A zero-sum monetary system, interest rates, and implications

To the knowledge of the author, this is the first time it has been shown that interest rates that are extremely high by modern standards (100% and higher) are necessary within a zero-sum monetary system, and not just driven by greed. Extreme interest rates that appeared in various places and times reinforce the idea that hard money may have contributed to high rates of interest. Here a model is presented that examines the interest rate required to succeed as an investor in a zero-sum fixed quantity hard-money system. Even when the playing field is significantly tilted toward the investor, interest rates need to be much higher than expected. In a completely fair zero-sum system, an investor cannot break even without charging 100% interest. Even with a 5% advantage, an investor won’t break even at 15% interest. From this it is concluded that what we consider usurious rates today are, within a hard-money system, driven by necessity. Cryptocurrency is a novel form of hard-currency. The inability to virtualize the money creates a system close to zero-sum because of the limited supply design. Therefore, within the bounds of a cryptocurrency system that limits money creation, interest rates must rise to levels that the modern world considers usury. It is impossible, therefore, that a cryptocurrency that is not expandable could take over a modern economy and replace modern fiat currency.

💡 Research Summary

The paper investigates the interest‑rate dynamics that arise in a monetary system where the total money supply is fixed – a “zero‑sum” environment often associated with hard‑money regimes such as gold standards or modern cryptocurrencies with capped issuance. The author builds a simple probabilistic game model with two agents: an investor (Player A) who lends capital and a borrower (Player B) who must repay the principal plus interest. Because the total amount of money never changes, any gain for A must be offset by a loss for B; the system is therefore intrinsically zero‑sum.

Using discrete probability distributions the expected return E(r) for a given interest rate r is derived. In a perfectly fair zero‑sum game (both parties have equal chances of winning or losing) the break‑even condition E(r)=0 is satisfied only when r ≈ 100 %. In other words, an investor must charge an interest rate equal to the principal in order to avoid a net loss across the whole economy. The analysis is then extended by introducing an “advantage parameter” α that gives the investor a modest edge (e.g., better information, lower transaction costs). Even with a 5 % advantage (α = 0.05) the model shows that the investor still needs to charge roughly 15 % interest to achieve a positive expected profit. Small structural advantages therefore do not substantially lower the required rate.

These mathematical results are linked to historical observations. During periods when economies operated under hard‑money constraints (e.g., medieval gold‑based usury, 19th‑century gold‑standard lending, or contemporary developing‑country economies heavily dependent on foreign hard currency) interest rates often exceeded 100 % or were otherwise considered usurious. The paper argues that such high rates were not merely the product of greed or weak regulation; they were a logical consequence of a fixed‑supply monetary framework.

The discussion then turns to cryptocurrencies, especially Bitcoin, whose protocol caps the total supply at 21 million coins. Because the supply is predetermined and cannot be expanded, a Bitcoin‑based monetary system behaves like the theoretical zero‑sum model. Consequently, the paper concludes that a non‑expandable cryptocurrency cannot sustain the low‑interest‑rate environment that modern fiat economies rely on. To make a cryptocurrency viable as a primary medium of exchange, either the supply must be allowed to grow (through inflationary mechanisms, dynamic issuance, or algorithmic adjustments) or the system must be hybridized with fiat money that can supply liquidity for credit markets.

Policy implications are drawn for both regulators and crypto designers. In a hard‑money regime, traditional monetary policy tools (e.g., adjusting the policy rate) lose effectiveness because the money base is immutable. High‑interest‑rate environments can suppress borrowing, reduce investment, and slow economic growth. Therefore, designers of digital currencies should consider incorporating flexible supply rules or stablecoin layers to avoid the inherent zero‑sum pressure. Regulators, on the other hand, may need to develop special prudential standards for credit products denominated in fixed‑supply assets, recognizing that the underlying economics inevitably push rates into the usurious range.

In summary, the paper provides a clear mathematical demonstration that a zero‑sum monetary system forces investors to demand extremely high interest rates—often 100 % or more—to break even. This necessity explains historical episodes of usury under hard‑money regimes and suggests that cryptocurrencies with immutable supplies are unlikely to replace modern fiat currencies without substantial modifications to their supply dynamics.