Contribution
It makes the indeterminacy of markets with increasing returns analysable. Instead of saying that several equilibria exist and stopping, it adds “historical small events”, here the order in which agents arrive, to the model and follows how they accumulate. It names four properties the increasing-returns process lacks and the diminishing-returns one has: efficiency, flexibility, predictability and ergodicity. It shows all four failing in a model simple enough to settle with the theory of random walks.
Key insight
“Small events” are whatever lies “outside the knowledge of the observer — beyond the resolving power of his ‘model’”. Under diminishing returns they average away, since the process “forgets its small-event history”. Under increasing returns each adoption raises the payoff to the next one, so an early lead makes everyone choose the leader, and the process “remembers its small-event history”. Complete knowledge of supply and demand then says that one technology will win and the odds of each, but not which.
Assumptions
- Two technologies, A and B, open to all and “not subject to strategic influence or manipulation”. An infinite pool of agents, each of whom adopts once, when his old equipment dies, and keeps what he chose.
- Two agent types, R and S, in equal numbers. Returns are linear in previous adoptions: for an R-agent a_R + r n_A for A and b_R + r n_B for B, for an S-agent a_S + s n_A and b_S + s n_B. a_R > b_R and a_S < b_S, so R prefers A and S prefers B at the start. Increasing, constant and diminishing returns are r, s > 0, = 0 and < 0.
- Agents are rational, fully informed of current returns, and myopic in structure: returns do not depend on future adoptions, so expectations play no part, and nobody can wait.
- The observer knows everything except the times of choice. To him the sequence of R and S agents is a fair coin.
- Definitions, verbatim in substance: the outcome is predictable if a forecast sequence comes ever closer to the market share with probability one; flexible if a change of either returns function by an arbitrarily small ε from any stage on can change future choices; ergodic if two sequences of small events lead to market shares whose difference goes to zero with probability one; efficient, as a search procedure, if no adopted option has lower returns to either agent type than an unadopted one.
Key results
- One agent type. With diminishing returns adoption follows the composite supply curve and the market is shared. With increasing returns the first agent’s choice is chosen by all the rest: “A ‘corners the market’ and B is excluded.” If returns rise at different rates, the winner can be the worse technology, and no marginal policy can close “the finite gap between the returns to A after n adoptions and the returns to B at the starting point”.
- Constant returns. R-agents always choose A, S-agents B, so d_n = n_A − n_B is a fair random walk, d_n/n → 0 and shares go to one half.
- Diminishing returns. Agents switch to the technology that is behind once the gap is large enough. d_n is a random walk with reflecting barriers, trapped between constants, and shares go to one half.
- Increasing returns. R-agents switch to B once B is far enough ahead, and S-agents to A once A is. The boundaries “absorb” the process. d_n is absorbed with probability one, so “the two technologies cannot coexist indefinitely”. The observer can give the probability that A wins (the OCR garbled the expression; re-derived as Δ_R/(Δ_R + Δ_S) with Δ_R = (a_R − b_R)/r and Δ_S = (b_S − a_S)/s in THEORY-863), but not the outcome.
- Table 2. Necessarily efficient, necessarily flexible, predictable, ergodic: constant returns yes, no, yes, yes; diminishing returns yes, yes, yes, yes; increasing returns no, no, no, no.
- Extensions. The same holds for N technologies and unequal proportions of types (the walk drifts). With finite agents, absorption has probability less than one. With nonlinear “parallel” returns the barriers stay constant and the results hold. With returns that level off at different heights the case approaches constant returns, and both technologies can share the market.
- Policy. Subsidizing the technology that has fallen behind “pushes policy onto a razor-edge. Small subsidies to the excluded choice will not re-establish it; large subsidies, on the other hand, will swing the market and drive the dominant choice out.” A planner with a favoured outcome should “‘tilt’ the process economically toward the favored technology at the outset”. “With increasing returns … timing becomes all-important.”
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | In the model, increasing returns make the adoption process converge with probability one to the exclusion of one technology | strong | random walk with absorbing barriers; re-derived and simulated in THEORY-863 |
| C2 | Which technology wins is decided by the order of arrivals, so the outcome is not predictable from the returns functions, though its probability is | strong | gambler’s ruin on the barriers |
| C3 | The locked-in outcome need not be the more efficient, and marginal changes to returns cannot dislodge it | strong in the model | one-type case (Fig. 1) and the absorbing barriers |
| C4 | Under constant or diminishing returns the outcome is predictable, ergodic and (with diminishing returns) flexible | strong | random walk without barriers or with reflecting ones |
| C5 | The results extend to N technologies, unequal type shares and parallel nonlinear returns, and weaken when barriers vary with n | moderate | stated, not proved in the paper |
| C6 | QWERTY, British rail gauge, US colour television and gasoline over steam are historical instances | weak | narrative examples, with a NASA study cited for steam |
| C7 | Historical explanation that looks for the winner’s superiority is valid only under constant and diminishing returns | moderate | follows from C4 and C1 within the model |
| C8 | Exact economic prediction may be impossible in principle where increasing returns amplify events below a model’s resolution | weak | speculation by analogy to weather forecasting |
Concepts
- Competing technologies: ways of fulfilling one purpose, such that adopting one tends to displace or preclude another, competing “in the unconscious, passive sense”.
- Historical small events: events or conditions “outside the knowledge of the observer”, here the times of choice. Not “pure chance”: “Randomness follows then from lack of knowledge.”
- Lock-in: absorption of the process into a region where both types choose the same technology.
- Non-ergodicity: dependence of the limit on the sequence of small events.
Connections
It cites Marshall’s case of firms with falling cost curves, where the winner is “whichever firm first gets a good start”, Schelling (1978), David (1975) for ergodicity in economic history, and Arthur, Ermoliev and Kaniovski (1983) for the generalized urn schemes behind the heterogeneous-agent extension. The 1989 article in the LIT is its published successor.
Bearing on the record
- THEORY-863. Filed Active: C1–C4 in the 1983 model, re-derived and simulated.
- CLAIM-408. A19 cited Arthur for “early contingencies can select durable technological advantages without an intrinsic superiority”. That is C1–C3. The two models differ where the claim says its own result stops. In CLAIM-408, restoring κ > α restores the equal allocation: no hysteresis in the constraint. In Arthur’s model the lock-in is an absorbing state. Once it is reached, a marginal change in returns has no purchase, and only a large one reverses it, by driving the other side out (the razor-edge). So Arthur supplies, in a different model, the persistence that CLAIM-408 says its pitchfork lacks, and the reason: the advantage is stored in accumulated adoptions, a state variable that does not decay when the conditions are reversed. Neither model has the advantaged party acquiring authority over the rule, the route CLAIM-408 names. The comparison is the record’s.
- CASE-112. Arthur’s planner who “tilt[s] the process … at the outset” is CASE-112’s tilt h applied before the symmetry breaks. Arthur adds that the same small tilt has no effect after lock-in, which is CASE-112’s hysteresis in h.
- Neutral rules, unequal outcomes. Arthur’s process is symmetric in the technologies when a_R − b_R = b_S − a_S and r = s, and still ends with one of them holding the whole market. That is A19’s “The rules of motion remain symmetric. The realized organization does not”, in a stochastic rather than a deterministic model.
- THEORY-429 (North) carries increasing returns from technologies to institutional matrices, which Arthur’s 1983 paper does not do.
No instruction for machine-learning practice; nothing for the anthology.
Limitations
- Not the published article. The 1989 Economic Journal version was not reached. Its framing, extensions and examples may differ, and the LIT’s claims about it rest on this precursor.
- A very special model. Two types, equal numbers, returns linear in past adoptions, no expectations, no pricing, no strategic sponsors. Arthur names each of these as open.
- “Efficiency” is weak. It is a search criterion (no unadopted option better than an adopted one), and the paper notes that greedy choice does not maximize aggregate payoff even when it holds.
- Examples are narrative. The QWERTY and steam-car stories are offered as illustrations and are not analysed. Their history has since been disputed in the literature, which the record does not hold.
- Extensions asserted. The N-technology, unequal-proportion and nonlinear results are stated without proof.
Open questions
- Arthur’s own: which increasing-returns dynamics have these properties, and what changes with strategic sponsors, expectations, or agents who can wait?
- For the record: is there a model in which an advantage selected by symmetry breaking persists after the constraint is restored because the advantaged party stores it (in adoptions, resources or authority over the rule)? Arthur’s accumulated adoptions are one such store. CLAIM-408 names another and does not model it.