Strangecoin: a nonlinear currency

In this post I sketch a proposal for a digital currency that works unlike other *coins that have recently become available. I'm calling it Strangecoin, both to highlight its uniqueness as a currency and as a reference to the strange attractor, a special kind of nonlinear system.

What's unique about Strangecoin?

• Strangecoin transactions can be nonzero sum. A Strangecoin transaction might result in both parties having more Strangecoin. 
• Strangecoin transactions can be one-sided and can be conducted entirely by only one party to the transaction. 
• The rate of change of one's Strangecoin balance is a more important indicator of economic influence than the balance itself.
• Optimal investment strategy in Strangecoin aims to stabilize one's balance of Strangecoin. 
• A universal account provides all users a basic Strangecoin income, effectively unlimited wealth, and direct feedback on the overall prosperity of the network.

I've only started thinking through the idea, and implementing it would take more technical expertise than I have alone. For instance, I'm not sure if Strangecoin can be implemented as an extension of the bitcoin protocol, or if some fundamentally new technology is required. If you know something about the technical details, I'd love to hear your thoughts. If you might know how to implement something like this, I'd love to help you try. 

But since I don't know of anything else that works like this, this proposal is mostly intended simply to put the idea out there, in the hopes of encouraging others to think in these directions.

Background and Motivation

If I give you a dollar for a burger, then I've lost a dollar and gained a burger, and you've gained a dollar and lost a burger. Assuming this was a fair trade (that dollars and burgers are of approximately equal value), then as a result of the transaction we've simply rearranged who has which good, and no additional value was created in the process. What I've lost you've gained and vice versa, so that the total value between us has not changed after the exchange is over.

In game theory, an exchange that results in all credits and debits balancing out across all players is called a zero sum game. Recording debits and credits works this way with every existing currency, including Dollars and Euros and all the traditional currencies, but also Bitcoin and other kinds of digital cyptocurrencies. If you want a currency to behave nonlinearly you need additional financial tools like debt and interest, or stocks and dividends, to describe how that money grows or shrinks over time as the result of our economic transactions.

Of course, when I give you a dollar for a burger that's not really a zero sum transaction, because otherwise we wouldn't be motivated to enter into the transaction in the first place. I give you a dollar because I want the burger more than I want the dollar, and if you accept the trade it's because you want the dollar more than you want the burger, so in a fair exchange we both feel like we've come out ahead. In other words, there is some additional value in our fair exchange that is not accounted for in the burgers and the dollars alone. But if our bookkeeping method only counts burgers and dollars, then it's not accounting for the value that accrues in our transactions.

In the proposal below, I'll describe Strangecoin as an method for keeping track of a nonzero sum game, where parties can enter into financial transactions that accrue value just by engaging in that transaction. In this way, Strangecoin is a model of the value that our complex economic relationships generate. The trick is to amplify the exchanged value of Strangecoin transactions relative to the interest of other parties who are not themselves involved in the transaction. If this seems counter-intuitive, a nonfinancial example might help: it's not unusual for two minor celebrities to achieve greater celebrity status upon entering into a romantic relationship. Although strictly speaking the romantic relationship is between the two celebrities, the general public interest in the celebrities results in more overall popularity in their union than either had on their own prior to the relationship.

As the example suggests, the dynamics of Strangecoin might be usefully thought of in terms of a "reputation system" rather than a strictly financial tool, even though the basic mechanics involve the regular method of exchanging currency for goods perceived by both parties to be of equal value. Because of the nonlinear relationships among Strangecoin users, each user effectively draws on a network of support in each economic transaction, coupling its activity to the successes (and failures) of the that network of activity. The result is a model of the complex interdependencies within a community of economic agents, and the dynamics by which those networks develop and decay. For this reason, Strangecoin might have implications for quantifying the role of individual choices and responsibility in the context of corporate action, and for resolving other difficult issues in the management and ethics of collective economic action.

I will say more about implications and consequences of Strangecoin at the end of the document. I turn now to a more detailed discussion of the Strangecoin protocol.

The Strangecoin network

The Strangecoin network is a directed graph with users as nodes and some time-dependent transactions as edges between them. Transactions describes how Strangecoin trade between users at each time step. Let S be our unit of Strangecoin, and let t be our basic unit of time.

A Strangecoin user is:

• An account balance B in S
• Income I in S/t, the sum of all incoming transactions. 
• Expenses E in S/t, the sum of all outgoing transactions. 
• So dB/dt = I - E
• An account balance cap C in S that represents the upper limit of Strangecoins in a user's balance.

Balance Penalties:

If B = C, then the user receives a penalty where income is forfeit until expenses reduce the balance below C. Income might gradually decay as B approaches C to postpone hitting the limit. Similarly, if B = 0, then the user receives a penalty where expenses are forfeit until income brings the balance above 0. Expenses might gradually decay as B approaches 0 to postpone hitting the limit. To avoid penalties, users must keep their balance 0 < B < C. In other words, users have an incentive to keep dB/dt near zero, so that total income balances with total expenses. 

Transactions:

A transaction indicates some trade in Strangecoin over some duration of time between two Strangecoin users with distinct accounts. Transactions come in five types described below. User X can initiate a transaction with user Y by specifying a transaction type and a duration of time, and then fixing the specific parameters of that transaction. If X can initiate the transaction without the approval of Y, the transaction is one-sided. If the transaction type requires Y's approval for initiation, it is a two-sided transaction. Users cannot engage in transactions with themselves. 

Payment is a two-sided transaction in unit time, or an immediate transfer of S from one balance to another in a single time step. Payment works exactly as you'd expect it to work from other currencies, and in this sense is the simplest of the five transaction types. If X pays Y a quantity p of S, then X subtracts p from their balance and deposits p in Y's balance. Payments are two-sided and requires approval from both sides, so initiate the transaction X specifies Y and p, and Y must approve. 

Support is a one-sided transaction over some duration t. If X supports Y over t, then X contributes additional S to Y's income from X's balance, expressed as a proportion s of Y's income over t. X's support effectively amplifies Y's income. To initiate this transaction, X specifies Y, t, and the proportion s of Y's income that X will contribute as support. Since support is a one-sided transaction, Y does not need to approve of the support to receive the additional income. 

Endorsement is a one-sided transaction over some duration t. If X endorses Y over t, then X contributes additional S to Y's outgoing expenses, expressed as a proportion e of Y's expenses over t. X's endorsement effectively amplifies the payouts of Y's expenses. To initiate the transaction, X specifies Y, t, and the proportion e of Y's expenses that X will contribute as endorsements. Since support is a one-sided transaction, Y does not need to approve of the endorsement or the additional expense, which is drawn entirely from X's account. 

Coupling is a two-sided transaction over some duration t. If X and Y couple over t, then changes in the income and expenses of X over t (apart from this coupling) result in proportional changes to the income and expenses of Y, and vice versa. Coupling "binds the fate" of X and Y over t, so that any change in one results in change for both. To initiate the transaction, both X and Y must agree on a duration t, and may specify distinct proportions c_x and c_y for coupling which must be approved by the other. With approval, coupling can involve both positive and negative correlations between income and expenses of two users. If X and Y are positively coupled, then increases in X's income and expenses results in some proportional increase in Y's income and expenses. This additional income or expense are drawn from or deposited to The Universal Account, as described below.

Inhibition is a two-sided transaction over some duration t. If X inhibits Y over t, then X reduces the income or expenses of Y over t by some proportion i. By inhibiting Y, X effectively reduces the impact that Y has on the Strangecoin network by i over t by forfeiting that proportion of income and expense. To initiate the transaction, X specifies Y, t, and i, which must be approved by Y.

The Universal Account (TUA):

Although individual transactions may be nonzero sum as described above, the overall Strangecoin network is zerosum, and uses The Universal Account to balance the network. TUA is a universal account that is positively coupled with all other users. TUA approves of transactions only in the scenarios described below. All newly mined Strangecoins are deposited directly into TUA, with a coupling bonus to the miner. All users are positively coupled with TUA with c_y = 0 so that all users effectively receive a basic income from TUA in proportion to TUA's balance. Users cannot support, endorse, or inhibit TUA.

X can make a payment to TUA at t only in the following situations:

• The have hit their account cap. All forfeit income is automatically deposited into TUA. 
• X is coupled to Y at t, whose expenses have changed. Additional expenses from X (in proportion c_x to Y's expense change) are automatically deposited into TUA.
• X is inhibited at t. All forfeit income at t due to inhibition is automatically deposited into TUA.

TUA can make a payment only in the following situations: 

• X receives income from coupling with TUA. 
• X's account balance = 0 at t. Any additional transactions outgoing from X at t are drawn from TUA. 
• X is coupled at t to Y whose income has changed. Additional income to X at t (in proportion c_x to Y's income change) is drawn from TUA. 
• X has income from an inhibited source Y whose balance is empty. The remaining balance of the transaction is drawn from TUA. 

All transactions with TUA are bare in the sense that they are stripped of any of the modifiers that might normally amplify transactions with X. Basic income paid from TUA to all other users is in proportion to the total users on the network, and TUA's balance. In this way, the basic user income is also a measure of the general health of the overall network. 

Discussion

The set of transactions described in the Strangecoin protocol motivate an incentive structure that is quite different from that of traditional currencies. I'll discuss some of these incentives and their impact below.

Most immediately, Strangecoin transactions are amplified by the network of economic relations employed by each party to the transaction. For this reason, the impact of a transaction isn't simply a matter of what is being traded and for how much. It also matters who you are trading with and their ongoing economic relations, which may have an important impact on the value of the transaction. This is the case even though Strangecoin are entirely fungible and Strangecoin transactions can be conducted pseudonymously.

Strangecoin is "backwards compatible" with traditional currencies, in that it supports the normal method of exchanging goods and services for some discrete quantity of coin in the form of a one-time payment. However, the other transaction types allow for much deeper forms of economic dependencies over time, and explicit representations of one's contribution to one's economic community. These provide incentives to engage in transactions other than payment, for instance by some duration of support or coupling. Securing large payments in a single time step may have very little impact on one's overall income over time, and therefore may be less desirable to users than securing time-extended transactions of other types. Large payments also threaten to bring users close to their balance penalties, providing more incentive to manage economic relationship through other types of transaction.

The most important incentive in the network is the incentive to balance one's account, so that dB/dt is close to 0, and overall income matches overall expenses. If dB/dt is far from zero, then balance penalties start to become an issue. If X is at the account maximum, any additional income over that balance is forfeit to TUA. In this case, user Y has no incentive to give additional support to X, since that additional support is simply forfeit to TUA. Similarly, if X is at the account minimum, any additional expenses are drawn from TUA free of any modifiers. In this situation, user Y has no incentive to endorse X, since that endorsement is again forfeit. In these cases, the transfer of Strangecoin is below its potential, so users are less likely to engage in these transactions; in other words, balance penalties shrink the amplification of one's support network. Users nearing a penalty cannot acquire or dump their balance through TUA, so must arrange transactions with other users to manage their account. There may be income penalties on large balance transfers to prevent users authorizing large payments in order to avoid balance penalties.

Because of these balance constraints, the optimal strategy for all users (including TUA) is to keep income and expenses near a 1:1 ratio. This might be handled in the traditional ways, through careful budgeting and account management. But this can also be handled by managing one's economic support network through transactions other than payment that will keep one's account balanced. If X has sufficiently large income, they must take on equally sizable expenses to avoid balance penalties. These expenses can come in the form of support and endorsements for other members of the network X wishes to support and endorse, effectively growing the network on the basis of their prosperity. The converse holds for users with large expenses. For this reason, prosperity in Strangecoin is measured by a user's throughput of Strangecoins over time, and not their raw quantity at any given time. Users with large throughput also occupy central hubs in the network, and their role and influence in the economic activity of the network is given quantifiable significance with Strangecoin, which can be used for making high-level policy decisions concerning the management and ethics of collective economic action.

Finally, balancing one's account requires, among other things, a consistent regular income from TUA. This gives all users an interest in the general health of TUA and of each user to maintain a relatively balanced account. In general, Strangecoin users seek out semi-persistent networks of support and coupling-- similar in some ways to investment, but investment in people-- and the overall stability of these networks account for the economic well-being of both users and the network as a whole. The incentive towards cooperative, stable, interdependent economic relationships takes place through an interface that bears an intuitive relation to traditional currencies, especially as it pertains to marketplaces of competition.

There's more work required to put flesh on the bones of this idea. There are many conversations to have about the dynamics of the network and the particular constraints it should operate within, both as a matter of practical operation and as a matter of sensible public policy.

I'd like to have those conversations with you.