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

This discussion is rooted in the argument that a universally accepted unit of account, representing a consistent share of total wealth, could encourage macroeconomic stability. The historical significance of the unit-of-account function in money is revisited, underlining its role in the enforcement of contracts and debts, as well as challenging the dismissal of credit by some within the Bitcoin community.

Further examination reveals skepticism regarding the application of Gresham's Law to Bitcoin, given its digital nature and absence of a physical form to compete with other currencies on nominal value. The critique extends to the use of the savings equals investment equation ($S=I$) for explaining Bitcoin's market position, suggesting instead that Bitcoin's value may derive from its potential role as an optimal unit of account in perfect capital markets. This perspective introduces the concept of a "Hayek," a theoretical unit of account that represents a constant fraction of total wealth, which could facilitate efficient price signal transmission across the economy. Bitcoin is proposed as the most probable real-world candidate for this role, providing a new academic rationale for its valuation beyond traditional arguments.

The necessity of an independent unit of account, such as a "Hayek," in perfect capital markets prompts a reevaluation of academic approaches to asset valuation, particularly highlighting a discrepancy in how these principles are applied to digital currencies like Bitcoin versus traditional financial instruments. This inconsistency calls for a reconsideration of digital currencies' potential roles within the global financial ecosystem, ensuring equitable and logical assessment standards are applied across different asset classes.

The narrative then delves into the complex paradox surrounding Bitcoin's potential as a universal unit of account, considering the dynamics of power and coordination. It discusses the possibility of a monopoly over Bitcoin if universally recognized as a dependable unit of account, exploring the implications of such a scenario, including the likelihood of a "hash war" among competing factions. However, coalitional game theory predicts a quick resolution in favor of a dominant coalition, highlighting Bitcoin's inherent vulnerability should it achieve inevitability status. This interplay between inevitability, vulnerability, and motives for attacking or defending Bitcoin underscores the nuanced challenges it faces in becoming a stable, universally accepted unit of account.

The critique of invoking Gresham’s Law in the context of Bitcoin’s usage as currency clarifies that this law is pertinent only to physical currencies with identical nominal values but different intrinsic properties, emphasizing the need for a more nuanced understanding of Bitcoin's position and potential within the economic landscape.