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

The discussion surrounding Bitcoin's potential as an inevitable or unique Schelling point in financial systems introduces a complex paradox rooted in game theory and the dynamics of power and coordination. The argument posits that if Bitcoin were universally recognized as a dependable unit of account, it would inherently attract efforts to monopolize control over it. This stems from the nature of power as fundamentally a coordination game, where the extensive period required to establish Bitcoin as the primary unit of account provides ample time for a relatively small yet powerful coalition of miners, world leaders, and venture capitalists to orchestrate a monopoly.

This scenario raises concerns about the stability of such a monopoly, with speculations about a possible "hash war" among competing factions. However, the concept of a hash war as a sustained conflict is dismissed by coalitional game theory, which predicts a quick resolution favoring a dominant coalition capable of securing more than 50% control, thereby ending the competition. This swift consolidation of power underscores the inherent vulnerability of Bitcoin should it reach the status of being inevitable. The very acknowledgment of Bitcoin’s potential inevitability makes it a target for consolidation and control, which paradoxically ensures its security and viability as long as it remains susceptible to failure. Thus, this intricate interplay between inevitability, vulnerability, and the motives for attacking or defending Bitcoin reveals the nuanced challenges facing its adoption and stability as a universal unit of account.