Skip to content
Mental Models

Path Dependence & Lock-In

The Four Engines of Increasing Returns

Lock-in doesn't happen by magic — it's driven by four self-reinforcing mechanisms that make an option more attractive the more it gets used. Learn Brian Arthur's four engines, how to spot each one, and why they usually run together.

12 min Updated Jul 6, 2026

By now you believe the claim: small early accidents can get amplified into standards that outlive their reasons. QWERTY, VHS, the 4-foot-8.5-inch railway gauge — history, not merit, wrote the winner. But “history got amplified” is a description, not a mechanism. What does the amplifying? What actual force reaches back and makes a choice better the more people pick it, so that a coin-flip lead snowballs into a monopoly no rival can dislodge?

The economist W. Brian Arthur answered this in the 1980s, and his answer is the mechanistic heart of this whole course. He identified four self-reinforcing mechanisms — four engines of increasing returns — that each turn adoption into an advantage, which drives more adoption, which deepens the advantage. This lesson names all four, gives you an analogy and a worked example for each, and teaches you to spot which one (or which several) is running in a case you care about. Because — spoiler — real lock-ins usually run more than one at a time, which is exactly why they’re so hard to break.

Before you read — take a guess

A software product gets *cheaper per user* the more people buy it, because its huge one-time development cost is spread across a bigger and bigger base while each extra copy costs almost nothing to ship. More buyers → lower cost per buyer → lower price → still more buyers. Which kind of self-reinforcing force is this, most precisely?

First, the weird part: increasing returns run backwards

Most of economics — and most of your intuition — runs on diminishing returns. The first slice of pizza is bliss; the eighth is a chore. The first hour of studying moves your grade a lot; the tenth barely nudges it. Pour more fertiliser on a field and yields rise, then flatten, then fall. This is the normal shape of the world: the more you have of something, the less each extra unit is worth. Diminishing returns are stabilising — they pull systems toward a comfortable middle, because whoever’s ahead finds it harder and harder to pull further ahead.

Increasing returns are the mirror image, and they feel almost unfair. Here, the more of something there is, the more valuable the next unit becomes. Whoever’s ahead finds it easier to pull further ahead. There’s no comfortable middle; the system runs to a corner. The biblical shorthand economists actually use for this is “them that has, gets” — success compounds into more success, and a small early lead is a down-payment on a total win.

That single reversal — from “leaders slow down” to “leaders speed up” — is what makes path dependence possible. Under diminishing returns, an early accident washes out; the field regresses to the mean and the best option eventually wins on merit. Under increasing returns, an early accident gets magnified, and a merely-lucky option can lock in for good. So the real question is: what physically produces increasing returns? Arthur’s answer is four engines. Meet them.

Info:

The one sentence to hold onto

A market has increasing returns when picking an option makes that same option more attractive to the next person. Every engine below is a specific reason why that happens. If none of them is present, you’re back in ordinary diminishing-returns land — and lock-in is unlikely.

Engine 1 — Large set-up / fixed costs (economies of scale)

The analogy. Imagine you’ve built a fabulously expensive bridge across a river. Building it cost a fortune; letting one more car cross costs essentially nothing. If ten cars a day use it, each “pays” a tenth of that fortune. If ten thousand cross, each pays a ten-thousandth. The bridge doesn’t get cheaper to build as more people use it — it gets cheaper per crossing. Volume dilutes the fixed cost.

The precise definition. This engine runs on a large upfront (fixed) cost plus a low marginal cost. Total cost = fixed cost + (marginal cost × units). Divide by units and you get average cost = fixed/units + marginal. As units rise, that first term shrinks, so average cost falls with scale. Cheaper per unit means a lower price, which pulls in more adoption, which spreads the fixed cost even thinner. The loop feeds itself. Crucially, this engine is about cost, not about users caring about each other — it’s the supply side getting more efficient.

Worked example — software’s near-zero marginal cost. A software company spends $50 million building an operating system. Shipping one more copy costs almost $0 (a download). Watch the average cost per user collapse:

UsersFixed cost / user+ marginal (~$0)Average cost per user
1,000$50,000$0$50,000
100,000$500$0$500
10,000,000$5$0$5
100,000,000$0.50$0$0.50

A rival launching fresh has to earn back its own $50M over a tiny user base — so its cost per user starts near $50,000 while the incumbent’s is near $0.50. The incumbent can price below anything the newcomer can survive, purely because it got big first. Railways, chip fabs, and nuclear plants all share this shape: monstrous fixed costs, trivial marginal ones.

How to spot it. Ask: does the cost per unit fall as volume rises, because a big upfront cost is being spread thinner? If the fixed cost dwarfs the per-unit cost, this engine is present. Tell-tale sign: the incumbent can undercut any newcomer not by being smarter but simply by being bigger.

Engine 2 — Learning effects (learning-by-doing and learning-by-using)

The analogy. The first cake you ever baked was a war crime. The fiftieth is muscle memory. You didn’t get a better oven — you got better, and so did your recipe, your timing, your tricks. Now imagine an entire industry doing that: every unit produced teaches the makers and users something, and that knowledge makes the next unit better and cheaper. The technology improves because it’s been used a lot.

The precise definition. Under learning effects, cost falls and quality rises as cumulative experience accumulates — not with the size of the market at a moment, but with the total number ever made or used. This is the famous learning curve (or experience curve): costs tend to drop by a roughly constant percentage every time cumulative output doubles. Two flavours: learning-by-doing (producers get better at making it) and learning-by-using (users, tools, docs, and an ecosystem of expertise get better at deploying it). More use → more accumulated competence → a better, cheaper technology → more reason to use it.

Worked example — a programming language’s ecosystem. Consider why a decades-old language stays entrenched even when newer ones are arguably cleaner. Every year of heavy use has accreted an ecosystem: millions of answered questions, battle-tested libraries for every task, mature debuggers and profilers, a generation of engineers who already know it, textbooks, hiring pipelines, and a folklore of “here’s the trap, here’s the fix.” A newcomer language may be lovelier by design, but on day one it has none of that accumulated learning. Choosing the old language means inheriting all that hard-won competence for free; choosing the new one means re-learning everything the hard way. The same story explains why aircraft and semiconductor production get relentlessly cheaper per unit as cumulative volume climbs — the makers have simply practised more.

How to spot it. Ask: is the option better today than it was a decade ago mainly because so many people have used it and pooled what they learned? If the advantage lives in accumulated skill, tooling, and documentation rather than in the raw design, this engine is running. Tell-tale sign: newcomers complain the incumbent “isn’t better, people just already know it” — which is precisely the point.

A city keeps expanding its existing metro rail system rather than switching to a competing transit technology. Officials explain: 'Our engineers, maintenance crews, and suppliers have spent 40 years getting extraordinarily good at *this* system — switching would throw all that expertise away.' Which engine is doing most of the work here?

Engine 3 — Coordination effects (network effects)

The analogy. A single fax machine is a paperweight — there’s no one to fax. Two fax machines, and you can send one message. A million fax machines, and each one is enormously useful, because of all the others. The value of your machine isn’t in the machine; it’s in the crowd already holding one. You benefit from doing what others are doing.

The precise definition. Coordination effects, better known as network effects, arise when an option’s value to you rises with the number of other people using the same option. Two forms:

  • Direct network effects — you benefit straight from other users. A phone network, a messaging app, a social platform: more users literally is more value, because there are more people to reach.
  • Indirect network effects — you benefit from a growing supply of complementary goods. More cars on the road → more petrol stations, mechanics, and spare-parts shops → more reason to buy a car → still more cars. More users of an operating system → more apps written for it → more reason to choose that OS → still more users. The complements and the platform pull each other up.

This is the engine most tightly wired to your critical-mass prerequisite: because value grows with the crowd, adoption has a tipping point. Below it, the option feels empty and stalls; cross it, and the network effect flips from a headwind into a tailwind and the option sweeps the market.

Worked example — a platform and its apps (indirect network effects). Suppose two operating systems launch neck-and-neck. OS-A edges slightly ahead — maybe by luck, maybe by a marketing push. Developers, seeing marginally more users on A, write their new app for A first. Those extra apps make A more useful, so more users pick A, so even more developers target A, so A gets even more apps. Within a few cycles A has ten times B’s app library and B is a ghost town — not because A’s kernel was better, but because the users-attract-developers-attract-users loop, once tipped, runs away. Nobody buys the phone with no apps; nobody writes apps for the phone with no buyers. Whoever tips first wins the whole thing.

How to spot it. Ask: would I still want this if I were the only user? If the honest answer is “no — its value comes from everyone else already being here,” you’ve found a network effect. Tell-tale sign: the product feels useless when small and unstoppable once big, with a sharp threshold in between.

Engine 4 — Adaptive expectations (self-fulfilling beliefs)

The analogy. A bank is perfectly solvent. A rumour spreads that it’s about to fail. Depositors, not wanting to be last in line for their money, rush to withdraw — and the stampede itself drains the bank and makes it fail. Nobody was right about the bank’s health; they were right that everyone else would act on the belief. The expectation validated itself.

The precise definition. Under adaptive (self-fulfilling) expectations, people choose the option they expect to win — precisely because they expect it to win — and the accumulated weight of that expectation makes it win. Nobody wants to be stranded on a dead-end technology (the person who bought Betamax, the developer who backed the losing platform), so the mere forecast of a winner triggers a bandwagon: everyone piles onto the presumptive victor to avoid being left behind, and the pile-on delivers the victory. The unnerving part is that this can lock in a standard before it has any real advantage at all — expectation alone, running ahead of merit, decides the outcome.

Worked example — a standards war decided by momentum. In a format war (think a high-definition disc standard, or a video cassette standard), the actual technical differences between rivals are often small and disputed. What tips it is perceived momentum. A retailer devotes shelf space to the format it thinks will win. A film studio releases exclusively on the format it thinks will win. A shopper buys the player for the format they think will win, terrified of owning a doorstop next year. Each of those bets is placed on the expected winner, and each bet is a vote that helps make that expectation come true. Hype, endorsements, and a well-timed “it’s basically over” headline can stampede the market onto a standard that never proved itself superior. The winner won because everyone agreed it would.

How to spot it. Ask: are people choosing this mainly to avoid backing a loser — because they think it’ll win? If adoption is driven by forecasts and fear-of-being-stranded rather than by present cost or present usefulness, this engine is live. Tell-tale sign: the word “momentum” doing a lot of work, and phrases like “you don’t want to bet on the next Betamax.”

Spot the trap. A founder pitches you: 'Our app gets a tiny bit cheaper to run per user as we grow, so we have increasing returns and lock-in is inevitable.' Their *only* increasing-returns claim is that mild cost-spreading. What's the sharpest reason to be skeptical that this alone will produce durable lock-in?

Sort the evidence: which engine is running?

You’ve met all four. Now prove you can tell them apart in the wild — the single most useful skill this lesson teaches. Drop each scenario into the engine that best explains it.

Sort each real-world scenario into the engine of increasing returns that best explains it.

  • A streaming service pays once to produce a show; each additional viewer costs almost nothing, so profit per subscriber climbs with subscriber count.
  • Studios release films exclusively on the disc format that pundits declared 'the likely winner,' terrified of backing the next Betamax.
  • A chip fab costs $20B to build but pennies per extra chip, so cost-per-chip plummets as it runs flat out.
  • A veteran database is chosen because 30 years of tutorials, libraries, and experts who already know it make it painless to deploy.
  • After a billion units made, a solar-panel line has quietly cut its cost per watt by 90% just from decades of accumulated production know-how.
  • Traders pile into a currency purely because everyone expects a rush into it, and the stampede itself pushes its value up.
  • You join the messaging app your entire family and workplace already use, because a chat app with no one to chat to is worthless.
  • A carmaker's electric model wins partly because a dense charging network already exists for it, and the chargers spread because so many of its cars are on the road.

Pin each engine to its exact definition

Match the engine (or key term) to the precise mechanism it names.

Match each engine or term to its precise definition.

Why naming the engine matters (the practical payoff)

This isn’t taxonomy for its own sake. The engine you’re facing determines how you build a lock-in — and, crucially, how you’d break one. You fight a network effect with a completely different move than you’d use against a learning-curve advantage. A quick preview of what lesson 6 will develop:

  • Beating economies of scale? Attack the fixed cost. New technology that slashes the upfront cost (cheaper tooling, cloud instead of owned data centres) erases the incumbent’s size advantage — small players can suddenly compete on unit cost.
  • Beating learning effects? You can’t skip the accumulated experience — but you can sometimes change the game so the old expertise no longer applies. A discontinuity (a new paradigm) resets everyone’s learning curve to zero.
  • Beating network effects? Solve the chicken-and-egg problem head-on: subsidise early adopters, build in backward compatibility so switchers keep their old network, or win a niche the incumbent ignores until it’s big enough to tip. You’re fighting the crowd, so you need a way to move the crowd.
  • Beating self-fulfilling expectations? Fight the narrative, because the belief is the battlefield. Flip perceived momentum — big endorsements, “it’s inevitable” signalling — before the bandwagon fully forms.

Same phenomenon (“lock-in”), four different pressure points. Diagnose the engine first; choose the crowbar second.

They usually stack (a lollapalooza note)

Here’s the punchline, and it connects straight back to critical-mass and the lollapalooza-effect: real lock-ins almost never run on a single engine. They run several at once, and the engines multiply rather than merely add.

Take a dominant operating system. It has large fixed costs (billions to develop, near-zero to copy). It has learning effects (a planet of users, admins, and developers who already know it, plus decades of tooling). It has network effects (millions of apps written for it, and users who need to swap files with other users of it). And it has self-fulfilling expectations (developers build for it because they expect it to stay dominant, which keeps it dominant). Any one of those would give a firm an edge. All four together, reinforcing each other, is a fortress — which is exactly why the biggest tech incumbents feel unassailable. Each engine defends the others’ flank.

This is also why lock-in has a threshold feel, just like the tipping points from critical-mass. Below a critical adoption level, none of the engines has enough fuel — costs are still high, little experience has accumulated, the network is thin, and no one expects you to win. Cross the critical mass and all four ignite at once, flip from headwind to tailwind, and the option locks in with startling speed. Small early accident, then four multiplying engines, then a standard that outlives its reasons. That’s the whole machine.

One more link: match each engine to the sharpest question that detects it in the wild.

Tip:

A quick field test

Facing a suspected lock-in, run all four diagnostic questions in a row. Usually two or three come back “yes.” The count tells you how deep the moat is: one weak engine is fragile; three engines reinforcing each other is a fortress. Never stop at the first “yes” — the stack is the story.

Check yourself

Question 1 of 40 correct

What single feature distinguishes increasing returns from ordinary diminishing returns?

Check your answer to continue.

Success:

Key takeaways

  • Increasing returns run backwards from intuition. The more of an option there is, the more attractive the next unit becomes — “them that has, gets” — which lets a lucky early lead snowball into lock-in.
  • Four engines produce them: (1) set-up / fixed costs — big upfront cost spread over volume drops unit cost; (2) learning effects — accumulated experience makes the tech cheaper and better; (3) coordination / network effects — value rises with the crowd (direct) or with complements (indirect); (4) self-fulfilling expectations — people back the expected winner, and the belief makes it win.
  • Spot them by their source: cheaper-with-volume = scale; better-because-practised = learning; valuable-because-of-others = network; chosen-to-avoid-a-loser = expectations.
  • Naming the engine tells you how to build or break the lock-in — a preview of lesson 6.
  • They stack. Real lock-ins run several engines at once, reinforcing each other past a critical-mass threshold — which is exactly why they’re so durable.

Where this goes next

You can now name the forces behind lock-in. Lesson 4 puts them to work in the arena where they’re fought most viciously: standards wars and switching costs — how firms deliberately engineer these engines to trap customers, why “the better product” so often loses, and what it actually costs you to leave a platform once its engines have you surrounded.

Mark lesson as complete