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Competing technologies, increasing returns and the role of historical events

Federico Frattini Economia Applicata Avanzata Advanced Applied Economics

• W. Brian Arthur (1989)

Competing technologies, increasing returns, and lock-in by historical events, The Economic Journal, 99(394): 116-131

Topic

«dynamics of allocation under increasing returns in a context where increasing returns arise naturally: agents choosing between technologies competing for

• adoption. [...] the more they are adopted, the more experience is gained with

them, and the more they are improved [learning by using: Rosenberg N. (1982), Inside the black box: technology and economics, Cambridge: Cambridge University Press]. When two or more increasing-returns technologies “compete”, insignificant events may by chance give one of them an initial advantage in adoption. This technology may then improve more than the

• thers, so it may appeal to a wider proportion of potential adopters. It may

therefore become further adopted and further improved. Thus a technology that by chance gains an early lead in adoption may eventually “corner the market” of potential adopters, with the other technologies becoming locked-out» (p. 116)

Multiple equilibria

«Competition between technologies may have multiple potential

• utcomes. [...] By allowing the possibility of “random events” occurring during

adoption, it might examine how these influence “selection” of the outcome – how the sets of random “historical events” might cumulate to drive the process towards one market-share outcome, others drive it towards another» (p. 116)

Increasing-returns properties /1

non-predictability «how increasing returns act to magnify chance events as adoptions take place, so that ex ante knowledge of adopters’ preferences and the technologies’ possibilities may not suffice to predict the “market

• utcome”» (p. 116)

potential inefficiency «how increasing returns might drive the adoption process into developing a technology that has inferior long- run potential» (p. 117)

Increasing-returns properties /2

inflexibility «once an outcome (a dominant technology) begins to emerge, it becomes progressively more “locke- in”» (pag. 117) non-ergodicity «historical “small events” are not averaged away and “forgotten” by the dynamics – they may decide the

• utcome» (p. 117)

Model

• dynamics of technologies’ “market shares” under condition of increasing,

diminishing and constant returns

• how returns affect predictability, efficiency, flexibility, and ergodicity
• the circumstances under which the economy might become locked-in by

“historical events” to the monopoly of an inferior technology» (p. 117)

Two unsponsored technologies

• two new technologies, A and B, “compete” for adoption by

a large number of economic agents

• the technologies are not sponsored or strategically manipulated

by any firm and they are open to all

• agents are simple consumers of the technologies who act directly
• r indirectly as developers of them (p. 117)

Agents

• agent i comes into the market at time ti : at this time he chooses

the latest version of either technology A or technology B; and he uses this version thereafter

• agents are of two types, R and S, with equal numbers in each
• the two types are independent of the times of choice but differing in their

preferences, perhaps because of the use to which they will put their choice

• the version of A or B each agent chooses is fixed or frozen in design

at his time of choice, so that his payoff is affected only by past adoptions of his chosen technology (p. 117)

Conditions for increasing returns

• returns [or net present value] to choosing A or B realised by any

agent [...] depend upon the number of previous adopters, nA and nB , at the time of his choice with increasing, diminishing, or constant returns to adoption given by r and s simultaneously positive, negative, or zero

• aR > bR and aS < bS , so that R-agents have a natural preference for A,

and S-agents have a natural preference for B (p. 118) Table: Returns to choosing A or B given previuos adoption (p. 118) Technology A Technology B R-agent aR + rnA bR + rnB S-agent aS + snA bS + snB

The observer

• an observer who has full knowledge of all the conditions and returns

functions, except the set of events that determines the times of entry and choice { ti } of the agents

• the observer thus “sees” the choice order as a binary sequence of

R and S types with the property that an R or an S comes nth in the adoption line with equal likelihood, that is, with probability one half

“historical events”

• «those events or conditions that are outside the ex ante knowledge of

the observer - beyond the resolving power of his “model” or abstraction of the situation» «The supply (or returns) functions are known, as is the demand (each agent demands one unit inelastically). Only one [...] element is left open, and that is the set of historical events that determine the sequence in which the agents make their choice. Of interest is the adoption-share outcome in the different cases of constant, diminishing, and increasing returns, and whether the fluctuations in the order of choices these small events introduce make a difference to adoption shares» (p. 118)

«[the process is] predictable if the small degree of uncertainty built in “averages away” so that the observer has enough information to pre- determine market shares accurately in the long run» (p. 118)

• if the observer can ex ante

create a forecasting sequence { xn* } with the property that | xn – xn* | → 0 with probability 1 as n → ∞ (p. 128)

Process properties /1

«[the process is] flexible if a subsidy or tax adjustment to one

• f the technologies’ returns can

always influence future market choices» (p. 118)

• if a given marginal adjustment g

to the technologies’ returns can alter the future choices (p. 128)

Process properties /2

«[the process is] ergodic (not path- dependent) if different sequences of historical events lead to the same market outcome with probability one» (p. 118)

• if, given 2 samples from the
• bserver’s set of possible

historical events { ti } and { ti’ } with corresponding time paths { xn } and { xn’ }, then | xn – xn* | → 0 with probability 1 as n → ∞ (p. 128) «[the process is] path-efficient if at all times equal development (equal adoption) of the technology that is behind in adoption would not have paid off better» (p. 119)

• if, whenever an agent chooses

the more-adopted technology z , versions of the lagging technology w would not have delivered more had they been [...] available for adoption [...] returns ∏ remain such that ∏z( m ) ≥ maxj{ ∏w( j ) } for k ≤ j ≤ m , where there have been m previuos choices of the leading technology and k of the lagging

• ne (p. 128)

Dynamics of adoption

• nA( n ) and nB( n ) are the number of choices of A and B respectively,

when n choices in total have been made

• the process is described by xn , the market share of A at stage n, when n

choices in total have been made

• dn = nA( n ) – nB( n ) is the difference in adoption

xn = 0.5 + dn / 2n

• through the variables dn and n is possible to fully describe the dynamics
• f adoption of A versus B (pp. 119-120)

[case] constant returns

• R-agents always choose A and S-agents always choose B,

regardless of the number of adopters of either technology

• the way in which adoption of A and B cumulates is determined simply

by the sequence in which R- and S-agents “line up” to make their choice ○ nA( n ) increasing by 1 unit if the next agent in line is an R ○ nB( n ) increasing by 1 unit if the next agent in line is an S ○ the difference in adoption dn moving upward by +1 unit or downward –1 unit accordingly

• to the observer the choice-order is random, with agent types equally

likely and the state dn appears to perform a simple coin-toss gambler’s random walk with each “move” having equal probability 0.5 (p. 120)

[case] increasing returns /1

• new R-agents, who have a natural preference for A, will switch

allegiance if by chance adoption pushes B far enough ahead of A in numbers and in payoff. That is, new R-agents will “switch” if dn = nA( n ) – nB( n ) < ∆R = ( bR – aR ) / r

• new S-agents will switch preference to A if numbers adopting A

become sufficiently ahead of the numbers adopting B, that is if dn = nA( n ) – nB( n ) > ∆S = ( bS – aS ) / s

• regions of choice now appear in the dn, n plane with boundaries

between them given by the two switching conditions ∆R and ∆S :

• nce one of the outer regions is entered, both agent types choose

the same technology, with the result that this technology further increases its lead (p. 120)

[case] increasing returns /2

• the two switching conditions in the dn, n plane describe barriers that

“absorb” the process: once either is reached by random movement

• f dn , the process ceases to involve both technologies – it is “locked-in”

to one technology only and the adoption process becomes a random walk with absorbing barriers (p. 121)

[case] diminishing returns

• the process appears to the observer as

a random walk with reflecting barriers

[discussion] long-term adoption shares

• constant returns

the adoption market is shared: standard deviation of dn increases with n1/2 (property of free random walk processes) and, as a consequence, dn / 2n → 0 and xn → 0.5 as n → ∞

• diminishing returns

the adoption market is shared: dn is trapped between finite constants ( ∆S < dn < ∆R ) and, as a consequence, dn / 2n → 0 and xn → 0.5 as n → ∞

• increasing returns

the adoption share of A ( or B ) must eventually become 0 or 1, because eventually dn > ∆S ( or < ∆R ) with probability 1: the two technologies cannot coexist indefinetly and one must exclude the other (p. 121)

[discussion] predictability

• constant returns

predictability is guaranteed, because the prediction xn* = 0.5 will be correct with probability 1

• diminishing returns

predictability is guaranteed, because the prediction xn* = 0.5 will be correct with probability 1

• increasing returns

predictability is lost, because either observer’s choice xn* = 1 or xn* = 0 will be wrong with probability 0.5 (p. 121)

[discussion] flexibility

• constant returns

flexibility is partial: policy adjustment to the return can affect choices at all times, but only if they are large enough to bridge the gap in preferences between technologies

• diminishing returns

flexibility is guaranteed: an adjustment g can always affect future choices (in absolute numbers, if not in market shares), because reflecting barriers continue to influence the process with probability 1 at times in future

• increasing returns

flexibility is lost: once the process is absorbed into A or B, the subsidy

• r tax adjustment necessary to shift the barriers enough to influence

choices increases without bound (p. 122)

[discussion] ergodicity

• constant returns

ergodicity holds, because only extraordinary line-ups with associated probability 0 can cause deviations from xn = 0.5 and the process forgets its small events history

• diminishing returns

ergodicity holds, because any line-up of the agents must still cause the process to remain between the reflecting barriers, drive the market to xn = 0.5 and forget its small events history

• increasing returns

process is path-dependent: some proportion of agent sequence causes the market outcome to “tip” towards A, the remaining proportion causes it to “tip” towards B and the small events that determine { ti } decide the path of the market shares (p. 122)

[discussion] path-efficiency

• constant returns

path-efficiency holds, because previous adoptions do not affect pay-off, each agent-type chooses its preferred technology and there is no gain foregone by the failure of the lagging technology to receive further development (further adoption)

• diminishing returns

path-efficiency holds: if an agent chooses the technology that is ahead, he must prefer it to the avalaible version of the lagging one, but further adoptions of the lagging technology by definition lowers its payoff and, therefore, there is no possibility of choices leading the adoption process down to and inferior development path

• increasing returns

path-efficiency is not guaranteed: suppose the market locks into technology A, so that R-agents do not lose, but S-agents would each gain ( bS – aS ) if their favoured technology B had been equally developed and available for choice – there is a regret, at least for one agent type (p. 122)

Proporties of the three regimes

Table: Properties of the three regimes (p. 121) Predictability Flexibility Ergodicity Necessary path-efficiency Constant YES NO YES YES Diminishing YES YES YES YES Increasing NO NO NO NO

Remarks /1

«cases where an early-established technology becomes dominant, so that later, superior alternatives cannot gain a footing» (p. 126)

Remarks /2

«the interpretation of economic history should be different in different returns regimes. Under constant and diminishing returns, the evolution of the market reflects only a priori endowments, preferences, and transformation possibilities; small events cannot sway the outcome. But while this is comforting, it reduces history to the status of mere carrier – the deliverer of the

• inevitable. Under increasing returns, by contrast many outcomes are
• possible. Insignificant circumstances become magnified by positive

feedbacks to “tip” the system into the actual outcome “selected”. The small events of history become important. Where we observe the predominance of one technology or one economic outcome over its competitors we should thus be cautious of any exercise that seeks the means by which the winner's innate “superiority” came to be translated into adoption» (p. 127)

Remarks /3

«The usual policy of letting the superior technology reveal itself in the outcome that dominates is appropriate in the constant and diminishing-returns cases. But in the increasing returns case laissez-faire gives no guarantee that the “superior” technology (in the long-run sense) will be the one that survives. Effective policy in the (unsponsored) increasing-returns case would be predicated on the nature of the market breakdown: [...] early adopters impose externalities on later ones by rationally choosing technologies to suit

• nly themselves; missing is an inter-agent market to induce them to

explore promising but costly infant technologies that might pay off handsomely to later adopters» (p. 127)