Firms' Network Formation Through the Transmission of Heterogeneous Knowledge

Andergassen, Rainer; Nardini, Franco; Ricottilli, Massimo Working Paper Firms' Network Formation Through the Transmission of Heterogeneous Knowledge Quaderni - Working Paper DSE, No. 543 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Andergassen, Rainer; Nardini, Franco; Ricottilli, Massimo (2005) : Firms' Network Formation Through the Transmission of Heterogeneous Knowledge, Quaderni - Working Paper DSE, No. 543, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4746 This Version is available at: https://hdl.handle.net/10419/159384 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/3.0/ Firms’ Network Formation Through the Transmission of Heterogeneous Knowledge Rainer Andergassen1, Franco Nardini2, Massimo Ricottilli1,3∗ 1Department of Economics, University of Bologna, Piazza Scaravilli 2, 40126 Bologna, Italy 2Department of Mathematics for the Social Sciences, University of Bologna, Viale Filopanti 5, 40126 Bologna, Italy 3Centro Interdipartimentale L. Galvani University of Bologna, Italy September 14, 2005 Abstract This paper studies the evolution of a network of leading firms that are engaged in an active search to improve their technological capability through interaction with knowledge-heterogeneous firms. Through the simulation of a linear model of technological spillovers we show the emergence of paradigm setters and the impact of search routines on the system’s average performance Keywords: Networks, Network formation, Innovation diffusion JEL: O33 ∗Corresponding author. Tel: +39 0512098128, Fax +39 051221968. E-mail addresses: [email protected] (R. Andergassen), [email protected]o.it (F. Nardini), [email protected] (M. Ricottilli) 1 1Introduction Recent literature has highlighted the crucial importance that networks have in spreading innovation-relevant information among interacting firms and consequently foster technological efficiency spillovers. It is indeed widely recognised that firm interaction is the process that accounts for much of the learning and useful knowledge acquisition that enable firms to innovate and that eventually renders some of them technological leaders. In economies at the cutting edge of their frontier the competitive drive compels leading firms to engage in these processes lest their advantage be lost to competitors and imitators. It is also well established that because of bounded rationality, the gleaning of relevant information occurs within the confines of neighbourhoods within which networking becomes both viable and result-bearing. This fact owes to firms’ limited ability to explore a given system’s cognitive complexity and comprehend all the agents that inhabit it. Those firms that at any particular point in time can be reached, understood and finally exploited in terms of their spillover potential are normally only a small share of the entire firms’ space. Nevertheless, an active process of searching and learning is the tool that eventually leads them to set up viable information linkages and gain technological capability. It has been persuasively argued that, thanks to this process, networks evolve: they change membership and mode of functioning. It is, therefore, their dynamics that determine a specific architecture the characteristics of which are conducive to a firm’s innovative performance and, in the aggregate, to that of the economy as a whole. This quest for information is largely an adaptive, gradual process in which internal, in-house resources generating innovation-worthy knowledge are woven together with those obtained through technological spillovers proceeding from other firms. In this context, the economy appears as a large interactive system (Kirman 1997a, 1997b). The importance of networks and their properties in the process of interaction has been highlighted in recent literature investigating technological and knowledge diffusion, see for example, Cowan and Jonard (2004, 2005), Silverberg and Verspagen (2002), Arenas et Alii, (2001, 2002). Seminal work in network connectivity and dynamics has been done by Albert and Barabasi, (2002) for an exhaustive review, Watts and Strogatz (1998), for the emergence of small worlds and Jackson (2005) and Jackson and Rogers (2005) for the economic implications. These findings have been deemed as quite relevant in the literature of innovation diffusion. This is because a ’Small World’ architecture, as represented in a graph, compounds the benefits of a localised transmission of spillovers with those obtainable from information broadcast by relatively distant nodes (agents), enhancing the average innovative performance of an economic system. In this framework, these nodes have the role of augmenting the pool of cognitive capabilities without the excessive dispersion that would occur if relational edges were wholly random. While these are undoubtedly relevant results that shed light on network properties, it is nevertheless necessary to take into account that evolution and architecture changes come about because of the specific searching behaviour and information gathering strategies that firms 2 implement in striving towards greater innovative prowess. Normally, in a rationally bounded world, these procedures take the form of routines, Cohen et Alii (1995), Egidi and Ricottilli (1997), that are aimed at the discovery and eventual adoption of more performing neighbours and to the dismissal of less effective ones. New edges in the firms’ graph are set up thanks to this adaptive but endogenous process. It can be shown that in a framework in which interaction takes place unfettered, if routines are adopted merging localised and moderately frequent across-the-board search of new neighbours, paradigm setters are likely to emerge (Andergassen, Nardini and Ricottilli; ANR, 2004). The latter are defined as firms whose technological features set a paradigm for most other firms with a positive probability as they are elected as spillover providers. Thus, while small worlds are normally well distributed and scale free networks, the world of paradigm setters is a technologically hierarchical one. In this paper, we distinguish two different but definitely complementary and overlapping ways through which searching and learning occur. The first exploits the spillover potential that lies in a firm’s network and thanks to which gathering innovation-useful information is actually possible. The second rests with the autonomous capacity that a firm possesses in order to carry out in-house innovative research. While these two searching processes not only coexist but are also reciprocally sustaining, we find it expedient to separate them by integrating a knowledge diffusion mechanism that propagates technological capabilities with an independent stochastic process capturing innovation arrivals due to internal R.&D. A network’s evolution depends on how firmsassesstheirperformance in terms of innovation-enabling spillovers. In a bounded rationality framework, firms normally explore a limited part of the firms’ space and require a protocol to target their information gathering efforts. The paper addresses this issue by designing a routinised behaviour according to which firms periodically reshape the neighbourhood that they observe to glean information by reassessing other firms’ contributions to their own capability. The way the specificneighbourchoosing routine is accordingly organised determines in a significant way firms’ average innovative capability. This feature is modelled by changing the span of network observation from a very broad setting, the whole economy, to a very narrow one, namely the most proximate neighbourhood membership. As a result of the structure of the model presented in the next section, there are two distinct but to some extent overlapping neighbourhoods which are relevant for firms’ interaction. The first is the neighbourhood whose members are observed by each firm and from which capability contributions are obtained. We term this neighbourhood inward. The second is the one made up by a firm’s observers, i.e. by firms observing and learning from it: it evolves as an active search for new inward members is carried out. We call this neighbourhood outward. This process of information interaction leads to the emergence of some firms that are observed by most of the remaining ones. It is they that provide some or much of the overall technological capability and that we term paradigm setters.We also assume that the in-house acquired capability is subject to structural shifts by means of periodic random shocks. A main feature of the model that is to follow is knowledge heterogeneity. Spillovers occur to the extent that a firm’s 3 technology can effectively be observed and learnt. Seen it from the point of view of those firms that actually provide information, a spillover depends on the share of their innovative capability that a common knowledge base permits to pass on to other firms. Technologies, however, are grounded on knowledge that is normally firm-specific rendering most economies cognitively heterogeneous, a fact that sets hurdles to the flow of information. We accordingly emphasise that, in consequence, knowledge and capability diffusion occur as an interaction of firms that possess differing broadcasting or understanding abilities. To keep the model mathematically tractable, we formalise the features stated above by means of a linear system in which technological capabilities are made to depend on a matrix of interaction with evolving outward neighbours as well as on a vector of in-house generated knowledge. The matrix records areas of firms’ different cognitive understanding , or areas of differing degrees of knowledge base translating into differing diffusion capacity. Within such areas firms feature a homogeneous diffusion coefficient. For simplicity’s sake, we limit the number of these cognitive areas to just two. The model is then simulated to determine the emergent properties of neighbourhood formation and stability together with average capability. We aim to identify (i) under what conditions the emergence of technological paradigm setters occurs, (ii) the pattern of neighbourhood formation and (iii) the average relative efficiency in terms of technological capability of the economy as a whole. Our findings suggest that the type of searching routine chosen is crucial to determine the emergence of paradigm setters. Furthermore, while average innovative performance is strongly affected by the selected routine it also shown that its performance worthiness crucially depends on how knowledge heterogeneous the economy happens to be. The plan of the paper is as follows: section two illustrates the linear model that is implemented to run simulations and the procedures utilised; section three discusses results obtained and section four draws conclusions and sets an agenda for further research. 2 Firms’ Technological Capabilities and Spillover Potential We view a firm’s technological capability as the outcome of an evolutionary process owing to learning, searching and gathering of information ultimately leading to innovation. We further regard this process to be largely but not entirely explained by the interaction taking place within the system thanks to information flows that proceed from sources that are cognitively heterogeneous in relation to the searching and learning firm. In the main, this heterogeneity is a consequence of knowledge specificity and diversity and it is, therefore, both a hurdle and a challenge setting bounds to the understanding and broadcasting of relevant information. In this section, we direct our analysis to investigate firms that are assumed to be technological leaders and whose major interest lies with innovation. We, accordingly, postulate that they possess ’in house’ innovative 4 capabilities resulting from past investment and that we distinguish, in a somewhat artificial manner but useful for modelling, from those that are entirely due to spillovers. It is important to stress that the latter do not accrue effortlessly butresultfromasteadyattempttoobserveotherfirmsofwhichlittleisknown a-priori and whose technological characteristics and thus whose worthiness to yield useful information must be discovered by the searching activity referred to above. Technological capabilities can be viewed and measured in a way akin to the more general category of a firm’s knowledge base, cognitive potential or set of skills, know-how and competencies: they can actually be modelled as either avectorarrangingdifferent indicators or more simply as a scalar compounding the whole. We choose the latter approach and propose as reference a general model that later will be simulated in a more simplified form. Let Vi(t)bethescalarthatattimetdesignates firm i’s innovative capability or, to use a term borrowed from biology, its innovative fitness. Then, V(t)is the vector V(t)=[Vi(t)],i=1,2....J arraying the fitness of all firms in the economy. By Ci(t)we further designate the in-house capability cumulated until time t. This magnitude is intended as an index measuring a firm’s capacity to innovate thanks to cumulated knowledge achieved by means of investment specifically aimed at this purpose. Indeed, investment is necessary not only to augment it but also merely to maintain it. Considerable efforts are therefore necessary to remain on the forefront of technological prowess, efforts which need not always prove successful; they may fail entailing a fall in capability rather than an improvement. Ci(t)is measured on a 0−1scale, Ci(t)∈(0,1),and it is accordingly assumed to be stochastically subject to change. C(t)is the corresponding vector. As it has been mentioned, a significant part of total technological capability is explained by interaction and therefore by the ease with which each firm is observable by other firms when broadcasting information. How much and how well a firm is capable to pass on information depend on the cognitive distance that a firm’s searching must ascertain. In the end, the intensity of interaction depends crucially on cognitive proximity. In a straightforward sense, we assume that the higher is the latter, the stronger is interaction and the greater is the associated spillover. Accordingly, the ability to broadcast relevant technological information can, in general, be postulated to be measured by a basic index specific to each pair ij of firms in the economy, although simulation in the following sections will consider only broad areas of proximity to simplify, without loss of generality, the dynamics of network formation and of average performance. Let aij indicate such an index in terms of the part of each firm j’s total innovative fitness that can cognitively be passed on to firm ishould the latter be in a position to observe the former. The entire web of interfirm technological spillover can then be designated by a square, JxJ, matrix A,its main diagonal being made up by aii =0since no firm broadcasts information to itself. Therefore, Asimply indicates the structure of cognitive proximity and thus of the technological information broadcasting capability of this economy. Firms possess bounded rationality. This is a stylized fact that carries the important implication that the actual number of firms each can observe is a 5 small subset of the whole. The neighbourhhood from which firms glean useful information, however, is subject to change since firms carry out a search for better alternatives. To single out neighbours better suited to pass on information when chance allows them to do so, firms resort to a routine, to a search protocol that leads them to identify new neighbourhood members, The breadth and range of this routine in terms of the sample of new firms from which to randomly choose from is a control parameter of ensuing simulations. It is, accordingly, assumed that each firm isearches among its potential information suppliers j with broadcasting capacity ai=(aij),j=1,2...J, those that at each point in time it is able to choose and that it can actually observe. This choice can be formalised by introducing the adjacency matrix B(t)=[bij (t)] where each bij(t)=1or 0accordingtowhetherneighbourjhas or hasn’t been identified as a useful contributor. This procedure defines matrix M(t)=(aijbij(t)).Thus, the innovative capability that is determined by interaction can be formalised by the system M(t)V(t)where actually observed firms are restricted to a limited number of neighbours. The general equation for firm i’s innovative capability is1 Vi(t)= J X j=1 aijbij (t)Vj(t)+Ci(t)(1) and the system for all firms: V(t)=[I−M(t)]−1C(t)(2) where [I−M(t)]−1plays the role of an endogenous matrix multiplier of in-house capabilities: different neighbourhood configurations lead to different multipliers as M(t)changes thanks to active searching. In order to evaluate the impact of cognitive heterogeneity, we assume that the economy is partitioned in clusters of roughly homogeneous cognitive areas and in order to simplify the exposition we postulate that matrix A=[aij]features only two different coefficients a2<a 1<1. This procedure defines two areas, one of cognitive similarity or of homogeneous proximity in which belonging firms broadcast and retrieve information according to parameter a1and an area of homogeneous cognitive distance made up by all other firms from which information flows according to a2. 2.1 Neighbourhood Structure The structure through which we describe firms’ innovative capability can be represented by a directed graph of Jnodes each of which is connected with other nodes in two different but overlapping ways. The first is the number of connections that each firm establishes when observing other firms to determine its own innovative capability. The number of ki,in << J connections defines 1Absorbing the impact of spillovers is clearly a process that requires an adjustment in time. We simplify this problem by assuming that the time required to complete adjustment is negligible in relation to the system evolution. 6 for firm ithe dimension of its inward neighbourhood. This number is substantially smaller than Jsince searching is costly and observation bounded . This neighbourhood can formally be defined as Γi(t)={j:j=1,2...J ∧bij(t)=1} This is the set of firms from which at any time tfirm iis able to glean innovative capability through observation and learning. Thesecondkindofneighbourhood,whichwetermoutward, is made up for each firm jby firms that actually observe it. It results as a consequence of their networking activity. Let it be defined by: Ψj(t)={i:i=1,2...J ∧bij(t)=1} Its size determines the impact of an observed firm’s technological capability as it propagates throughout the economy contributing to overall performance. For this purpose, we classify the population of firms according to quantiles of their outward neighbourhood size and then define an impact factor by ranking them. Definition 1 Global technological paradigm setters emerge when the probability of each impact factor rank defined over the entire economy is positive. Local paradigm setters emerge when the probability of each impact factor defined over the subset of cognitively homogeneous firmsispositive. Therefore, we consider as global paradigm setters firms included in the last quantile, that is those being or that have been observed by almost all firms in the whole economy. On the contrary, if we consider just the cognitively homogeneous clusters of firms, we may observe the emergence of local paradigm setters likewise defined as firms being observed by almost all other firms within the cluster. 2.2 Evolution Given this neighbourhood structure, evolution owes to two basic determinants: search routines and exogenous changes of individual firms’ in-house innovative capabilities. Searching, while bounded by the neighbourhood in which the firm happens to be nested, may take place according to a variety of algorithms. We have chosen one that responds to the criteria of bounded rationality and satisficing. We propose two versions that respectively capture a strong and a weak form of bounded rationality. In both, we first conjecture that the cardinality of Γiis |Γi|=ki,in ¿Jand generate the choice of neighbours and the evolution of this neighbourhood according to the following routine:eachfirm iassesses the fitness contribution of its existing neighbours and picks out the least contributing one: γi(t−1) = arg min j∈Γi(t)[aijbij (t−1) Vj(t−1)] 7 We then consider two alternative procedures, a local and a global one. In the case of weak bounded rationality, the local procedure, we take each firm’s neighbours’ neighbours as the actual set of reachable, information-wise, technological sources. Thus, the identified firm is substituted with a new one by randomly drawing from this set. In the case of strong bounded rationality, the global procedure, we instead allow the firm to randomly draw from the remaining J−ki,in −1members of the entire economy. In either case, to generate a new Γi(t)it is necessary that this simple condition be satisfied: Vi(t)>V i(t−1) If not, firms reinstate the neighbour they have chosen for substitution. This is because other firms’s in-house capability and transmission coefficient are not observable. This procedure redefines at each time step M(t)and the system then generates a new set of solutions. Next to the dynamics generated by neighbourhood adjustment we introduce in the system the autonomous and independent dynamics involving the in-house capability C(t). This vector is subject to change by a random draw of some i∈(1,2...J)andbyrandomlyredefining the ith component by a new random value Ci(t)uniformly chosen between 0and 1. These occurrences are arrivals that take place according to a predetermined mean waiting time µ. The two crucial variables that are tuned in following simulations are (i) the neighbour searching routine designated by τand (ii) the relative cognitive distance δ=a2 a1 , a measure of the economy’s knowledge heterogeneity. Variable τmeasures how local the search for a new neighbour is. 1 τis then the probability of engaging in global search and 1−1 τthat of engaging in local search. Thus, when τ=1the search routine is always global and as τincreases searching becomes increasingly local, when τ→∞it is accordingly always local. 3 Simulation results In this section we run simulations with a population J=64of firms, setting the number of inward neighbours kin =3. For simplicity’s sake, we carry out the experiment by assuming the economy to be divided in four symmetric blocks of 16 firms that have the same knowledge base and that interact with each other by swapping spillovers by means of parameter a1. Symmetrically, each of these four blocks is surrounded by three, equally numbered, blocks of distant knowledge firms with which interaction occurs through parameter a2. Simulations with only two symmetric blocks have also been carried out with no appreciable qualitative difference with this more general case. More refined differentiation is clearly possible but this simple framework suffices to check for the impact of knowledge heterogeneity. To insure solutions for system (2) we constrain a1to be a1≤1 kin . 8 The paper main findings can be summarised in the following points. (i) Global paradigm setters emerge when the cognitive heterogeneity of the economy is not very high. They begin to emerge only for intermediate values of the measure of heterogeneity. (ii) For high levels of cognitive heterogeneity, the economy becomes partitioned into separate parts; in each homogeneous one, local paradigm setters emerge. (iii) Highest technological capabilities are achieved neither with a general searching routine that spans the whole economy nor with very local ones in which only neighbours’ neighbourhoods are sampled. Thus, tuning short-sightedness and farsightedness improves the system’s innovative efficiency. Past a given combination of the two, the system slides towards increasing mediocrity but paradigm setters emerge as a permanent and systematic feature of the economy. (iv) How local searching should be to attain the best performance peak depends crucially on how heterogenous the knowledge base is. Seeking good contributors to technological capability is subject to the double constraint of cognitive attainability and neighbourhood narrowness. Our findings show that to ease this constraint the more heterogeneous is the firms’ knowledge base, the more wide ranging should the required search routine be: firms ought to look across the whole economy more often to replace a poorly contributing neighbour. Thus, tuning far-sightedness with short-sightedness is very much a knowledge dependent task. Further research is required to investigate the trade offbetween knowledge heterogeneity and average innovative performance when paradigm setters’ emergence occurs. A highly heterogeneous economy, knowledge wise, is a highly specialised one in which broadly diffusing information flows and spillovers are likely to be specificity constrained. Such an economy may yet be more innovative. 5 References References [1] Albert R, Barabasi A-L (2002) Statistical mechanics of complex networks. Reviews of Modern Physics 74:47—97. [2] Andergassen R., Nardini F., Ricottilli M.(2004). The Emergence of paradigm setters through firms’ interaction and network formation. Forthcoming in A. Namatame, T. Kaizouji, Y. Aruka (Eds.). Economics and Heterogeneous Interacting Agents. Springer Verlag Lecture Notes in Economics and Mathematical Systems. [3] Arenas A, Diaz-Guilera A, Pérez CJ, Vega-Redondo F (2002) Self-organized criticality in evolutionary systems with local interaction. Journal of Economic Dynamics and Control 26:2115—2142. 15 [4] ArenasA,Diaz-GuileraA,GuardiolaX,LlasM,OronG,PérezCJ,Vega- Redondo F (2001) New Results in a Self-organized Model of Technological Evolution. Advances in Complex Systems 1:1—12. [5] Michael D. Cohen & Roger Burkhart & Giovanni Dosi & Massimo Egidi & Luigi Marengo & Massimo Warglien, (1995).Routines and Other Recurring Action Patterns of Organizations: Contemporary Research Issues, Working Papers 95-11-101, Santa Fe Institute. [6] Cowan R, Jonard N (2004) Network Structure and the diffusion of knowledge. Journal of Economic Dynamics and Control 28:1557—1575. [7] Cowan R, Jonard N (2005) Innovation on a network. Forthcoming in Structural Change and Economic Dynamics. [8] Egidi M, Ricottilli M.(1997). Co-ordination and specialisation.In Conte R. Hegselman R., Terna P.(eds). Simulating Social Phenomena. Lecture Notes in Economics and Mathematical Systems, Springer Verlag. [9] Jackson O M (2005). The Economics of Social Networks. Forthcoming in the Proceedings of the 9th World Congress of the Econometric Society, edited by Richard Blundell, Whitney Newey, and Torsten Persson, Cambridge University Press. [10] Jackson O M and B Rogers (2005) The Economics of Small Worlds. The Journal of the European Economic Association (papers and proceedings), 3(2-3): 617-627, 2005. [11] Kirman A (1997a) The Economy as an Evolving Network. Journal of Evolutionary Economics 7:339—353. [12] Kirman A (1997b) The Economy as an Interactive System. In Arthur W B, Durlauf S N, Lane D (eds) The Economy as a Complex Evolving System II. Santa Fe Institute, Santa Fe and Reading, MA, Addison-Wesley. [13] Watts D J, Strogatz S H (1998) Collective Dynamics of ’small world’ networks. Nature 393:440—442. 16