Geoeconomics Analysis · 30 March 2026 · Analysis-002

a* = argmax min U_A(s,a) The Dominant Strategy Trap

Why the United States cannot escape the Yuan row of the payoff matrix. Why both U.S. strategy columns are negative. Why the (0,0) status quo is permanently inaccessible once Iran's dominant strategy is active — and why Washington has been choosing Accommodate since day one.

−HU.S. Accommodate payoff
−H−E*U.S. Escalate payoff
G+S=18Iran dominance margin
(0,0)Status quo — inaccessible
Explore the trap ↓
01 · The Function

Equation 4

−H < 0 ∧ −H−E < 0 ⟹ a* = argmax min U_A = Accommodate
−H
U.S. Accommodate payoff
The cost the U.S. pays when Iran shifts to yuan and Washington does not escalate. H = hegemony loss — the erosion of dollar reserve-currency privilege. At calibrated values H ≈ 7. Always negative; the trap cannot produce zero.
−H−E
U.S. Escalate payoff
The cost the U.S. pays when it chooses High Response. Worse than Accommodate by exactly E (the escalation cost). At 30 March 2026 calibration with E* replacing E: −H−E* = −7−13.7 = −20.7. The deterrence gap is E* = 13.7.
a*
U.S. minimax strategy
The action that maximises the minimum payoff (minimax). Since −H > −H−E always (E≥0), Accommodate is always the minimax solution. The U.S. is not maximising — it is minimising its minimum loss. That is the trap.
(0,0)
The inaccessible status quo
The Dollar/Accommodate cell where Iran accepts dollars and U.S. maintains hegemony at zero cost. Payoff: (−S, 0). Since Yuan ≻ Dollar for Iran (G+S>0), Iran never plays Dollar. The U.S. is permanently locked out of this cell.
E ≥ 0 always
Since escalation cost E is non-negative, −H > −H−E is always true. Accommodate dominates Escalate for the U.S. regardless of parameter values.
G + S > 0 → trap active
Iran's dominance condition G+S>0 locks the U.S. into the Yuan row. The trap exists because Iran's strategy is fixed, not because U.S. options are symmetric.
NE at (Yuan, Accommodate)
The unique pure-strategy Nash Equilibrium. Iran prefers Yuan given U.S. plays Accommodate. U.S. prefers Accommodate given Iran plays Yuan. Both conditions hold simultaneously.
02 · The Trap Geometry

Why Both Payoffs Are Negative

01

Iran's dominant strategy locks the U.S. into the Yuan row

Yuan ≻ Dollar ⟺ G + S > 0

Since G (yuan gain) > 0 and S (sanctions cost of staying in dollars) > 0, their sum is always positive. Iran's yuan shift is strictly dominant. The U.S. cannot reach any Dollar-row cell — Iran never plays it. The game is permanently in the Yuan row.

02

Both Yuan-row U.S. payoffs are negative

U_A(Yuan, Acc) = −H < 0 AND U_A(Yuan, Esc) = −H−E < 0

H > 0 (hegemony loss is real) and E > 0 (escalation has costs). Therefore both payoffs in the Yuan row are strictly negative. The U.S. cannot obtain a non-negative payoff in this game — the status quo (0,0) requires Iran to play Dollar, which Iran never does.

03

U.S. minimax: choose the less-negative option

a* = argmax{−H, −H−E} = Accommodate (since −H > −H−E for all E>0)

The U.S. cannot maximise — it can only minimise losses. Since −H is always greater than −H−E (by exactly E), Accommodate is always the minimax solution. This is not a preference — it is forced by the structure of the trap.

04

Nash Equilibrium verification

Iran: G ≥ −S ✓ | U.S.: −H ≥ −H−E ⟺ E ≥ 0 ✓

Both NE conditions are satisfied simultaneously. No player can improve their payoff by unilaterally deviating. Iran cannot do better than Yuan given U.S. plays Accommodate. U.S. cannot do better than Accommodate given Iran plays Yuan. The equilibrium is stable and unique.

Status quo (0,0) — inaccessible
Dollar / Accommodate cell
Iran payoff −S. U.S. payoff 0. Requires Iran to play Dollar. Iran never does (G+S>0). Permanently locked out.
NE: (Yuan, Accommodate)
Iran +G, U.S. −H
The equilibrium cell. Iran collects +8 per round. U.S. pays −7 per round. Stable, unavoidable, indefinite.
Trap deepens with E*
Escalate: −H−E* = −20.7 (30 March 2026)
As Hormuz credibility rises, E* replaces E. The Escalate cell worsens from −12 to −21. The trap tightens automatically.
Day 30 — Accommodate confirmed repeatedly
U.S. playing Accommodate empirically
Bessent waiver (19 Mar, Sr=0.78), Trump talks signal (23 Mar, Brent −11%), 2,500 Marines deploying (Sr=0). All consistent with minimax a*=Accommodate. Three independent confirmations by day 30.
03 · The Full Payoff Matrix

2×2 Payoff Structure

The original two-column matrix from Equation 1. Each cell shows (Iran payoff, U.S. payoff). The Yuan row is the only row Iran ever plays. The Dollar row is permanently inaccessible. The U.S. chooses between two negative payoffs.

The trap in one sentence
Because Iran's Yuan strategy is strictly dominant (G+S>0), the U.S. is permanently locked into the Yuan row — where both payoffs are negative and Accommodate is always the minimax choice.
What breaks the trap
Only a sanctions relief offer Sr ≥ G+S = 18 breaks Iran's dominance, making the Dollar row accessible. No military option delivers Sr. The Navy delivers Sr = 0. Only the Treasury can break the trap.
04 · Parameter Sensitivity

Trap Depth Across G × S Space

The dominance margin G+S determines how deep the trap is. The table shows Iran's dominance margin across all combinations of yuan gain G and sanctions cost S.

G \ SS=4S=6S=8S=10S=12S=14
1–8 · weak trap 9–14 · active trap 15–20 · deep trap 21+ · extreme trap ★ current (G=8, S=10)
05 · Historical Cases

Five Worked Examples

06 · Interactive

Live Trap Simulator

Adjust parameters and watch the trap geometry update. Drag Sr rightward to see what sanctions relief would be required to break dominance.

8
10
7
14
0
Dominance: G+S−Sr = 8+10−0 = 18 > 0 → Trap active
Dominance margin
+18
U.S. Accommodate
−7
U.S. Escalate
−21
Deterrence gap E*
14
Iran Yuan payoff
+8
Sr coverage
0%
U.S. Accommodate −H U.S. Escalate −H−E* Iran Yuan +G Iran Dollar −S+Sr