The Emergence of Paradigm Setters through Firms' Interaction and Network Formation

Andergassen, Rainer; Nardini, Franco; Ricottilli, Massimo Working Paper The Emergence of Paradigm Setters through Firms' Interaction and Network Formation Quaderni - Working Paper DSE, No. 525 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Andergassen, Rainer; Nardini, Franco; Ricottilli, Massimo (2004) : The Emergence of Paradigm Setters through Firms' Interaction and Network Formation, Quaderni - Working Paper DSE, No. 525, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/4765 This Version is available at: https://hdl.handle.net/10419/159366 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/ The Emergence of Paradigm Setters through Firms’ Interaction and Network Formation Rainer Andergassen1, Franco Nardini2, Massimo Ricottilli1,3∗ 1Department of Economics, University of Bologna P.zza Scaravilli 2, 40126 Bologna, Italy 2Department of Mathematics for the Social Sciences, University of Bologna, Viale Filopanti 5, 40126 Bologna, Italy 3Centro Interdipartimentale Luigi Galvani, Bologna, Italy Abstract. Technological innovation requires the gathering of information through a process of searching and learning. 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 innovationuseful information is actually possible. The second is the autonomous capacity that a firm possesses in order to carry out in-house innovative search. We build a model where rationally bounded firms try to increase their innovative capability through endogenous networking. The paper characterizes the emergence of technological paradigm setters in terms of network properties as they result from searching routines, furthermore the corresponding average efficiency of the system in terms of innovative capability is assessed. JEL classification numbers: L14, O33. Keywords: Networks, Bounded Rationality, Technological Change, Innovative Capability, Paradigm Setters. ∗Corresponding author. E-mail addresses: an[email protected] (R. Andergassen), [email protected] (F. Nardini), [email protected] (M. Ricottilli). 0 1Introduction Technological innovation requires the gathering of information through a process of searching and learning. In economies at the cutting edge of their frontier the competitive drive compels leading firms to engage in this process lest their advantage be lost to competitors and imitators. This quest for information is largely an adaptive, gradual process in which internal, in-house resorces generating innovation-worthy knowledge are woven together with that obtained through technological spillovers proceeding from other firms. Firms, and agents within firms, exhibit bounded rationality and their success is largely due to but also constrained by their technological capabilities that are, nevertheless, magnified by interaction with other firms. The implication is that the process of search is local and confined within a neighbourhood that is cognitively reachable and that is, therefore, the medium of effective information flows. To this effect, the role of a network in which firms nest is paramount Because of bounded rationality and radical uncertainty, the process of reciprocal observation and learning occurring through interaction between firms and making the spreading of technological spillovers possible takes place in.viable networks. Their importance has been highlighted in recent leterature investigating technological and knowledge diffusion , see for example, Cowan and Jonard (2004), Silverberg and Verspagen,(2002), Arenas et Alii,(2001, 2002). Networks, however, are subject to change and growth : connectivity between members, linkages between firms,can be viewed as a process in time. Seminal work in this field has been done by Albert and Barabasi, (2002)for an exaustive review, Watts and Strogatz (1998), for the emergence of small worlds. When seen as an interactive system (Kirman 1997a,1997b ), the economy generates capabilities that are mutually acquired rendering firms technologically interdependent. It must, nevertheless, be recognised that capability-building also depends on in-house efforts supported by investment in formal and informal research and development . In this paper we treat technological capabilities as a stock of firm-specific knowledge cumulated through time by every single 1 firm in the economy. We, accordingly, propose a model in which it is posited that each firm is endowed with a measurable index of innovation-enabling knowledge that is subject to change as a consequence of an active searching policy. 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 is the autonomous capacity that a firm possesses in order to carry out in-house innovative search. While these two searching processes not only co-exist 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 firms assess its performance 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 specific neighbour-choosing routine is accordingly organised determines in a significant way firms’ average innovative capability. This feature is modelled by changing the span of 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 firms observing and learning from information flowing from another neighbouring firm: 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 mostly observed by others thus providing some or much of their 2 technological capability. It is these firms that we term paradigm setters. Wealsoassumethat in-house acquired capability is subject to structural shifts by means of periodic random shocks. 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 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 (iv) the average relative efficiency in terms of technological capability of the economy as a whole. The plan of the paper is as follows: section two illustrates the linear model that is implemented to run simulations; section three describes the simulation procedures and the indexes employed to assess results; section four discusses results obtained and section five draws conclusions and sets an agenda for further research. 2 Firms’ technological capabilities and spillover potential Afirm’s technological capability is the upshot of an evolutionary process owing to learning, searching and gathering of information. It is, indeed, these capabilities that ultimately lead to that to innovate, much being explained by interaction taking place within the system. These three categories, however, are largely overlapping since neither can exist without the two others. In this section, we direct our analysis to investigate firms that are technological leaders and whose major interest lies with innovation. We, accordingly, assume that they possess ’in house’ innovative capabilities resulting from past investment and that we, therefore, distinguish in a somewhat artificial manner but useful for modelling, from those that are entirely due to spillover from other firms’ own. These capabilities can be viewed and measured in a way akin to the more general category of 3 afirm’s knowledge base, cognitive potential or set of skills, know-how and competencies: they can actually be modelled as either a vector arranging different indicators or more simply as a scalar compounding the whole. We choose the latter approach. 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. As mentioned above, the latter, while embodying cumulated knowledge, requires investment to be preserved and eventually improved. Considerable efforts are therefore necessary to remain on the forefront of technological prowess; effortswhichneednot always prove successful. It is, accordingly, assumed that Ci(t)be stochastically subject to change and Ci(t)∈(0,1).C(t)is the corresponding vector. Asignificant part of total technological capability is explained by firms’ interaction with other firms. As mentioned above, this is due to searching activity and to the ease with which each firm is observable by other firms when broadcasting information of its own innovative capability. For searching to be significant and transmission possible, it is necessary that cognitive proximity generate interaction to let an effective spill over take place. The ensuing capacity to broadcast relevant technological information may be measured by a basic index specific to each pair ij of firms in the economy. Accordingly, let aij indicate this 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 spill over capacity can then be designated by a square, JxJ, matrix A. The main diagonal of this matrix is made up by 0’s, aii =0,sincenofirm broadcasts information to itself. Matrix Ais simply an indicator of how well observing firms understand the technology of other firms and, therefore, it states no more than a spill over potential as a structural characteristic of the economy. Bounded rationality restricts the number of neighgbours that a firm can usefully search to glean technological information and furthermore it hinders an optimal choice of a new nieghbour when 4 afirm gets the chance to adjust its neighbourhood.. Actual observation is restricted to a more or less narrow neighbourhood made up by firms whose informative usefulness has been discovered by a searching process. We accordingly postulate that firms carry out an active search to single out neighbours best suited to pass on innovative capability. It is assumed that each firm isearches among its potential information suppliers jwhose broadcasting capacity is ai=(aij),j=1,2...J, those that at each point in time it is able to choose as a target for innovative information and actually observe. This choice can be formalised by introducing the proximity matrix B(t)=[bij (t)] where each bij(t)=1or bij(t)=0accordingtowhetherneighbourjhas been or hasn’t been identified as a useful contributor. This procedure defines matrix M(t)=(aij bij (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) The system describing innovative capability in time is V(t)=[I−M(t)]−1C(t) where [I−M(t)]−1plays the role of an endogenous matrix multiplier of in-house capabilities. Since firms are bounded in their rationality, different neighbourhood relationships lead to adifferent multiplier. This change occurs because firms attempt to improve their capabilities through networking. 2.1 Neighbourhood structure The structure in 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 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 5 to determine its own innovative capability. The number of ki,in << J connections defines 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 and it forms the neighbourhood resulting from their active searching as they pursue improvement. The second kind of neighbourhood, which we term the outward neighbourhood,ismadeup for each firm jby firms that actually observe it. It passively results as a consequence of their networking activity. Let this neighbourhood be defined by: Ψj(t)={i:i=1,2...J ∧bij =1} Its size determines the impact of an observed firm’s technological capacity as it propagates throughout the economy contributing to overall performance. For this purpose, we classify the population of firms according to classes of their outward neighbourhood size and thus define an impact factor by ranking them in terms of the number of outward neighbours: Definition 1 Technological paradigm setters emerge when the probability of each rank of the impact factor is positive. 2.2 Evolution Given this neighbourhood structure, evolution owes to two basic determinants: search routines and exogenous changes on individual firms’ in-house innovative capabilities. Firms construe their inward neighbourhood by an active search aimed to single out members that contribute capability to their own. This search, 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 firstconjecturethatthe 6 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)] Secondly, the identified neighbour is substituted with a new one by randomly drawing among the limited number of the latter own neighbours, in the case of weak bounded rationality, or by randomly drawing among the remaining J−ki,in −1members of the entire economy, in the case of strong but bounded rationality. In either case, to generate a new Γi(t)it is necessary that this simple condition be satisfied: Vi(t)>V i(t−1) 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. 3 Parameters and benchmarking The purpose of this model is to study the emergent properties of neighbourhood formation their stability and impact on average technological capabilities. In order to check for the impact of randomness in firms’ searching activity we simplify the model by assuming parameters that insure an even field of equal starting points. It is, accordingly, conjectured at firstthatallfirms have the same skill in broadcasting information and in spilling over their innovative capability. Matrix Awill, therefore, be set at A=(aij =a),∀i, j. Parameter ameasures the strength of interaction 7 5Conclusions The foregoing analysis highlights the importance of searching and networking in fostering the development of technological capabilities to innovate in a context of bounded rationality. Firms obtain information and learn when crucially placed in a cognitive and information providing neighbourhood. Technological spillovers flow and give other firms the opportunity to learn only if networks form to give shape to searching and make learning possible. This paper depicts this process as an effort by firms, which do carry out their own in-house innovation capability building, to seek out high performers able to contribute to the latter. Routines differ according to the breadth of this search. Thanks to a simulated, simple, linear system, it is shown that broad, economy wide search routines are inefficient. The system’s average innovative capability rises when searching is more local and firms are constrained to seek out new neighbours only among their discarded neighbour’s neighbours. Up to a point. While the said ploy implies a technological lock-in, the probability of finding better performing firms increases. This result, however, occurs only if firms still carry out a broad, economy wide search with a frequency that simulations approximately identify. Thus, tuning short-sightedness and far-sightedness improves the system’s innovative efficiency. Past a given combination of the two, the system slides towards increasing mediocrity but paradigm setters emerge as permanent and systematic feature of this hypothetical economy. The more local search is, the greater is the likelihood that paradigm setters’ emergence occurs. When searching is highly and in the limit exclusively local, a lock-in into mediocre paradigm setters takes place and neighbourhoods are no longer providers of efficient spillovers. Exogenous shocks set another time scale to the system and upset the learning and neighbour choosing adjustment. As shock arrival waiting time increases the system’s technological efficiency rises but there is very little impact on paradigm setters’ emergence that, therefore, appears to depend only on the chosen routine pattern. 14 Further research is required to investigate the effects of a lopsided distribution of spillover coefficients (a0 ijs) and the possibility that inward neighbourhoods may evolve to produce emergent properties of the system’s innovative capabilities. References Albert, R. and A.-L. Barabasi, 2002. Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47 - 97. Arenas, A., A. Diaz-Guilera, C. J. Pérez and Fernando Vega-Redondo, 2002. Self-organized criticality in evolutionary systems with local interaction. Journal of Economic Dynamics and Control, 26, 2115-2142. Arenas, A., A. Diaz-Guilera, X. Guardiola, M. Llas, G. Oron, Conrad J. Pérez and F. Vega- Redondo, 2001. New Results in a Self-organized Model of Technological Evolution. 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