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Network game

Pressure meets pressure.

Each state puts in effort in proportion to its stake and to its rivals' effort. The engine solves the equilibrium every time a stake moves.

Try it liveRead the formats
A geoeconomics simulation on a globe in the CommandAGI workbench: oil flows from the Persian Gulf to China, India, Japan, South Korea, Europe and the United States drawn as arcs, each country coloured by its oil inflow, while the globe turns slowly from the Gulf toward the Pacific.
Recorded in the workbench: the geo-hormuz world on its globe. Its numbers are illustrative, not data.

The equilibrium

x* = (I − λG)⁻¹ a.

The interior Nash equilibrium of Ballester, Calvó-Armengol and Zenou (2006). G is the rivalry relations, a the live stakes, λ the complementarity, which is required and never defaulted.

How the game of pressure closes the straitIran's stake builds over twenty days, holds, and eases from day 70 to day 100. The United States' and Saudi Arabia's stakes move with the oil price. The rivalry relations couple their efforts, and the game solves the equilibrium. Iran's effort above 1.5 closes the strait, which cuts the oil flows and raises the price, which raises the others' stakes.Iran's effortstakeIranstake: escalation, overdays 0–100United Statesstake: 0.8 + (price − 80)/ 100Saudi Arabiastake: 0.5 + (price − 80)/ 400The game: tensionλ = 0.3, rivalry rates 1,0.6, 0.3Strait closureclamp((effort − 1.5) /2.5, 0, 0.9)Oil pricethe ledger's supply lossHow the game of pressure closes the straitIran's stake builds over twenty days, holds, and eases from day 70 to day 100. The United States' and Saudi Arabia's stakes move with the oil price. The rivalry relations couple their efforts, and the game solves the equilibrium. Iran's effort above 1.5 closes the strait, which cuts the oil flows and raises the price, which raises the others' stakes.Iran's effortstakeIranstake: escalation, over days 0–100United Statesstake: 0.8 + (price − 80) / 100Saudi Arabiastake: 0.5 + (price − 80) / 400The game: tensionλ = 0.3, rivalry rates 1, 0.6, 0.3Strait closureclamp((effort − 1.5) / 2.5, 0, 0.9)Oil pricethe ledger's supply loss

Read the formats

Efforts, day by day.

scripts/sites/case-studies.mjs hormuz stepped the shipped world at escalation 1.8 and complementarity 0.3.

geo-hormuz · tension.<state>.effortthe engine's numbers · simulation · 2026-11-04
day   0  Iran 0.39  United States 0.97  Saudi Arabia 0.57  closure  0.0%
day  20  Iran 2.37  United States 1.65  Saudi Arabia 0.94  closure 30.5%
day  40  Iran 2.59  United States 2.02  Saudi Arabia 1.05  closure 43.7%
day  70  Iran 2.61  United States 2.05  Saudi Arabia 1.06  closure 44.2%
day  90  Iran 1.20  United States 1.36  Saudi Arabia 0.75  closure  0.0%
day 120  Iran 0.39  United States 0.97  Saudi Arabia 0.57  closure  0.0%

The equilibrium over time

The United States doubles its effort.

From 0.97 to 2.05 at the height, because the price raises its stake (case-studies/hormuz/stats.json).

Refused when it diverges. A game with λ·ρ(G) ≥ 1 has no interior equilibrium. The engine stops the run and says why. Coupled by equations. There is no bus. A game reads each entity's stake, and each entity writes its stake from what it sees. Declared payoffs. The equilibrium is of the payoffs the file declares. It is structural, not a forecast of what states will do.

Iran's effort, day 0 to day 70
0.39 → 2.61
the United States' effort
0.97 → 2.05
the strait's closure at the height
44.2%

Simulated

Equilibrium efforts in the game of pressure
The numbers
Equilibrium efforts in the game of pressure
DayIranUnited StatesSaudi Arabia
00.390.970.57
101.321.260.74
202.371.650.94
302.561.931.03
402.592.021.05
502.62.041.06
602.612.051.06
702.612.051.06
801.971.810.94
901.21.360.75
1000.471.020.59
1100.40.980.57
1200.390.970.57
ProvenanceFile cloud://global/examples/template-library/worlds/geo-hormuz/world.tsxOutput case-studies/hormuz/stats.jsonTool scripts/sites/case-studies.mjs hormuz: sim-engine.jsRan on This computer (dell-gb10-1)When

Change λ. Find the tipping point.

Complementarity runs from 0 to 0.6 in the world's parameters.

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