A Game-Theoretic Approach to Bitcoin’s Valuation in Equilibrium

The discussion begins with a critique of applying Gresham's law to bitcoin, emphasizing that Gresham's law pertains only to physical currencies with identical nominal values but differing intrinsic properties. The argument extends to clarify that this law is not applicable to bitcoin since it lacks a physical form and does not operate alongside currencies with a non-bitcoin nominal value pegged to it. Moreover, the assertion that the equation $S=I$ (Savings equals Investment) explains bitcoin's equilibrium is contested, highlighting that this equation merely reflects an accounting identity rather than providing substantive insights into bitcoin’s dynamics or valuation.

Subsequently, the narrative shifts towards exploring the valuation of bitcoin within the framework of theoretical financial economics, particularly focusing on asset pricing theory and the concept of perfect capital markets. It underscores the necessity of assuming perfect capital markets, devoid of frictions like transaction costs, to analytically determine bitcoin’s market value. This approach sets aside conventional attributes attributed to bitcoin, such as its censorship resistance, transaction finality, or limited supply, suggesting these features do not confer unique utility in a hypothetical scenario of perfect capital markets.

The core of the argument proposes that under the assumptions of perfect capital markets, the value of Bitcoin primarily derives from its role as a unit of account. It suggests that an optimal unit of account in such a market would represent a constant fraction of the economy's total wealth, facilitating efficient price signal transmission across the economy. This perspective draws upon Hayekian principles, proposing the notion of a "Hayek" - a unit of account characterized by independent valuation, fungibility, finiteness, and inertness, where its value is determined at the maximum utility by every economic actor without central authority imposition.

Finally, the argument posits that under the conditions of perfect capital markets, a "Hayek" must exist and proposes bitcoin as the most probable contender for this role, hence attributing value to bitcoin from a probabilistic standpoint. This conclusion aims to provide a novel academic rationale for bitcoin's valuation, diverging from traditional arguments and offering a unique perspective to both academic and general discussions on cryptocurrency.