Bitcoin Exit Dominance in Monetary Coordination Games

Abstract

In a multipolar world with no trusted monetary coordinator, how do rational actors settle large-value transactions across trust boundaries? We model this as a non-cooperative game—the "Exit Game"—in which capital allocators choose between capturable settlement systems ("Stay") and neutral settlement ("Exit"). The model rests on four empirical axioms: persistent multipolarity, rational self-interest, computational hardness, and network effect persistence. We prove three results. First, the payoff advantage of Exit over Stay is strictly increasing in adoption: every term in the payoff differential favors Exit under maintained monotonicity conditions, and each actor's adoption threshold approaches zero under structural debasement (Theorem 1). Second, no coalition can sustain coordinated Stay, because permissionless access makes defection costless and the first defector captures fleeing capital (Theorem 2). Third, the resulting equilibrium is absorbing: the monotone adoption process converges to full adoption once a critical mass is reached, because trust conditions required for coordinated return cannot be reestablished (Theorem 3). The model is explicitly falsifiable: six conditions are identified under which the central claims would fail. Bitcoin is the unique asset satisfying the necessary properties for neutral settlement—a result proved by systematic elimination across seven asset classes in Hash (2026b).