Structural Change and Economic Dynamics

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1 Structural Cange and Economic Dynamics 21 (2010) 5 16 Contents lists available at ScienceDirect Structural Cange and Economic Dynamics journal omepage: Industry dynamics in complex product spaces: An evolutionary model Luigi Marengo a, Marco Valente b, a LEM, Scuola Superiore Sant Anna, Pisa, Italy b Università de L Aquila and LEM, Pisa, Italy article info abstract Article istory: Received November 2009 Accepted November 2009 Available online 26 November 2009 JEL classification: O33 L11 B52 In tis paper we present an evolutionary simulation model of industry dynamics wit product innovation and differentiated demand in complex product industries, i.e. industries were products are made of many components, possibly belonging to different tecnologies, and providing a variety of services to consumers wo ave eterogeneous preferences. We analyze ow te complexity of te product space, te strategies tat firms follow to searc tis space eiter innovating or imitating, and te differentiation of consumers preference interact to determine te structure and evolutions of te industry Elsevier B.V. All rigts reserved. Keywords: Innovation Complex products industries Industry evolution 1. Introduction From a macro-economic perspective Saviotti ave been keen to stress te importance of variety in economic systems in order to promote and sustain growt (Saviotti, 1996; Saviotti and Pyka, 2008). A crucial mecanism of is vision is te necessity of economic sectors to finance te resources required for innovation, wic is te core element of growt. Witout variety costs-reducing competition would limit te resources available for innovation, depressing furter growt and variety, wit te system approacing a Maltusiam steady state at zero growt. Hence, we expect tat variety, represented by new and diversified sectors, ensures positive profits for investments in furter innovation, and eventually results as a necessary condition for growt. Te link between variety, innovation and te accompanying financial requirements is owever mostly ignored in Corresponding autor. addresses: luigi.marengo@sssup.it (L. Marengo), marco.valente@univaq.it (M. Valente). more traditional evolutionary models of industrial dynamics. Evolutionary models of industrial cange, pioneered by Nelson and Winter (1982), ave mostly concentrated on process innovation, typically modelled by an increase in labour productivity, in an industry were firms compete by producing a omogeneous product. Toug very fruitful, tis perspective as mostly overlooked some important empirical facts and teoretical developments tat, on te contrary, evolutionary teory sould be well equipped to deal wit. First, it is beyond dispute tat nowadays a big part of te innovative effort is devoted to product innovation and tat generating a continuous stream of product innovations as become a key competitive factor in many industries. Besides, process innovation also often originates by a stream of (product) innovations in capital goods, reinforcing te pressure to consider te economic effects of innovations embodied witin products. Second, in many industries tis continuous stream of product innovation goes in parallel wit product diversification. Far from competing on omogeneous products, firms use innovation to bring to te market ever new varieties of products and create new market nices. Product X/$ see front matter 2009 Elsevier B.V. All rigts reserved. doi: /j.strueco

2 6 L. Marengo, M. Valente / Structural Cange and Economic Dynamics 21 (2010) 5 16 differentiation on te supply side is te counterpart of te differentiation of demand. Buyers are eterogenous in teir needs and preferences and markets are segmented. Tus product innovation is constantly creating sub-markets (Klepper and Tompson, 2006), i.e. transforming industries into systems of weakly competing eterogeneous market segments, wit new segments appearing all te time and attracting new potential buyers, and old segments disappearing. Tird, in many industries suc products are more and more multi-component and multi-tecnology. Actually suc multiplicity of components and tecnologies is wat enables and feeds diversification. Te standard model of one tecnology, one product, and one market is less and less adequate to describe te reality of many important industries and especially teir patterns of innovation. Products are complex bundles of tecnical components wic map into service caracteristics (Saviotti and Metcalfe, 1984; Saviotti, 1996). Alike te genotype penotype relation, tis mapping of tecnical components into service caracteristics is a key mecanism wic drives evolutionary dynamics: selection operates on service caracteristics but te unit of selection are te underlying bundles of tecnical features. A recent line of enquiry as begun analysing tecnologies and products as complex systems made of many non-linearly interacting components. Using for instance fitness landscapes models (Kauffman, 1993) it is possible to sow tat as te extent of interdependencies among components increases, te searc space becomes more and more rugged and less and less correlated, tat is caracterized by many local optima and by large and non-monotonic variations of performance also for small canges in te value of components. In suc searc spaces usually only local and myopic searc is possible because of teir combinatorial nature and because interdependencies are only partly known, tus global knowledge of te searc space is not possible and only a small portion of te searc space can actually be explored. However te presence of interdependencies makes local searc igly sub-optimal and pat dependent as it will only locate te nearest local optimum and be unable to move from tere. However insigtful are tese results, tey ave mostly concentrated so far on te properties of searc processes of individual organization and ave been seldom been extended to te encompass market competition forces as drivers of searc (one of te very few notable exceptions being Lenox et al., 2006). In particular, two forces are particular relevant to determine te evolutionary dynamics of firms searcing on a complex tecnological or product space. First, firms are not interested in tecnological performance per se, but in te profits tat may (or may not) derive from it. In turn profits contribute to determine, along wit oter financial resources, te amount of R&D effort, bot innovative and imitative, and terefore te intensity, speed and possibly te scope of searc. Second, te landscape on wic firms move is not only determined by te tecnological or product performance surface, but also by demand. Also in tis respect tecnological performance per se does not ave muc meaning: products ave to be sold to potential buyers wo indeed value te performance of a product but also its price and te extent to wic its caracteristics matc teir own specific taste. If consumers ave eterogeneous tastes te tecnological landscape on wic firms move is not only rugged and multi-peaked, but different areas of suc landscape may be diversely populated by potential consumers and may terefore present diverse profit opportunities. In tis paper we propose an evolutionary simulation model, or rater a general framework for a breed of possible simulation models, of industry dynamics centred upon te interplay between market competition and product innovation as searc in a complex space. Te model is meant to be a first step towards a broader understanding of ow competition sapes tecnological innovation, and ow innovative patterns affect te competitive environment. Concerning te model structure, it may be tougt as made of two overlapping modules: market competition and tecnological innovation. Te competitive environment is represented by a demand formed by a population of consumers wit eterogeneous tastes for product caracteristics wose purcasing decisions are represented by a standard utility function comprising products quality, prices and individual tastes. Te novelty of te model in respect of economic competition lies in te representation of suppliers as endowed wit two complementary strategies: innovation/imitation and pricing. Te former strategy allows firms to improve te appeal of teir products to consumers, wile te latter varies prices depending on te relative competitive condition. In particular, contrary to most of te evolutionary models based on mark-up pricing, in our model prices are endogenously determined by eac firm in order to exploit tecnological leadersip, or to compensate for tecnological inferiority, in order to maximize te expected profits. 1 Te link from competitive conditions to tecnological innovation are te (realized) profits tat determine te amount of resources available for innovation. Te reverse link, from innovations to products quality affecting consumers decisions, depends on te complexity of te tecnological space, tat is central in our model. Products are made of many interdependent components and possess many interdependent caracteristics. Firms can innovate by introducing better performing components and/or by introducing new combinations of components. Components can be improved by means of innovation (searc for a new product) and imitation (copy te products of more profitable firms). Bot innovation and imitation, operated at te level of components, are difficult and uncertain, in te sense tat interdependencies among components generate complex trade-offs and tere is no guarantee tat better components will necessarily increase te overall performance of te product. 1 Note tat we are not assuming tat our firms can actually maximize profits, but only tat tey take decisions aiming at tat objective. Te gap between te purported aim and actual result depends on te uncertainty of future tecnological innovations and competitor s actions. Assuming ard Knigtian uncertainty, expectations in our model suffer from systematic bias, preventing even stocastic ex post profits maximization.

3 L. Marengo, M. Valente / Structural Cange and Economic Dynamics 21 (2010) Te paper is organized as follows: in Section 2 we briefly review te related literature. In Section 3 we present te core elements of te model. In Section 4 we discuss some insigts obtained by exploring te beaviour of te model under several assumptions on te model parameters. Finally in Section 5 we draw te main conclusions. 2. Previous literature Tis paper tries and combine two recent and still relatively scarce streams of researc: evolutionary models of industry dynamics wit product innovation and eterogeneous demand and evolutionary models of tecnologies and products as complex systems. As to te former, studies ave mainly concentrated on eterogeneous consumer preferences as source of product and industry life cycles and as factors tat may prevent te emergence of a dominant design. Saviotti (1996) and Windrum and Bircenall (1998) model te emergences of market nices along te product life cycle as a consequence of te eterogeneous tastes of consumers. Adner and Levintal (2001), Adner (2003), Windrum and Bircenall (2005) and Sy (1996) study te conditions under wic a new tecnology can displace an old one due to network externalities and/or bandwagon effects. Malerba et al. (2007) instead of network externalities and bandwagon effects focus upon te role of pioneer, experimental consumers wo enable a market nice to get enoug momentum for firms serving it to survive and invest in tecnological progress. Dawid and Reimann (2005) on te contrary considers te drawbacks of competition based upon product diversification tat, by pusing firms to introduce new products at a fast rate, may finally inder product quality. Turning to te modelling of products as complex system, a recent family of models as used Stuart Kauffman s model of fitness landscapes, te so-called NK model (Kauffman, 1993) and generalizations tereof (Altenberg, 1995; Frenken et al., 1999). Tese models sow tat wen products and tecnologies are complex systems made of many non-linearly and non-monotonically interacting elements, local improvements and decentralized searc coordinated by market mecanisms are ineffective searc strategies. On te oter ad decomposition of te searc space and modular searc strategies are necessary in order to make te complexity manageable. Tus te evolution of te system is a matter of a delicate balance between decomposition and integration wit multiple equilibria and pat dependency caracterizing it (Frenken, 2006a; Marengo et al., 2005; Marengo and Dosi, 2005; Frenken, 2006; Auerswald et al., 2000; Etiraj and Levintal, 2002). Usually owever tese papers do not refer to competitive forces and market demand as te basic engine fuelling and directing searc in te tecnological space (notable exceptions being Lenox et al., 2006 and Ciarli et al., 2008): firms searc te space implicitly motivated by te quest for better fit tecnologies and products. Moreover in te fitness landscape models te searc space is finite and is terefore inappropriate to model open-ended processes of continuous innovation. In tis paper we sall try and fill tis gap, suggesting a new variant of te model wit an infinite tecnological space, searced by firms motivated not by tecnological improvements per se but by te quest for iger profits. Tus firms move on space tat is actually te result of te coupling between te tecnological space and te space constructed by demand, were te latter is determined by a population of eterogeneous consumers. In te following section we describe suc a model. 3. A model of competition in complex tecnological spaces We model te market for a complex semi-durable product, tat is one made of multiple components interacting togeter to produce an overall performance made of multiple functionalities. Firms compete on te basis of prices, quality of te product and by offering different combinations of caracteristics. Moreover tey invest profits into R&D activities tat may allow tem to introduce new and more profitable products into te market and/or imitate te products of better performing competitors. Products are demanded by a population of potential buyers. Potential buyers enter progressively te market, ave initially a limited knowledge of te caracteristics of te products but tey refine it as time passes. After making te first purcase tey replace te good at random intervals (as already mentioned te good is durable and as random finite life) by buying te product tat, according to teir knowledge of its caracteristics, maximizes individual utility. Te latter is a function of price, quality or performance of te product and its proximity in te space of caracteristics to an idiosyncratic ideal profile tat caracterizes eac consumer. In te sequel we describe te main features of te model Product space We model products as systems made of n components {x 1,x 3,...,x n }. Eac component can take one out of a set of values x j R +, wic are labels for different and progressively better, in a mere tecnological sense, types of components (e.g. different CPU types, different wing sapes, different brake cooling systems, etc.). 2 We call X te set of all te possible products, i.e. of te vectors x i = [x i 1,xi 2,...,xi n ] wit x j R +. Te performance (or quality) f of a product x is a function of its specific combination of components: n n f (x) = xi ( i,j x i x j ) + B (1) i=1 j=1 2 We suppose tat tere is a clear direction of tecnological improvement for eac component, tat is tat in some engineering sense we can say tat today s CPU is more performing tan a CPU of some years ago. Tis is reflected in our model tat firms try to move forward (towards iger values) in te space of components and not backwards. However, because of interdependencies, a iger valued component does not necessarily improve te overall performance of a product if te oter components are not co-adapted. Tus at te product level altoug tere is a notional direction for tecnological improvement, te pat may be very rugged and go troug deep valleys on lower performance.

4 8 L. Marengo, M. Valente / Structural Cange and Economic Dynamics 21 (2010) 5 16 were i,j [0, 1] represents ow te contribution of component i to te overall quality is affected by component j, and B is a constant. 3 Te overall performance of a product depends bot on te values of its components (iger values tend to determine iger performance) but also on teir compatibility tat is tuned by te parameters i,j.if i,j = 0 i, j components are independent and any improvement in any component increases te performance of te product. If, on te contrary, i,j /= 0 i, j, better components increase overall performance only insofar as tey are compatible wit in oter. In particular, Eq. (1) assumes tat in order to be fully compatible components must ave te same value. Tis kind of functionalities or caracteristics representation of products is bot reminiscent of te some models of genotype penotype maps in biology and in particular of tose based upon generalized NK fitness landscapes (Altenberg, 1995) and of some models of product and industry evolution in te economics of tecnical cange (Saviotti, 1996). For a discussion of te relationsips between tese two apparently distant lines of researc te reader is referred to Frenken (2006). Moreover, our definition of complexity includes and extends te standard representation used for instance in Kauffman s NK model of fitness landscape (Kauffman, 1993), were complexity is given by te K parameter tat stands for te seer number of coupled components. In our model we not only may represent te presence of interactions between components by setting i,j /= 0 wen components x i and x j are coupled, but also tune te intensity of te interdependency 4 by coosing te value of i,j [0, 1]. As to te extent of suc interdependencies, single components may interact wit just a few oters, or viceversa all n components may interact togeter. A special and important case is wen interactions ave a modular or quasi-decomposable structure (Simon, 1969; Baldwin and Clark, 2000), i.e. wen te set of components is divided into subsets caracterized by strong interactions witin eac subset and weak or no interactions among subsets. Te reader is referred to Frenken et al. (1999); Marengo et al. (2005) and Marengo and Dosi (2005) for a more detailed and formal treatment of tese cases and teir properties. All in all, te features of te performance surface describe te difficulty 5 of te innovation process. At one extreme we ave te case witout interdependencies and wit ig correlation among te performances of similar products, in wic autonomous local (i.e. on single components) improvements can generate a steady stream of innovation. Innovation can be effectively decentralized and innovators can specialize on single components 3 Since performance values are later used to compute consumers utility of consumers we want tem to be always non-negative and set B accordingly. 4 See Valente (2008b) for a discussion on te limits of te NK model and on te properties of possible alternative representations. 5 Tis is only one of te many possible sources of difficulty or complexity of tecnological innovation, te one wic stems from te interdependencies between te parts of te tecnological system and of te underlying knowledge. Oter possible sources are not modelled ere. or small modules, wereas coordination is effectively ensured by market selection forces. At te oter extreme we ave non-monotonic widespread interactions wic generate uncorrelated performance surfaces. In tis case autonomous local canges are generally ineffective and innovation requires coordinated searc on many, possibly all, components togeter and a deliberate re-designing of te system. Decentralization is igly ineffective in te latter case (see Marengo and Dosi, 2005 for a more detailed and formal development of tese arguments) Demand We model two penomena contributing togeter to te formation of aggregate demand for te industry: te dynamics of te number of purcases, determined by a process of entry of new consumers and a process of replacement of te installed base wit new products, and te dynamics of demand for eac product, determined by individual consumers coices, in turn based upon price and quality of te products and ow well tey fit eterogeneous individual tastes on te caracteristics Consumers entry We model an emergent market tat initially contains only a andful of firms and a small set N 0 of consumers. Ten, new consumers progressively enter te market following a sort of word-of-mout pattern. Eac consumer in N 0 as a small number H of acquaintances, and one of tem at eac period may be introduced to te product and may become a new consumer if buying te product gives positive utility. In turn eac of tese new consumers as H 1 acquaintances wo may ten be introduced to te product; and so on until te H + 1-t coort of consumers, wo do not ave oter acquaintances apart from tose already in te market. Te result is a S-saped temporal pattern of te number of consumers in te market. Te total dimension of te market depends on N 0 and H, wile te speed of consumer entry depends on te time lag between te arrival of new consumers. We assume tat te introduction of new consumers follows a stocastic function governing te time of entry of new consumers. Te model imposes 0 probability of introducing a new acquaintance wen a consumer just entered te market itself. At eac time step te probability is increased by a small amount, until a new entry occurs. At tis moment te consumer wo introduced te new entrant as its probability of introducing a new consumer reset to zero. Consumers enter te market by purcasing one unit of te good and ten make a new purcase at eac time step wit a probability tat increases wit te time elapsed since te last purcase. Consequently, at any one time we ave only a sare of all consumers actually making a purcase, wile te complementing sare ang on to te product currently owned Consumers beaviour Wen making a purcase, a consumer looks at prices, overall performance and te combination of caracteristics of products. We follow te literature on discrete coice

5 L. Marengo, M. Valente / Structural Cange and Economic Dynamics 21 (2010) model for products defined in te space of caracteristics, and in particular Anderson et al. (1989). Eac consumer as an ideal product profile, i.e. er type t i = [t i 1,ti 2,...,ti n ] n wit =1 ti = 1, defined by an ideal combination of caracteristics te consumer would like to find in te product. A consumer s utility depends upon four factors, namely te overall product performance, te distance between te product profile and te consumer s ideal one, te price and a normally distributed random error. We assume tat te elasticities of utility wit respect to te first tree factors are consumer specific. Te utility of consumer i buying product x j is given by ( p 1 i U i (x j ) = Af wf i j p j ) w d wd i (i, t) (2) i,j were f j and p j are performance and price of product x j, d i,j is te distance between te product s profile and consumer s i type t i, (i, t) is a normally distributed error centred on 1 and wose standard deviation varies wit time: (i, t) N(1,(t t i )). Te standard deviation (t t i ) is a decreasing function starting at a given level at te time of entry t i of consumer i in te market, and ten decreasing asymptotically to 0. Tis term represents a learning process by consumers wo are assumed to poorly evaluate te products on offer wen first entering te market but increase teir knowledge of te true product caracteristics as tey gain more experience. Finally, w f i, w p and w d are consumer specific elasticities wit respect i i to performance, price and distance and A is a constant. Te distance d i,j of product j from consumer i s ideal profile is computed as n d i,j = x j, t i (3) =1 As already mentioned, te good is durable. Terefore after making a purcase a consumer keeps te product for a random number of iterations. Tus, we ave two measures of market penetration for eac firm: one computed on te actual sales at any period, and te oter based on te products owned by consumers at eac moment in time. We call te former market sares and te latter installed base sares Firms beaviour Firms produce only one type of product in te amount demanded by te market and take decisions on prices and R&D investment. Concerning R&D investment decisions, we follow te pilosopy of evolutionary models of tecnical cange and industrial dynamics (Nelson and Winter, 1982; Winter, 1984, 1993) and assume tat firms take routine decisions by applying rules-of-tumb. In particular we assume tat firms invest in R&D a given sare of teir profits, relating potential innovation to competitive success. As to price decisions we assume instead tat firms are more rational tan usually assumed by evolutionary models, in particular we make te ypotesis tat tey aim to maximize profits but are myopically rational in te sense tey do not act strategically and do not compute optimal prices at every iteration but only at some intervals Price decisions We assume tat te price setting procedure is rational, i.e. based upon deliberate profit maximizing calculations and upon perfect knowledge of demand, but non-strategic, in te sense tat is based upon te assumption tat te oter firms will not respond by modifying teir prices 6 In brief, we assume tat a price setting firm computes te igest price at wic eac individual consumer would buy from te firm itself and ten computes te profit maximizing price, assuming constant variable costs. Te routine setting te price for a firm is implemented as follows: 1. Find for eac consumer te competitors product wic would maximize is/er utility; 2. For eac consumer, compute te price tat te firm sould carge for its product in order to be cosen by tat consumer, i.e. te price tat would make te utility of tat consumer iger wen buying its own product tan te best competitor s; 3. Rank consumers for descending values of suc a price; 4. Identify te profit maximizing price. Tis routine also identifies expected profits and expected sales, tat, as we will see, will be used to decide weter to implement an innovation R&D investment, innovation and imitation Bot innovation and imitation are costly and require R&D investment. Excluding, for te sake of simplicity, external financial sources, our firms invest a sare of te profits cumulated since last innovation into R&D in order to searc te product space eiter in new directions (innovation) or trying to move closer to a successful competitor (imitation). Firms wit low cumulated profits invest only in imitation, wic is less costly and risky, wile firms wit ig cumulated profits invest mainly in innovation, depending on a biased random decision assigning iger probability to innovation tan to imitation. Te amount of profits, and terefore of R&D investment, determines ow many trials te firm may possibly perform eiter in te course of an imitation or innovation routine. Te iger te number of trials te larger is te tecnological space explored by a single round of innovation or imitation. Bot innovation and imitation rely on wat may be considered as a searc strategy in te space of tecnologies. Given te complexity of suc a space, an important variable is te breat of searc expressed in te number of components on wic searc is activates. A narrow searc strategy concentrates R&D resources on only few (possibly only one) components. Conversely, a broad searc 6 We also assume tat firms base teir pricing decisions upon te long term potential profit, i.e. on te assumption tat all consumers wose utility is maximized by product x i will actually buy tis product, toug, as we mentioned before, consumers do not immediately switc to teir utility maximizing product and before tey do products and prices may ave furter canged.

6 10 L. Marengo, M. Valente / Structural Cange and Economic Dynamics 21 (2010) 5 16 strategy spreads R&D investment over a larger number (possibly all) of components. Given te same amount of R&D investment, a narrow searc will tend to produce relatively larger improvements on few components, wile a broad searc will tend to attempt comparatively smaller improvements but on many components. Te breadt of searc is represented by te parameter 1 C n, tat is used to decompose te n dimensional product space into blocks made of C components eac. Imitation. We model imitative searc in a straigtforward way: te imitating firms selects a block containing C components. It ten cooses randomly one firm for eac of te components in te block, wit probabilities proportional to te level of sales (obviously excluding itself, but allowing for replication). It ten compare te values of te components in its own product as compared to te values in te firms, and ranks te components giving iger priorities to te components wit te wider gap, tat is, tose wit te igest potential of improvements by imitation. Subsequently, te firm determines ow many mutation trials are possible given its available R&D investment. Finally, mutations are performed, beginning from components wose value for te imitator s product is furter away from tose of target product. For eac of te available trials a mutation consists in increasing te level of te component by a fixed amount, and ten re-ranking te components in te block as specified above. If te target product is perfectly copied before all possible mutations ave been performed te procedure alts. Te values to be imitated are influenced by two assumption, one concerning te degree of imitability, and te second on te time profile of imitation. Concerning te maximum level of imitation, te model includes a parameter determining te degree to wic components can be imitated. Te value of a component x i can be imitated up to a maximum of x i, wit [0, 1]. If, for example, = 0.95 imitators are only able to reac te 95% of te component s level for te imitated firm. Tis parameter is meant to include bot imperfections in te observability of te actual caracteristics of a tecnology and limits to te imitability of suc caracteristics (e.g. because of tacit knowledge, firm specific uman capital and skills, etc.). A furter assumption on imitation concerns te temporal dynamics of te imitable values. Eac value of a component tat can be imitated by oters, tat is, x i,is used as a limit tat imitating firms can observe only after sufficient time is passed since te innovation introducing x i. Tis assumption ensures tat innovating firms enjoy a temporary monopoly on teir innovation, wic is gradually eroded wit time as imitating firms develop te awareness of te new level and te capacity to imitate it. In practice, te model includes a variable defined as x MaxImm = x i i tat determines te maximum level of tat may be imitated. Wen an imitating firm observes te components of imitated ones, owever, te value to imitate is a companion variable x Imm i,t = x Imit t 1 + (1 )xmaximm i, were [0, 1] is set very close to 1. Consequently, te imitated values do not cange immediately after a potentially imitated firm increases a x i wit an innovation. Te level tat can be imitated grows wit time reacing te maximum imitable level only after a sufficiently long period. After carrying out updating of te components values, te imitating firm computes te optimal price and te expected profit it could earn wit te new product, using te same price setting procedure described in te previous section. If te expected profit for te new product is iger tan te current level te firm adopts te new imitated product, oterwise keeps offering te current one. More in detail, te routine for imitation follows te following steps: 1. compute te optimal price, and te corresponding expected profits and expected sales of te current product; 2. coose randomly a block, tat is a subset of C components; 3. for eac component in te block coose a target firm wit probabilities proportional to sales; 4. compute te number of possible mutations given te current R&D investment; 5. being x i te -t component of te imitating firm s product i and j x Imit te imitable level for same component of te target firm j, compute all distances ( j x Imit x i ); 6. increase x i by 1, starting from components for wic te distance from target firms is iger and update distance ( j x Imit x i ); te increment is reduced if te distance is smaller tan te unit, so tat te imitator can never reac levels above j x Imit ; 7. decrease by 1 unit te number of possible mutations; 8. if tere are still possible mutations and x i < jx Imit for some witin te cosen block, return to point 6; 9. compute performance, optimal price, expected sales, and expected profits of new product; 10. if te new product as iger expected profits or equal profits and iger performance adopt it; 11. else keep te old product. Two furter details are wort stressing. First, for te sake of simplicity we assume tat imitation is not limited by patents and oter property rigts. In a companion paper presenting a sligtly simpler model we focus on ow different intellectual property rigts regimes may act upon industry dynamics, innovation and consumers welfare (Marengo et al., 2009). Second, coerently wit te findings of te empirical literature on tecnological cange, in our model imitation is bot costly and difficult. It is costly because also imitation requires R&D investment, and it is difficult because large gaps can be filled only step by step, and, as already discussed, wen products are complex suc stepwise imitation strategy does not guarantee to deliver a better product. Te larger te gap te more R&D investment is needed to fill it and te more likely tat performance will drop wile attempting to imitate. Innovation. Te routine for innovation is similar to te one for imitation, except tat of course tere is no target product to be imitated, but mutations are made in random directions starting from te firm s current product. Also in

7 L. Marengo, M. Valente / Structural Cange and Economic Dynamics 21 (2010) tis case te number of possible improvements is proportional to R&D investment and te latter is divided among a number of components given by te firm s breat of searc parameter C. Differently from te case of imitation, eac product generated during an innovation round is a candidate for sale, tus its optimal price and te expected profits are computed. After all possible mutations ave been performed, only te most profitable product among te current one and all tose generated during te innovation round will actually be marketed. Moreover, we also assume tat te size of te steps in innovative searc decreases wit te tecnological level already reaced, introducing a form of decreasing returns of innovation. Te routine for innovation follows te following steps: 1. compute te optimal price, te corresponding expected profits, and te expected sales of te current product; 2. coose randomly a block, tat is a subset of C components; 3. increase te value x of te randomly cosen component in te block by 1/x ; 4. compute performance, optimal price, expected sales, and expected profits of te new product; 5. decrease by 1 unit te number of possible mutations; 6. if tere are still possible mutations to be made, return to point 3; 7. if te best version tested provides iger expected profit adopt it; 8. else do not implement innovation and keep te old product Entry and exit Wen a firm does not sell any unit of product for a given number of iterations, ten it exits te market. At eac iteration a new firm may enter wit a small probability. New entrants randomly copy components of existing products in te market and price it following te same procedure as all oter firms. 4. Simulation results In tis section we present some results produced by testing te model on a few configurations. 7 We discuss below te goals of te simulation exercises we aim to address, and ten devote te furter paragraps to discuss a few insigts gained by te analysis of te simulation results Simulation goals Te goal of te exercises discussed below is obviously not to assess universal properties of te model, nor to fully test te effects of eac and every parameter of te model. 7 Te model was implemented on te Laboratory for Simulation Development platform (Valente, 2008a). Software and documentation for te platform are available at Te code and configuration files of te model, along wit its documentation, is available from te autors upon request. Tese two objectives are not only precluded because tey are un-feasible given te complexity of te dynamics involved and te dimension of te parameters space, but tey are also, in our opinion, not wort pursuing. In fact, we are not proposing our model as a universal formal system wose properties are reflected in real-world markets, wic would require a toroug analytical or quantitative assessment. Rater, we consider te model a logical system for ig level, abstract representation of markets to be used for investigating te logical consequences deriving from te assumptions implemented in te model s equations. A simulation run allows to observe te effects of te assumptions, and its analysis offers te opportunity to reason about te aggregate and dynamic effects generated by a relatively large number of entities troug a relatively long virtual time. Te simulation exercises are terefore used to answer specific questions related to te elements implemented in te model and concerning te penomena unfolding during te virtual istory of a simulation run. Answering tese questions, we claim, enables us to gain insigt on te understanding of real-world situations. Te issues tat we claim our model can cast ligt on concern te penomena generated by te interplay of market dynamics (e.g. market concentration, pricing, profits, etc.) and tecnological searc on complex spaces (ow easy it is to get products quality improvements by local myopic searc). Te model can be tougt as producing two opposing forces. On te one and we ave implemented a positive cycle linking profits to innovation, wic favour market concentration. A firm enjoying an initial iger quality product is likely to gain iger profits enabling larger R&D investments, wic will reinforce its market leadersip. On te oter and, price competition reduces profits for all producers, restricting te scope for innovation because of lower profits, and giving even more competitive relevance to prices. Te former cycle will produce a maximally concentrated market were a market leader will sustain a continuous flow of innovation. Te latter will instead result in a competitive market were many firms barely survive in a state of continuous price war, resulting in little or no resources to spare for R&D, producing little or no innovation. In te following paragraps we will discuss ow te balance between te two forces is affected by tree conditions: complexity of te tecnological space, searc strategy adopted by firms in order to innovate or imitate, and ease of imitation. Te complexity of te tecnological space is controlled by setting te number of te interdependency parameters i,j /= 0. We will consider two extreme cases: maximum and minimum complexity. Te maximum complexity is produced wen all coefficients are positive, so tat every component affects te contribution of every oter component, and te value of te parameter is maximum, tat is i,j = 1, i, j. Conversely, minimum complexity is generated by setting all interdependency parameters to 0: i,j = 0, i, j. Te searc strategies of firms concern te dimension of te blocks tat firms use to divide te searc space, tat is, te number of components tey can vary simultaneously wile innovating or mutating, tat we referred to as

8 12 L. Marengo, M. Valente / Structural Cange and Economic Dynamics 21 (2010) 5 16 Fig. 1. Number of consumers in te market. C. Again, we consider te extreme cases of maximally and minimally modular strategies. Te maximum in modularity consists in aving C = 1, in wic an innovating firm operates on a single component at eac round of innovation. Conversely, te least modular, or te most integral, strategy consist in always operating on all components, C = n. Finally, te coefficient for te maximum level of imitation is set to eiter of two levels, 0.95 and Obviously, te first case makes imitation less efficient tan in te second case, since imitating firms can only reac 95% of te components levels of te imitated products. Te next paragrap describes briefly te basic features of te market dynamics common to all te simulation runs. Te remaining paragraps comment upon te interpretation of te results produced by te different combinations of te parameters Overall dynamics We first report on some basic variables describing te dynamics of te market. Fig. 1 sows te number of consumers in te market, wose dynamics reflects te entry process discussed in Section Sales increase accordingly and generate a typical pattern caracterized by an initial large number of firms followed by a sake-out. Tis pattern is caused by te steep increase of consumers s entry and by te fact tat tey initially make mistakes in te evaluation of te products, tus teir purcases are dispersed among a large numbers of firms. As consumers improve teir knowledge of te true caracteristics of te products te selection pressure on producers becomes more intense. Depending on te parametrization used, te market may generate an oligopolistic core formed by a few firms offering superior products, or produce directly a monopoly were only one firm dominates te market. In bot cases we do observe a strong increment of concentration. Fig. 2 sows te number of firms active on te market (upper series) and te inverse Herfindal (dispersion) index (lower series). Te results we will present below are based on te study of simulation runs, analysing individual series and comparing tem across different settings. Given te metodological approac used, we base te support of our claims on te logic of te explanations proposed for te penomena generated in te simulations. Te grap Fig. 2. Number of firms (upper series) and inverse Herfindal index (lower series). Te index reports te number of firms wit equal size tat would generate te same concentration as tat measured in te actual market, consequently measuring te dispersion (or inverse of concentration) of te market. reported are meant to provide a visual support to our reasoning, and are meant to be only a presentation tool. Robustness tests are not reported, since te relevant results are, as said, logically deriving from te model s assumptions, or simply not relevant. For example, for simulations ending up in a monopoly eac run provides a different firm as te eventual monopoly, but our claim consists in te existence of monopoly, not in te identification of te monopolist. For obvious reasons of space we will limit to report for eac configuration te time series pattern of overall quality for all firms of eac simulation run. Tese graps permit also to appreciate, indirectly, oter properties of te simulated system. 8 For example, sort lines spanning only a few time steps refer to firms tat enter and exit rapidly, evidently failing to gain sufficient profits to survive longer. A large number of performance series at similar levels indicates a relatively dispersed market, were many firms can be expected to make positive sales. Conversely, a single line far above tose of competitors reflect a ig concentration, particularly wen te tecnological laggard sow a sort life, indicating tat tey make no sales and consequently no profits Complexity and innovation As first exercise let us consider te effects of tecnological complexity on te market. We assume imitation to be relatively difficult, setting = 0.95, and firms to adopt maximally modular strategies, operating on single components wen innovating and imitating, C = 1. In suc conditions we expect tat more complex spaces, faced by producers wit igly modular searc strategies, will limit te possibility of tecnological improvements. As expected, te overall quality levels improves more markedly in te case were te tecnological space is modular, witout interaction among components (see Fig. 3). Te result canges sensibly wen we impose a complex tecnological space, in wic te overall performance of a product includes interactions among all te components. 8 Te simulation program used allows interested readers to generate graps and statistics for every variable in te model.

9 L. Marengo, M. Valente / Structural Cange and Economic Dynamics 21 (2010) Fig. 3. Firms product performance troug time in a simple tecnological space ( i,j = 0, i, j), modular searc strategies (C = 1) and difficult imitation ( = 0.95). Fig. 4 reports te performance of all products under tese conditions. Tis figure sows tat te quality levels for all firms are sensibly lower tan te previous modular case. For a relatively long period, after te usual initial period wit low concentration, a few firms survive wit relatively constant quality levels, not being able to break out of te local peaks reaced. Interestingly, we can see tat tere are two groups of firms, wit different quality levels, indicating a segmentation of demand were different groups of consumers consistently coose products wit a caracteristics profile closer to a group of consumers tastes. At about te last fift of te simulation run a radical innovation, introduced by a new entrant, breaks te old order, temporarily unifying te two different segments, toug quickly new firms reac a still iger quality levels. All in all, te simulations confirms tat a iger complexity makes more difficult to reac ig quality levels, a result not surprising given te existing literature on modularity and complexity. However, we can appreciate its implications witin a context of market competition. In a simple tecnological space a modular innovation strategy succeeds in producing more and more quality increments. Suc improvements allow te innovative firm to gain extra-profits tat finance furter innovation, extending te probability of sustained market leadersip. Conversely, a complex tecnological space makes modular innovation far less effective. In tis case, price competition is more likely to intensify, reducing profits and consequently te resources available for researc investments. Consequently, quality improvements are far less frequent and Fig. 4. Firms product performance troug time in a complex tecnological space ( i,j = 1, i, j), modular searc strategies (C = 1) and difficult imitation ( = 0.95). Fig. 5. Firms product performances troug time in a complex tecnological space ( i,j = 1, i, j), integral searc strategies (C = 10) and difficult imitation ( = 0.95). smaller. In our settings te tecnological lock-in s affect incumbents only, since new entrants pick eac component s initial quality from different firms. Consequently, tey are allowed to mix and matc different profiles. Toug most of te entrants will not be able to produce a good quality products, a few lucky ones ave te cance to succeed in finding a ig quality product by picking te best components from different incumbents. Te considerations concerning tecnological innovation are also reflected on te market conditions. Te first case, wit low complexity, generates a igly concentrated market, were a single market leader faces only sort-lived new entrants, wo never reac te dimensions required to callenge te leader s R&D investments. Te second case, wit a igly complex tecnological space, generates instead a more articulated market distribution, wit market segmentation reflecting consumers tastes. Te complexity of te tecnology and te witin-segment competition (depressing prices) prevents incumbents from producing a sustained tecnological growt. Complex tecnologies embody interactions among components tat are ignored wen innovators adopt a modular searc strategy. However, we expect tat wen firms increase te range of researc on more tan one component, te innovating efforts sould succeed in producing product improvements wit iger probability, since te effects of interactions among modules are taken into account. Fig. 5, to be compared wit te equivalent Fig. 4 were firms adopt modular searc strategies, confirm tis ypotesis sowing ow broad researc strategies, encompassing all te modules, allow innovators to successfully deal wit te complexity of te tecnological space in generating iger quality. Interestingly, owever, te complexity of tecnological space ensures a relatively ig degree of dispersion. Tis is due to te fact tat te complex space make te overall growt of performance, toug feasible, anyway quite difficult. In tese conditions te variety of demand, as represented by consumers eterogeneous tastes concerning te relative composition of single components qualities, becomes relatively more relevant. Suc penomenon is responsible for te apparently puzzling result tat, toug rarely, some firms make innovations resulting in decreasing performance. Tis is due to te fact tat firms do not pursue tecnological improvements, but profits growt. Te complexity of te space, in fact, generates cases in

10 14 L. Marengo, M. Valente / Structural Cange and Economic Dynamics 21 (2010) 5 16 Fig. 6. Firms product performances troug time in a simple tecnological space ( i,j = 0, i, j), modular searc strategies (C = 1) and easy imitation ( = 0.99). Fig. 7. Firms product performances troug time in a complex tecnological space ( i,j = 1, i, j), modular searc strategies (C = 1) and easy imitation ( = 0.99). wic tecnologically inferior innovations (producing a decrease in overall performance) increase te appeal to some segment of consumers, and become consequently attractive to profit-seeking producers Innovation and imitation Te role of imitation wit respect to innovation is not univocal. In fact, on te one and we can expect imitation to inder innovation because te limited time span of tecnological superiority is likely to put a strong pressure on prices, and consequently on profits and R&D investment. 9 However, imitation of successful components may increase te number of combinations experimented by producers, terefore increasing te probability of discovering igquality products. Te following two figures confirm bot tese ypoteses, sowing tat te eventual net effect depends on te complexity of te tecnological space. If te tecnological space is simple, witout interaction among components, tan te innovation-depressing role of imitation is relatively strong, and we observe a lower level of quality increments in respect of cases in wic imitation is more difficult (compare Fig. 6 wit te previous Fig. 3). Conversely, wen te tecnological space is complex, imitation allows for an increasing variety of te supply side, so tat in wat could be a market wit no or little innovation, we observe relatively more frequent and diffused quality increments. In a sense, imitation serves as a counter-balance to te myopia of modular searc in a complex space, as we deduce by comparing Fig. 7 wit te previous Fig. 4, wic refers to te same context but wit more difficult imitation. 5. Conclusions Tis paper is meant to analyze te interactions between two aspects concerning market evolution tat, toug obviously related in real markets, ave been mostly studied separately in te exiting literature: market competition and tecnological complexity. 9 Note tat in our model we do not include expectations, so tat imitation plays no role in influencing innovative beaviour in terms of expected profits. Evolutionary teory attributes a central role to innovation as a factor saping market competition. However it uses a rater simplified representation of tecnological cange, usually modelled as a random draw of a better productivity coefficient, were te size of te improvement depends on te R&D investment. On te oter and, most of te literature on tecnology as complex system represents tecnology as a non-omogeneous rugged searc space, but assumes tat actors freely move on te landscape, being only motivated by te pursue of iger tecnological efficiency, rater tan responding to market forces. Two relevant differences apply wen we consider competitive firms engaged in tecnological competition in a complex landscape. Firstly, firms are not interested in tecnological innovation per se, but rater in profits, wic are affected by oter factors suc as prices, te beaviour of competitors and te tastes of consumers. Secondly, firms require resources to fund investments on innovation and imitation. Far from being free, moving in te tecnological space, is a costly activity tat needs to be financed by past profits. Te model proposed in tis paper considers a standard, stylised competitive environment represented by two elements. Firstly, consumers are assumed to trade off products qualities, prices, and caracteristics, creating an economic environment in wic firms need to associate an innovative policy (ow to searc for better and better products) wit a pricing policy, setting te price for teir product. We assume tat firms try primarily to improve te tecnological content of teir product, and, accordingly, determine te price depending on te demand and competitive conditions. Te pricing strategy adopted by firms consists in setting te price suc tat expected profits are maximized, assuming firms know te consumers preferences and assuming adaptive expectations on competitors beaviour. Te model terefore introduces a link between te possibility of innovation and te capacity of funding suc activity: toug an innovation may be tecnically witin reac, lack of funding may prevent te firm to actually adopt te innovation. Since R&D is funded by profits, te necessity to figt a price war may reduce te profits to te level in wic innovation cannot be pursued for economic reasons, even toug it is, in teory, easy to access from a tecnological point of view.