice’s best possible deal.

The tooltip shows you that after being paid by Alice, if you head off to spend those ⱡ11.0 with Charlie you’ll be able to buy 0.9 items. You sold 1 item for only 0.9 items in return, that was an unprofitable sale.

This shows the user that not only who pays them but also who they buy from matters. It’s the job of the vendor to balance those two forces: they’d like to attract the customer, but they’d like to do so at the maximum possible price. Of course, this is already true about selling any product, you’re trying to compete on quality and price while keeping your costs low, this just adds an additional dimension: values.

As you can see in the video, increasing your valuation tends to cause the bars to fall, at least for the players that hold that particular currency.

The purpose of this affordance is to make players contend with the core tension of index wallets: your economic interests and value preferences conflict.

I don’t have time to capture all my thoughts on the experiments that we ran. Long story short, it worked: people knew that they didn’t understand. They couldn’t figure out how to use valuations. This is progress, it’s also a fairly strong negative result against the utility of index wallets.

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Some of the observations from playing with a bigger group

We had the opportunity to play with a group of 9 players.

This was a special experiment because we began it by giving players a 30 minute presentation on what index wallets are and how they work, so, at least in principle, they should have been familiar with the main idea.

Nonetheless, by the time it was their turn to set their valuations they became extremely confused. In some sense, this is a good thing. It means that the affordance forced them to contend with the underlying dynamics.

This would have been good reason for us to stop if we thought there wasn’t a way around this problem. But we have an idea for what the issue might be.

One player mentioned, “it seems like this puts valuing public goods in conflict with buying goods and services.” she meant it as a critique, but another player immediately said something like, “yes, but in some sense that’s already true about the world, this is just revealing that underlying tension.”

This player was also totally able to understand the app’s dynamics, and they played very well. So, it’s not that everyone had trouble, it was that it took some onboarding.

It wasn’t clear that valuations are a way to attract new customers.

Admittedly the teaching process of this particular session was a bit botched. What I learned was that:

Players first need to understand the actions they can take in the board game

Then they need to understand the goal and scoring

Only then can they be introduced to the app (otherwise they get lost in exploring it) and they need to be introduced to the app page by page

Here’s your home page (page 1) where you can see all the currencies you own

Here’s your donation page (page 4), where you can donate to a particular cause. Let’s go ahead and donate to the cause of your choice. You can see that added the currency to your home page (and mention they got 2 points for it)

Here’s your valuations page (page 2) (we’re now calling it their storefront) you can entice customers to buy from you here by valuing their currencies more. It’s like a discount for their cause token, bigger valuations give bigger discounts.

Here’s your game info page (page 5), you can see all the currencies that each player holds, this can be very helpful for figuring out which currencies to value

Here’s your buy page (page 3), this is where you go to make payments to players

Finally, walk them through one round of someone purchasing from another player

Nonetheless, despite the somewhat shaky introduction of the game, playing with 9 people was still informative.

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