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 others, 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 outcomes . [...] 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 potential inefficiency «how increasing returns act to «how increasing returns might drive magnify chance events as adoptions the adoption process into developing take place, so that ex ante a technology that has inferior long- knowledge of adopters’ preferences run potential» (p. 117) and the technologies’ possibilities may not suffice to predict the “market outcome”» (p. 116)
Increasing-returns properties /2 inflexibility non-ergodicity «once an outcome (a dominant «historical “small events” are not technology) begins to emerge, it averaged away and “forgotten” by the becomes progressively more “locke- dynamics – they may decide the in”» (pag. 117) outcome» (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 or indirectly as developers of them (p. 117)
Agents ● agent i comes into the market at time t i : 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, n A and n B , at the time of his choice with increasing, diminishing, or constant returns to adoption given by r and s simultaneously positive, negative, or zero ● a R > b R and a S < b S , 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 a R + rn A b R + rn B S-agent a S + sn A b S + sn B
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 { t i } 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 n th 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)
Process properties /1 «[the process is] predictable if the «[the process is] flexible if a small degree of uncertainty built in subsidy or tax adjustment to one “averages away” so that the observer of the technologies’ returns can has enough information to pre- always influence future market determine market shares accurately choices» (p. 118) in the long run» (p. 118) ● if a given marginal adjustment g ● if the observer can ex ante to the technologies’ returns can create a forecasting sequence alter the future choices (p. 128) { x n * } with the property that | x n – x n * | → 0 with probability 1 as n → ∞ (p. 128)
Process properties /2 «[the process is] ergodic (not path- «[the process is] path-efficient if at dependent) if different sequences of all times equal development (equal historical events lead adoption) of the technology that is to the same market outcome with behind in adoption would not have probability one» (p. 118) paid off better» (p. 119) ● if, given 2 samples from the ● if, whenever an agent chooses observer’s set of possible the more-adopted technology z , historical events { t i } and { t i ’ } versions of the lagging with corresponding time paths technology w would not have { x n } and { x n ’ }, then delivered more had they been [...] | x n – x n * | → 0 with probability 1 available for adoption [...] returns as n → ∞ (p. 128) ∏ remain such that ∏ z ( m ) ≥ max j { ∏ w ( j ) } for k ≤ j ≤ m , where there have been m previuos choices of the leading technology and k of the lagging one (p. 128)
Dynamics of adoption ● n A ( n ) and n B ( n ) are the number of choices of A and B respectively , when n choices in total have been made ● the process is described by x n , the market share of A at stage n , when n choices in total have been made ● d n = n A ( n ) – n B ( n ) is the difference in adoption x n = 0.5 + d n / 2 n ● through the variables d n and n is possible to fully describe the dynamics of 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 ○ n A ( n ) increasing by 1 unit if the next agent in line is an R ○ n B ( n ) increasing by 1 unit if the next agent in line is an S ○ the difference in adoption d n 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 d n 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 d n = n A ( n ) – n B ( n ) < ∆ R = ( b R – a R ) / r ● new S-agents will switch preference to A if numbers adopting A become sufficiently ahead of the numbers adopting B, that is if d n = n A ( n ) – n B ( n ) > ∆ S = ( b S – a S ) / s ● regions of choice now appear in the d n , n plane with boundaries between them given by the two switching conditions ∆ R and ∆ S : once 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 d n , n plane describe barriers that “absorb” the process : once either is reached by random movement of d n , 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
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