Each round of yuan-denominated Hormuz transit compounds the erosion of dollar hegemony. Iran's payoff is constant at G every round. U.S. payoff compounds downward. The trap tightens automatically without any strategy change — and the erosion does not reverse when the guns go quiet.
Each round, a fraction of remaining hegemony is lost — not a fixed amount. This geometric decay means the absolute loss slows as H approaches zero, but H never fully recovers. Compare with arithmetic decay (H_{t+1} = H_t − c): geometric decay is more realistic because the dollar's strategic value scales with its current share, not an absolute quantity.
The product of all prior decay factors gives hegemony at round t. Each factor is less than 1, so the product strictly decreases with t. As n grows (more Swing states switch), the factors themselves shrink, accelerating the compounding.
U.S. payoff becomes less negative over time as H decays — but this is not improvement. A smaller |H| means less hegemony remaining to lose, not a recovery. The U.S. is not recovering from the trap — it is watching the strategic stakes of defending the dollar gradually fall to zero.
Iran's payoff is a constant G every round. It requires no new action, no strategy change, no investment. The U.S. payoff compounds downward each round, requiring ever-greater diplomatic and military investment to defend a position that is shrinking anyway. Time works for Iran and against Washington.
These effects are permanent. They do not reverse when the Hormuz crisis ends. Each represents an increase in the decay rate or a direct H reduction that no subsequent policy can undo.
Fraction of original hegemony remaining after t rounds across different decay rates ρ_I + n·ρ_S. Current estimated zone highlighted.
| t \ ρ_total | 0.02 | 0.04 | 0.06 | 0.08 | 0.10 | 0.15 |
|---|
Watch H decay over rounds as decay rates and Swing state switches accumulate. Iran's payoff line stays flat at G every round.