Economic Law & Competition Economics

0. Why this chapter, and what the term means

Economic law — *droit économique*, *Wirtschaftsrecht* — is a continental European category with no clean Anglo-American equivalent. It is broader than antitrust: it covers the whole legal framework of economic activity. Competition law sits inside it alongside state aid, sector regulation, the internal market freedoms, consumer protection and trade.

1. The schools of thought, and where he sits

Competition law has been fought over by successive schools, each with a different answer to *what is competition for*. You need to recognise the names, because they get invoked as shorthand.

The schools, on two axes

          INTERVENTIONIST
                 ^
                 |
   HARVARD /     |      NEO-BRANDEISIAN
   STRUCTURALISM |      (Khan, Wu, 2017-)
   (1950s-70s)   |      structure matters again;
   structure =   |      bigness itself is a harm;
   conduct =     |      democracy & labour, not
   performance   |      just price
                 |
   ------------- + ----------------->  more
                 |                     DYNAMIC
   POST-CHICAGO  |      AUSTRIAN /
   (1990s-)      |      SCHUMPETERIAN
   game theory,  |      competition IS disruption;
   strategic     |      monopoly profit is the
   behaviour     |      REWARD that drives entry
   can be real   |
                 |      COMPLEXITY ECONOMICS
   CHICAGO       |      (Arthur; SCHREPEL)
   (Bork, Posner)|      markets as evolving
   markets self- |      adaptive systems:
   correct;      |      emergence, path
   consumer      |      dependence, non-linearity
   welfare only  |
                 v
            NON-INTERVENTIONIST


  WHERE HE SITS: bottom right, and explicitly
  CRITICAL OF BOTH the neoclassical mainstream AND
  the neo-Brandeisian critique of it.

  He describes the descriptions of markets and firms
  offered by BOTH as reductionist.

  => Do NOT arrive in a camp. He is not in one.

The bottom-right quadrant is the one to understand. Schrepel's published position is that complexity science offers a higher-resolution account of markets than either the neoclassical models or their neo-Brandeisian critics, because both reduce markets to something simpler than they are. Turning up as a neo-Brandeisian would be a misread.

School	Core claim	What it implies for enforcement	Where it fails
Harvard / structuralism	Market structure determines firm conduct, which determines economic performance. Concentration is itself the problem	Break up concentrated markets; treat high share as presumptively bad	Structure turned out to be a poor predictor of conduct. Concentrated markets can be fiercely competitive
Chicago	Markets self-correct; most apparently anticompetitive conduct has an efficiency explanation. The only legitimate goal is consumer welfare, measured as price and output	Intervene rarely, and only on demonstrated price effects. Error costs of over-enforcement exceed under-enforcement	Assumes rational actors and reversible entry. Badly placed to handle zero-price markets, network effects and data
Post-Chicago	Game theory shows strategic conduct — raising rivals' costs, foreclosure, predation — can be rational and harmful	Case-by-case economic analysis. The effects-based approach the Commission adopted	Expensive, slow and indeterminate. Duelling experts, and the burden sits on the authority
Neo-Brandeisian	Consumer welfare was always too narrow. Concentration harms workers, suppliers, innovation and democratic self-government — bigness is a political problem	Structural presumptions, ex ante rules, scepticism of efficiency defences. Intellectual backdrop to much of the DMA's design	He is explicitly critical of it. Restores structure as a proxy without fixing why structure was abandoned, and conflates distinct harms under one label
Austrian / Schumpeterian	Competition is the process of disruption. Monopoly profit is the prize that induces the next entrant — a temporary monopoly can be the engine, not the pathology	Protect the possibility of entry rather than current market structure. Be slow to intervene against innovation	Hard to falsify, and prone to excusing durable positions as temporary
Complexity economics	Markets are adaptive systems that evolve rather than settle. Outcomes emerge from interactions; feedback, path dependence and non-linearity are normal rather than exceptional	Assess trajectories and contestability rather than snapshots. Expect emergence; be humble about prediction	His own position, and the open problem is operationalising it — a theory of markets as complex systems does not yet yield a test an authority can apply

2. The economics a lawyer actually needs, with the formulas

Six concepts carry most of the work in a competition case. Each has a formula, and knowing the formula lets you say where the measurement is fragile — which is your job rather than producing the estimate.

\text{HHI} = \sum_{i=1}^{N} s_i^2 \qquad \text{where } s_i \text{ is firm } i\text{'s market share in percent}

The Herfindahl-Hirschman Index is the sum of the squared market shares of every firm in the market.Runs from near 0 to 10,000 (one firm at 100 percent). Squaring is the whole point: it weights large firms far more heavily than small ones. Four firms at 25 percent each gives 2,500; one at 70 and six at 5 gives 5,050. The Commission's horizontal merger guidelines treat post-merger HHI below 1,000 as unlikely to raise concerns, and use the delta — the change caused by the merger — alongside the level.

\varepsilon_{A} = \frac{\%\,\Delta Q_A}{\%\,\Delta P_A} \qquad\qquad \varepsilon_{AB} = \frac{\%\,\Delta Q_A}{\%\,\Delta P_B}

Own-price elasticity is the percentage change in quantity of A divided by the percentage change in the price of A. Cross-price elasticity is the percentage change in quantity of A divided by the percentage change in the price of B.Cross-price elasticity is the empirical core of market definition. If raising B's price pushes buyers to A, they are substitutes and arguably in the same market. Positive means substitutes, negative means complements, near zero means unrelated. The problem in digital markets: when the price is zero there is no percentage change in price to divide by, so the standard tool is undefined — which is why zero-price markets broke the inherited method rather than merely stretching it.

\text{SSNIP: would a } 5\!-\!10\% \text{ price rise be profitable?} \qquad \text{Critical loss} = \frac{\Delta P}{\Delta P + m}

The SSNIP test asks whether a hypothetical monopolist could profitably impose a small but significant non-transitory increase in price. Critical loss is the price increase divided by the price increase plus the margin.The hypothetical monopolist test: start narrow, ask whether a sole supplier could raise price 5 to 10 percent profitably. If customers would switch away enough to make it unprofitable, widen the market and repeat. Critical loss makes it operational — compare the sales you could afford to lose against the sales you would actually lose. High margins mean a small critical loss, so highly profitable firms are more easily found to be in narrow markets, which is counterintuitive and frequently litigated.

L = \frac{P - MC}{P} \qquad\qquad L = -\frac{1}{\varepsilon}

The Lerner index is price minus marginal cost, divided by price. At a profit-maximising price it equals minus one over the own-price elasticity of demand.A direct measure of market power as a markup: 0 means price equals marginal cost (perfect competition), approaching 1 means a large markup. The second identity is the useful one — market power and demand elasticity are two views of the same quantity, so a firm facing inelastic demand has power by construction. The practical obstacle is that marginal cost is rarely observable, and for software it is close to zero, which makes the index approach 1 for any firm charging anything at all.

Concept	Plain meaning	Why digital markets break it
Market definition	The set of products and geography within which competition is assessed. Everything else — share, dominance, HHI — is computed inside it	Zero prices make SSNIP undefined; multi-sided platforms serve distinct groups who are not substitutes for each other; ecosystems compete across several markets at once. The Commission revised its Market Definition Notice in 2024 partly for these reasons
Network effects	The product gets more valuable as more people use it. Direct within one side, indirect across sides	Creates tipping: beyond a threshold the market may flip to one winner, so a share snapshot taken before tipping and after measures different things
Two-sided / multi-sided markets	A platform serving distinct groups whose value depends on each other — buyers and sellers, users and advertisers	Pricing below cost on one side can be rational rather than predatory, so single-market predation tests give wrong answers. This is the core analytical difficulty in platform cases
Switching costs and lock-in	What it costs a user to leave — data, learning, contracts, network. Lock-in by historical events is Arthur's phrase	Interoperability and portability duties in the DMA are direct attempts to lower these, which makes the DMA a theory-driven instrument rather than a list of grievances
Contestability	Whether a position could be challenged, regardless of whether anyone currently is	The concept the DMA is built on — the word appears in its own objectives. It is forward-looking and therefore closer to the dynamic view than to a share snapshot
Barriers to entry	What stops a new competitor. Sunk costs, regulation, scale, and in digital markets data and compute access	This is where the GenAI layer-interaction argument bites: a training-efficiency advance can collapse a compute barrier overnight

3. Complexity economics — his position, properly

Complexity concept	What it means	The competition-law consequence
Emergence	System-level patterns arise from local interactions and are not properties of any participant. No individual firm contains the market structure	Supra-competitive pricing can emerge without an agreement to characterise. The algorithmic-collusion literature is exactly this, and Article 101 needs a meeting of minds that may simply not exist
Non-linearity	Small causes can have large effects and vice versa. Responses are not proportional to inputs	Remedy design becomes genuinely hard: a proportionate-looking intervention can have an outsized effect, or none. It also means effects are not reliably extrapolable from a counterfactual
Path dependence / increasing returns	Where early advantage compounds, outcomes depend on history rather than on efficiency. Arthur's lock-in by historical events	A dominant position may be an accident of sequence rather than evidence of merit — which cuts against the Chicago inference from durability to efficiency
Feedback loops	Output becomes input. More users give more data, improving the product, attracting more users	Schrepel and Pentland's point about foundation models: strong loops mean firms compete for the market rather than in it — but the strength of the loop differs by model type, which is the qualification that makes it an empirical question rather than a slogan
Adaptive agents	Participants change their behaviour in response to the system, including in response to being regulated. Agents face ill-defined situations rather than solved optimisation problems	Enforcement is part of the system it observes. Deploy a screen and the conduct adapts to it — which is the concept-drift point, arrived at from economics instead of machine learning
Ecosystems	Systems whose agents interact such that the interactions create patterns affecting the environment, which in turn shapes each agent's behaviour	His working hypothesis is that ecosystems — now routinely invoked by agencies — can only be properly understood through complexity science, and that enforcers have shown limited interest in it so far

Static against complexity assessment, on the same market

  STATIC / SNAPSHOT VIEW
  ==========================================
   t = today
      |
      v
   measure shares -> define market -> compute HHI
      |
      v
   "Firm A holds 70%. Dominant. Special
    responsibility attaches."

   Assumes: the market is a thing that EXISTS
            and can be measured at a moment.


  COMPLEXITY / DYNAMIC VIEW
  ==========================================
   t-3 ---- t-2 ---- t-1 ---- today ---- t+1?
     |        |        |         |
     v        v        v         v
   who entered? who exited? what tipped?
   which advantage COMPOUNDED and why?
   what would a credible entrant need NOW
   (not what did the last one need)?
      |
      v
   "Firm A holds 70%, reached through an
    early advantage that compounded via a
    feedback loop whose strength has FALLEN
    since training costs collapsed.
    Contestability is rising."

   Assumes: the market is a PROCESS, and a
            share is a residue of that process.


  THE ENFORCEMENT PROBLEM THIS CREATES
  ==========================================
   the static view is WRONG but ADMINISTRABLE
   the dynamic view is RIGHT but you must prove
   a trajectory to an evidential standard

        ^^^ this gap is where computational
            methods are supposed to help, and
            where almost nothing exists yet

The last box is your opening. The complexity critique of static assessment is well made and widely accepted in principle; what is missing is a method that turns a trajectory into something an authority can put in a decision and defend on appeal. That is a measurement problem, which makes it the computational position's problem rather than the legal tracks'.

4. Dynamic competition, predatory innovation, ecosystems

Idea	What it holds	His connection to it
Dynamic competition	Competition over time through innovation and entry, rather than price rivalry within a fixed market. The relevant question is whether a position is contestable, not whether it is large	He co-founded the Dynamic Competition Initiative with Nicolas Petit. If asked, treat this as the research programme and complexity science as its method
Predatory innovation	Innovation deployed not to serve users but to disadvantage rivals — a technical change whose primary effect is exclusion. Breaking interoperability, for instance, with no user benefit	His own book, L'innovation prédatrice en droit de la concurrence. The analytical difficulty is that courts are rightly reluctant to call innovation an abuse, so the test has to separate genuine improvement from exclusion dressed as improvement
Ecosystems	Interdependent products and services across multiple markets, where competition happens between ecosystems rather than within any single market	He has written a working theory of ecosystems in antitrust via complexity science, noting agencies now use the concept while showing little interest in the science that would make it coherent
Error-cost framework	Enforcement choices are decisions under uncertainty, so the question is the relative cost of false positives and false negatives	Not distinctively his, but it is your best bridge: it is a statistical decision problem stated in legal language, and you can formalise it

The error-cost bridge, which is the most useful thing in this section

The error-cost framework asks whether over-enforcement or under-enforcement is costlier, and the Chicago school used it to argue for restraint. But it is literally a decision problem with a loss function, and that means it is computable. A false positive is an innocent firm raided; a false negative is a cartel that continues. Those have different costs, the ratio determines the optimal threshold, and no instrument states either. So an argument that has been conducted rhetorically for forty years has a quantitative form nobody has written down — and that is precisely the kind of contribution a cross-project computational researcher exists to make. This connects the oldest debate in the field to the calibration point, and it is yours.

\text{act if } \;\; P(\text{infringement} \mid \text{evidence}) \;>\; \frac{C_{FP}}{C_{FP} + C_{FN}}

Act when the posterior probability of an infringement given the evidence exceeds the cost of a false positive divided by the sum of the false positive and false negative costs.The standard decision-theoretic threshold. Read what it requires: a posterior probability, which needs a calibrated model and a base rate, and a cost ratio, which is a normative judgment. If false positives are deemed nine times as costly as false negatives, the threshold is 0.9. If equally costly, it is 0.5. No EU instrument states a cost ratio, and no agency publishes a calibrated posterior — so the threshold in operation is an artefact rather than a decision. That sentence is the whole argument, and the formula is why it is unanswerable.

5. The rest of economic law, briefly

Skim this. You will not be examined on it, but knowing the shape of the field prevents a blank look if someone refers to it.

Area	Provision	One line
Competition	Arts 101, 102 TFEU; Reg 1/2003; EUMR	Agreements, abuse, mergers. Covered in its own chapter
State aid	Arts 107–109 TFEU	Member States may not selectively advantage undertakings in a way that distorts competition. Live for AI: public compute subsidies and national champion programmes are state aid questions
Internal market freedoms	Arts 34, 45, 49, 56, 63 TFEU	Free movement of goods, workers, establishment, services, capital. The constitutional backdrop against which digital regulation is justified
Consumer protection	UCPD 2005/29; CRD 2011/83; UCTD 93/13	Goanta's territory. Unfair commercial practices, information duties, unfair terms. Dark patterns are increasingly analysed here as well as under the DSA
Sector regulation	Telecoms, energy, financial services	Ex ante obligations on designated firms. The DMA borrows this architecture and applies it to platforms, which is why it feels like regulation rather than competition law
Data and digital	GDPR, DMA, DSA, Data Act, AI Act	The package. Read as a single reconstitution of economic law for a digitised economy rather than as five separate statutes

6. How this connects to ATLANTIS

Strand	The economic-law question underneath it
Accuracy	Can a computational finding meet an evidential standard? This is the error-cost problem made quantitative — and it requires a calibrated posterior and a stated cost ratio, neither of which exists
Fairness	Which errors are acceptable, and to whom? The impossibility results mean this cannot be settled technically, so it is a normative choice currently being made by default parameters
Institutional arrangements	Who validates the authority's own instrument? Sector regulation has precedents for supervising a supervisor; competition law does not, and the AI Act's sandboxes assume a firm bringing a product to a regulator rather than the inverse

7. What is unexplored, and three projects

Project	The question	How you would do it
The error-cost framework, quantified	Forty years of rhetorical argument about false positives against false negatives, and nobody has written the loss function down	Formalise the threshold rule above. Elicit implied cost ratios from decided cases and from the fine-setting guidelines — the revealed ratio is recoverable from what authorities actually did. Then compare it with the ratio implied by a screen's operating threshold. If they differ, the tool is operating at a cost ratio the institution never chose, and that is a finding
Market definition as a measurement-validity problem	HHI measures your market definition more than it measures concentration. How sensitive are findings to definitional choices?	Take decided cases with published share data, perturb the market definition across the range the parties actually argued for, and report how often the dominance finding flips. Cheap, purely doctrinal inputs, and nobody has published it. It is the overfitting argument applied to market definition
Operationalising contestability	The DMA is built on contestability and does not define how to measure it	Build candidate indicators — entry and exit rates, share volatility, time-to-scale for entrants, switching rates — and test them against markets where contestability was later demonstrated by actual entry. A trajectory measure validated retrospectively, which is the administrable test complexity economics is missing

8. Your CV, mapped onto this chapter

From this chapter	What you can genuinely claim
Error-cost as a decision problem	Direct. You have computed thresholds, false discovery rates and the base-rate inversion, and your paper reports exact tests rather than approximations
Measurement validity	Your crimes-against-women paper is entirely about a measurement problem masquerading as a behavioural finding — police records measure reporting, not offending. That is the same structure as a screen measuring detection rather than collusion
Path dependence and adaptive agents	The Bayesian Structural Time Series isolating the 2013 Amendment as an administrative reporting shock of about 88,879 cases a year is precisely a case of the measurement system responding to an intervention
Agent-based modelling	Do not claim it. You have not built one. You can discuss what it supports — possibility claims, not predictions
Econometrics	Be careful. You have hierarchical mixed-effects models, fixed-effects panel regression and causal inference, which is genuine applied econometrics. You do not have industrial organisation theory, and the two are not the same. Claim the first, disclaim the second
Complexity science	Claim familiarity with the concepts, not expertise. The honest line: I have read the complexity-minded antitrust argument and I think the open problem is operational — turning a trajectory into something that meets an evidential standard

9. If you remember ten things

Economic law is broader than antitrust — competition, state aid, internal market, consumer, sector regulation. The Digital Acts are one reconstitution of it, not five statutes.
He is critical of both the neoclassical mainstream and the neo-Brandeisians, describing both as reductionist. Do not arrive in a camp.
Complexity economics: markets evolve rather than settle. Emergence, non-linearity, path dependence, feedback loops, adaptive agents. Lineage runs through W. Brian Arthur.
HHI is the sum of squared shares and it measures your market definition more than it measures concentration. That is the point to make, not the arithmetic.
Cross-price elasticity is the empirical core of market definition — and it is undefined at a zero price, which is what digital markets actually broke.
Lerner index: markup over price, equal to minus one over elasticity. Marginal cost is near zero for software, so it approaches 1 for anyone charging anything.
Act when the posterior exceeds C-FP over C-FP plus C-FN. That needs a calibrated probability and a stated cost ratio. Neither exists in any instrument, so the operating threshold is an artefact.
Agent-based models support possibility claims, not predictions. Keeping that line is the difference between a contribution and an unfalsifiable model.
The fair criticism of complexity framing is that it has no administrable test yet — and *we cannot predict* is also an argument for inaction. State the objection; offer the measurement as the fix.
Every school failed on a measurement problem, and ATLANTIS is a measurement project. That is the sentence that makes the accuracy strand central rather than peripheral.