EuroStack game theory: the models, live

The puzzle. European cloud providers are several times cheaper for raw compute and win independent benchmarks, yet their share of their own market has roughly halved since 2017 while three US firms hold about 70%. Cheaper, and losing: why doesn't price work?
The answer. Buyers need a mix of two things: commodity infrastructure, where Europe is cheap, and differentiated platform and AI services, where network effects rule and Europe is thin. Each firm's mix is its altitude, and each picks the provider that serves its mix, so the market sorts: commodity-heavy firms go European, platform-heavy firms go American. Value keeps migrating up-stack, so the US share climbs on its own. Subsidising the cheap layer moves almost nobody, because the buyers a cheaper basement would win barely exist. The levers that work act on the bundle: letting firms split their stack, and cutting the cost of coupling to a European secondary, which is what the Data Act's egress rules do.
Try it. (1) Click Baseline calibration: one filled dot near m = 0.75, today's market. (2) Drag γ up past ~0.7: a second filled dot appears, and the market now has two possible resting points, with history deciding which one you get: that is a tipping market, and price cannot un-tip it. (3) Click The commodity subsidy saturates, then push π_C even higher yourself and watch how little the dot moves. (4) Drag τ down and watch Europe's secondary-beachhead share grow: the egress lever. (5) Or play a firm yourself: pick a persona on the right and read your own ledger.

Parameters

π_C EU commodity advantage π_D US differentiated advantage γ network strength τ coupling cost (egress lever) low-altitude weight w₁ bump centers c₁, c₂ spread s

The paper's experiments

Every point where the curve crosses the diagonal is a possible market outcome. Filled dots: outcomes the market can rest at. Open circles: knife-edges between them.

The population of firms by altitude. Firms right of the red line choose the US stack; left of it, the European one. The two humps are the measured market: infrastructure-heavy firms and platform-native firms, few in between.

You are a firm. Make your move.

your altitude (share of your needs that are platform/AI)

Equilibrium

m = the share of firms whose primary stack is American.

What the paper says here

Move a slider, or run one of the experiments on the left. Sliders re-solve the fixed-point problem m = 1 - G(a*(m)) exactly as the verified suite does.

The puzzle. A procurement office wants genuinely European suppliers. A global firm can incorporate an EU subsidiary, host the data locally, staff it with EU residents, and pass every operational audit. Which requirements actually tell the two apart?
The answer. Only requirements that target an attribute on which the genuine and the pretender differ in cost, and which the buyer can verify. Data residency and operational practice fail the first condition: a global firm does them as well as anyone, so auditing them detects nothing, and no price, penalty, or audit intensity repairs it (the paper's Theorem 2, and the EUCS story in one line). Verifying who actually controls the supplier restores separation, and the accuracy needed is set by the richest would-be pretender. When several attributes are verified, the cheap-to-verify, high-difference ones should come first: each one burns part of the pretender's stake, so the next needs less accuracy (Theorem 1, the audit cascade).
Try it. Set the behavioural audit α_O to 1.0, a perfect operational audit, and watch the red region stand still: perfection on the wrong attribute buys nothing. Then raise φ_J, the cost of faking control, and watch the green region grow. And click any square on the map: the round plays out there, move by move, with the pretender's arithmetic on the table.

Washing region (Theorem 2)

α_O behavioural audit accuracy φ_J cost of faking control φ_O cost of faking operations C_JG genuine control cost C_O operations cost π_G genuine profit L penalty on detection

Cascade (Theorem 1)

type-cost gaps Δ₁, Δ₂, Δ₃ audit unit costs c₁, c₂, c₃ stake multiple Ω/ΣΔ

For each combination of "how verifiable is control" (x) and "how much the pretender stands to gain" (y): green if some contract separates genuine suppliers from pretenders, red if faking wins at any price. The dashed line is the theorem's exact boundary when control is unverified.

The cheapest audit that deters all fakes: verify attributes in the best order, each bar showing how accurately that attribute must be checked. Later attributes need less: the earlier ones already burned part of the pretender's stake.

Play one round

Click any square on the map: the game plays out there, with the numbers.

Waiting for a click.

Reading

The paper's claims

The map paints, for each (structural verifiability α_J, mimic stake gap e) pair, whether any price can separate the types. Move the sliders; the dashed line marks the price-independent boundary e = φ_J − C_JG at α_J = 0.

The puzzle. Two rival sovereignty policies: mandate portability (make leaving any provider easy) or screen ownership (verify who really controls the supplier). Advocates treat them as substitutes. Which should a buyer choose?
The answer. They are complements, and the model says exactly when. An exit mandate shrinks the lock-in rents a fake "European champion" would capture if it slipped through the screen; a smaller prize needs less audit accuracy to deter. So there is a whole band of realistic verification capability where the ownership screen works only with the exit mandate beside it. Below the band, neither instrument reaches the exposure: buying portability there and calling the workload protected is a category error, because portability insures harms that announce themselves and does nothing about the ones that do not.
Try it. Drag your verification capability along the line and watch the verdict switch through all three regimes. Then raise Δ_lock, the lock-in the mandate destroys, and watch the golden band widen: better portability rules make ownership screens easier to run.

Exit or own (Prop 1)

your verification capability α_J mimic stake π_B − π_G lock-in rents cut by exit Δ_lock φ_J C_O C_JG π_G L

The audit accuracy an ownership screen needs: the red line without an exit mandate, the green line with one. Gold band between them: the screen works only if the mandate is there too.

Verdict

The paper's claims

The number line shows the accuracy the ownership screen requires without the exit mandate (α*(e=0)) and with it (α*(e=1)). Between them: the strict-complementarity band, where the screen works only with the mandate.

The puzzle. Between 2019 and 2026 the EU faced the same problem twice: foreign suppliers of critical infrastructure whose home state can compel them. For Chinese telecom vendors it wrote a structural screen (who owns and controls you: the 5G Toolbox, 2020). For US cloud providers it deleted the structural draft criteria (March 2024) and kept behavioural ones (where is the data, who operates it). One Union, one decade, opposite screens. Why?
The answer. Two forces, both from the models on the other tabs. Verifiability: state control of a Chinese vendor is public and needs no audit; effective control behind a US subsidiary must be established against expert legal engineering. And influence: lobbying flows to wherever discretion is highest and salience lowest. A legible criterion is expensive to attack in daylight, so it passed at design and was eroded quietly in national enforcement; a hard-to-verify criterion dies cheaply in a low-salience drafting room, so it never reached enforcement at all. The matrix below is that record.
Try it. Click the four cells for the documented record; then the three predictions, each carrying a live falsifier: an observable event that would prove this explanation wrong.

	Design stage	Enforcement stage
5G / Chinese vendors	Capture fails: salient, security-framed, and the criterion's near-perfect verifiability makes both the rule and any weakening of it legible	Capture partially succeeds: national implementation is discretionary, technical, quiet (until the 2026 Cybersecurity Act revision tries to buy the margin back)
Cloud / US providers	Capture succeeds: low-salience certification venue; deleting a hard-to-verify criterion reads as a drafting choice	Moot: nothing structural left to enforce

Click a cell or a chip.