203 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 M@n@gement Copies of this article can be made free of charge and without securing permission, for purposes of teaching, research, or library reserve. Consent to other kinds of copying, such as that for creating new works, or for resale, must be obtained from both the journal editor(s) and the author(s). M@n@gement is a double-blind refereed journal where articles are published in their original language as soon as they have been accepted. For a free subscription to M@n@gement, and more information: http://www.management-aims.com © 2010 M@n@gement and the author(s). Isabelle LEROUX Alain BERRO 2010 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement, 13(1), 38-69. M@n@gement est la revue officielle de l’AIMS M@n@gement is the official journal of AIMS ISSN: 1286-4892 Editors: Emmanuel Josserand, HEC, Université de Genève (Editor in Chief) Jean-Luc Arrègle, EDHEC (editor) Stewart Clegg, University of Technology, Sydney (editor) Philippe Monin, EM Lyon (Editor) José Pla-Barber, Universitat de València (editor) Linda Rouleau, HEC Montréal (editor) Michael Tushman, Harvard Business School (editor) Thibaut Bardon, Universté Paris-Dauphine, CREPA - HEC, Université de Genève (editorial assistant) Florence Villesèche, HEC, Université de Genève (editorial assistant) Martin G. Evans, University of Toronto (editor emeritus) Bernard Forgues, EMLyon Business School (editor emeritus) accepted by Jean-Luc Arrègle A s s o c i a t i o n I n t e r n a t i o n a l e d e M a n a g e m e n t S t r a t é g i q u e 38 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 Public/private negotiation and strategic co-evolution in a biocluster Isabelle Leroux Alain Berro GRANEM – UMR MA 49 Université d’Angers et Agrocampus Ouest UFR Droit Economie Gestion isabelle.leroux@univ-angers.fr IRIT-UT1, UMR 5505, CNRS Université de Toulouse alain.berro@irit.fr Abstract Clusters are characterised by partnership practices that lead to a high level of competitiveness. However some of them encounter coordination difficulties due to conflicts over the appropriation of collective gains. This is more specifically the case of bioclusters because of their sectoral particularities and because of the different public policies that apply. Stemming from an analysis of conflicts at stake in a biocluster, this article aims at bringing to light how firms and insti- tutions strategies emerge and co-evolve as their actions are characterised by divergent interests. According to an evolutionary perspective, we propose an exploratory simulation leading to an analysis of the mutual adaptation dyna- mics developed by the agents involved. The results show on the one hand that firms adjust their bargaining strategies according to uncertainty and to their perception of the gains which might be generated at the collective level. On the other hand, the model shows that local authorities can play a regulatory part in the game. This exploratory research provides insight into management public modalities so as to generate cooperation and innovation within bioclusters. Key-words Cluster, biotechnology, co-evolution, adaptative complexe system. 39 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 INTRODUCTION Over the last fifteen years, research on industrial clusters has deve- loped considerably, with growing interest in the phenomena of locali- sation, industrial organisation and the spread of innovation (Krugman, 1991; Brezis et al., 1993; Porter, 1998). The notion of cluster is defined by Porter (1998) as a group of geographically close firms and institu- tions, whose activities are complementary and characterised by a high level of specialisation and technological transfer. The cluster is based on dense inter-organisational networks characterised by cooperative and competitive relations. These robust connections produce collective benefits, such as quasi-rents1 due to the operation of licences or the ef- fects of the agglomeration (Klein et al., 1978; Zucker and Darby, 1997; Dyer and Singh, 1998; Simonin, 1999). As the OECD’s 2007 report shows, the most significant development of geographical clusters has come about through voluntarist policies in activities linked to health, the environment or seed production, such as the Medicon Valley on the border between Denmark and Sweden. These policies of developing and supporting bioclusters are giving rise to renewed interest on the part of organisational science researchers. While the literature on biotechnology clusters focuses mainly on the high level of competitiveness in such systems of innovation, some stu- dies relativise these successes, emphasising coordination difficulties linked to conflicts over the sharing and redistribution of resources and collective benefits (Owen-Smith and Powell, 2003). This is especially the case of biotechnology clusters due to three characteristics specific to them. First, biotechnologies involve strong interconnections between plant, animal and human biology (Argyres and Liebeskind, 2002). This cross-disciplinarity requires that research communities unaccustomed to working together open up to one another. Second, within biotechno- logy clusters, small firms are particularly dependent on the big industrial groups in pharmaceuticals and seed production, their cooperation for- ming an asymmetric alliance (Yan and Gray, 1994). This organisation, described by Roijakkers et al. (2005) as a dual market organisation, is often marked by a climate of mistrust, with the small firms seeing their negotiating power diminished in the face of the large groups. Finally, since biological research is not easily understood due to its technical nature, those in the public sector responsible for financing research programmes are extremely cautious when making funding decisions (Leroux, 2004). The question of genetically modified organisms is hi- ghly controversial, and so potential public reactions to such decisions must be considered. Another difficulty is that they are subject to pres- sure by the large industrial groups (Bonardi et al., 2005). They therefore need to weigh up the demands of local development, the interests of the large groups and the perception of what public opinion might make of support for research in controversial areas. A complex collection of negotiation strategies emerges from all of this, and the firms’ goal is to get the resources or collective benefits for themselves. Following this, the matter for the decision-makers’ atten- tionis that of the co-evolution of strategies in the context of uncertainty 1. The notion of quasi-rent enables the identi- fication of revenues arising from the association of two complementary assets in a cooperative situation. The gains generated by the financial externalities that occur in clusters are thus known as organisational quasi-rents. 40 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 about the behaviour of the partners. Co-evolution refers to the fact that the firms and institutions adopt evolving strategies without, however, being autonomous or self-adapting (Koza and Lewin, 1998; Bourguin and Derycke, 2005) inasmuch as they take into account the partners’ strategies, and the impact of those strategies on the biocluster. Co- evolution refers to continuous negotiated and situated adjustments between the different actors involved. While the notion of co-evolution is used in research literature to deal with technological diffusion (Suire and Vicente, 2004; Steyer and Zimmerman, 2004) and environmental adaptation (Lewin and Volberda, 1999), it is little used in developing ideas of actors’ strategies and their impact on the system as a whole. In reflecting on appropriation conflicts liable to divide firms and instit tions, the objective is to understand how these actors’ strategies emer- ge and evolve during negotiations for the sharing of collective gains. An exploratory study, based on a simulation model, sheds light on the mutual adaptation mechanisms at work. Its results expose the dyna- mics at work within the different stages of negotiation strategies within a cluster, and reveal the regulatory role of the institutions. This study, therefore, paves the way for several lines of research in the public management domain as applied to clusters, and particularly the mana- gement of cooperation and innovation in local systems. The first section of this article presents the state of the art. In the se- cond section, an exploratory methodology based on simulations is of- fered, the results of which are presented in the third section. The fourth and final section is dedicated to a discussion of the results. PUBLIC/PRIVATE STRATEGIC CO-EVOLUTION IN BIOCLUSTERS Numerous offerings in economics and organisational science raise questions regarding the appropriation and vulnerability of clusters ac- cording to different analytical views. Starting with an analysis of techno- logical diffusion (Arthur, 1994), this paper goes on to look at problems linked to public policy decisions (Feldman and Massard, 2002; Bona di et al., 2005) before finally focusing on approaches defining the different sources of opportunism and uncertainty surrounding the behaviour of partners (Klein et al.,1978; Zucker and Darby, 1997). Following, an ap- proach to the cluster as the locus of co-evolution of local firm-institution strategies is offered (Arthur et al.,1997). public/private strategies and appropriation conflicts in bioclusters Cluster vulnerability is often studied in the literature as the result of congestion phenomena (Arthur, 1994; Suire and Vicente, 2004). From this structural perspective, the technological diffusion process re ches a saturation or congestion threshold when one kind of technology be- comes dominant through self-reinforcement effects. Brezis et al. (1993) present an additional analysis in terms of life cycle. New technologies 41 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 replace the old ones, and new clusters emerge while other clusters ex- perience a decline. Clusters’ survival capacity therefore depends on the actors’ ability to ensure knowledge transfer, taking advantage of their geographic proximity. However, beyond these structural factors, the strategic behaviours of the actors also merit consideration. From the point of view of public policies, the decision-makers are driven to make a choice between the strategy of regional redistribution, based on spatial equity in the redistri- bution of wealth, and the policy of cluster growth based, on the contra- ry, on the concentration of economic activities (Feldman and Massard, 2002). Thus, in the short term they face a dilemma between equitable redistribution and supporting innovation, knowing that the elector may express his discontent by ‘voting with his feet’. Along similar lines, Bo- nardi et al. (2005) develop the idea of a political market to analyse the links between public and private actors, with the institutions as givers and the firms as seekers of a given policy. In the case of intense rivalry between firms, the policy decision-maker will satisfy the interests of the most powerful group. This concept is limited to a view which reposes upon market-based coordination. In this example, policy is defined as a pre-existing, exogenous given, and the relations between firms and ins- titutional actors are reduced to an exchange rather than a constructed and negotiated process. Furthermore, biotechnologies excite contro- versy in public opinion, and pose public and private management dif- ficulties in the light of ethical and regulatory issues (Chataway et al., 2004; Dasgupta and David, 1994; Etzkowitz and Leydesdorff, 2000; Lehrer and Asakawa, 2004). Thus, public policy decisions have to be made which ensure the development of relations between firms and pu- blic research laboratories while taking into account the possible views of a public which does not accept genetically modified organisms. As well as approaches which focus strictly on public strategy decisions, coordination flaws within clusters are also studied relative to appropria- tion conflicts: conflicts about the appropriation of resources, quasi-rents or monopoly rents (Klein et al., 1978; Zucker and Darby, 1997; Simonin, 1999; Hamdouch and Depret, 2001). In this case, it is the opportunism of actors in uncertain situations which is in question.Some actors try to appropriate these rents individually, to the detriment of the others, thus taking advantage of the incompleteness of the rules of the game established at the outset. The problem, then, for the local authorities, is to find a management style which allows the harmonisation of conflic- ting interests while remaining aware that they are subject to strategic influencing (Bonardi et al., 2005). These conflicts of interests can be explained, firstly, by the existence of aduality between cooperation and competition within the clusters. While this duality may be emulated (Teece, 1989; Gulati et al., 2000), it can also lead, in certain cases, to a free-riding type of opportunistic behaviour which manifests itself in the unequal acquisition of resources or collectively generated rents (Nooteboom, 1999). This is a particu- larly frequent occurrence within biotechnology clusters because of their cross-sector nature (health, food-processing, environment) and also the 42 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 fragmented nature of their activities, as Argyres and Liebeskind (2002) demonstrate. Indeed, the asymmetry of information, linked to the co- existence of the different types of logic at work in the different sectors (plant, animal, health, nanotechnologies), contributes to the emergen- ce of opportunistic behaviours. These conflicts can thus be explained by the heterogeneity of the firms involved (Saviotti, 1998; Powell et al., 2005; Roijakkers et al., 2005). The bioclusters, like the majority of clus- ters, are organised as dual markets, based on partnerships between big, international ‘leader’ firms and small and medium-sized compa- nies. Yet these partnerships can lead to unbalanced power relations, opportunistic behaviour and even distrust when a small company en- ters into a dependence situation in relation to a large group2.This re- sults in instability which is sometimes ‘chronic’, and even the compart- mentalisation of the links between small and large firms, which might cast doubt on the performance of the biotechnology clusters. Finally, coordination flaws also arise from the simultaneously public and private, highly regulated and much debated nature of biotechnolo- gical innovation activities. Numerous works, such as those of Lawson (2004) and Sherry and Teece (2004), show that conflicts arise over the negotiation of ownership rights to research materials (fragments of DNA) as well as the sharing of rents from the joint operation of licen- ces. Other studies, concentrating on network dynamics, deal with the question of ‘partial embeddedness’ between public and private sphe- res. Owen-Smith and Powell (2003), for example, show that research laboratories have to establish a strategic equilibrium between acade- mic priorities (precedence rule) and industrial priorities (secrets rule) in order to avoid ‘the danger of being captured – instrumentalised – by industrial interests’ (p. 1695). As suggested by Chataway et al. (2004), Leroux (2004) and Raus- ser et al.(2000), stra tegic relations between firms and local authorities are above all asymmetric power relations. Every appropriation conflict masks a power conflict (Dockès, 1999), just as is the case with al- liances, particularly asymmetric ones (Yan and Gray, 1994). Working from stylised facts, Leroux (2004) shows that firms develop negotiation strategies aimed at getting collectively generated resources and in- fluencing the decisions of local authorities, guarantors of the general interest. If the firms develop more or less opportunistic strategies to get the quasi-rents for themselves, the local authorities are capable of expressing their discontent through a reduction in the allocation of public aid. Neverth less, the firms can respond to this with a threat of di- sengagement. In this way, the relationship becomes one of negotiation in the face of ultimatum, and is characterised by uncertainty. The local authorities have to live with uncertainty surrounding the implantation on their territory of the firms concerned, and the firms with uncertainty surrounding the possibility of securing public resources. At this point, the local authorities are in a position where they must make conces- sions rather than be responsible for a company’s relocation. Further- more, these local authorities develop strategies to get the quasi-rents through taxing, or from encouraging the firms to finance local research. The income from taxes is then redistributed in different ways: direct 2. Asymmetric alliances pose even more stabil- ity problems because of the asymmetry of gains which can result. Whatever the nature of the gain that is sought through the alliance, there is always the risk that this gain will be less than the investment that is sought (Kale et al., 2000). Whether we look at a competences approach, or a transaction costs approach, the problem posed is clearly one of appropriation (Prévot, 2007) and of opportunism, as proposed by Williamson (1999). The risk of conflict remains, even along- side the effects of reputation and confidence (Gu- lati, 1995 ; Doz, 1996 ; Dollinger et al., 1997). 43 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 finance (loans, subsidies) or indirect (exemptions); benefits in kind of a private nature (buildings) or public (infrastructure); staff services. Com- plex and sometimes ambivalent negotiation strategies arise from these inter-organisational relations. The actors, firms and institutions thus find themselves in a doubly uncertain situation: uncertainty over the strate- gic behaviours of the partners in the short, medium and long term and uncertainty about the cluster’s regenerative ability. While these analyses greatly help to explain firm-institution conflicts, they only provide a snapshot of the most likely situations without de ling with their evolution over time, or their impact on cluster performance. This is a matter of looking at the links between the adaptation of oppor- tunistic behaviours in uncertain situations and the biocluster’s vulnera- bility. From this perspective, the co-evolution approach can contribute to a dynamic analysis of mutual strategic adaptations within bioclusters. towards an approach to bioclusters based on strategic co-evolution Co-evolution, in its widest sense, describes the transformations and reciprocal adaptations between two living species during the course of their evolution. From this viewpoint, the biocluster may be seen as a complex evolving system (Nicolis and Prigogine, 1994; Janszen and Degenaars, 1998). What is interesting in this approach is that it takes into account internal adaptation and decision-making mechanisms, both in their development and their reversal. Based on such a variety of partnerships and strategies linking private and public players, though, the evolutionary trajectory of the cluster can prove to be unstable, or even, in some cases, chaotic (Luukkonen, 2005; Mangematin et al., 2003; Stuart and Sorenson, 2003). Consequently, in the development of lines of questioning on evolutionary trajectories (Mangematin et al., 2003) and on the strategic dimension of coordination (Chataway et al., 2004; Rausser et al., 2000; Etzkowitz and Leydesdorff, 2000), this a proach enables the dynamic analysis of actors’ strategies in uncertain situations. Approaches which concentrate on strategic co-evolution within bioclus- ters are, in the literature, based on behavioural models from an evolutio- nary standpoint (Arthur et al., 1997; Kirman, 1997) directly linked to the cognitive paradigm (Simon, 1955; Walliser, 2000). Five major principles govern these coordinations in such models : 1) the principle of the he- terogeneity of the agents; 2) the variability principle, which matches the system’s endogenous capacity to produce new trajectories dependent on internal behavioural mutations; 3) the path dependency principle, which refers to learning effects and to auto-rei forcement mechanisms leading to some irreversibility in the evolutionary dynamic; 4) the induc- tive learning principle, according to which the agents are individually part of a cognitive problem-resolution process and learn and adapt their behaviour according to their experience; and 5) the situated rationality principle, according to which agents’ rationality is formed through inte- raction and leads to adaptive agents. The agents are thus part of the relations within which the formalisation of knowledge is ‘impregnated 44 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 with the singularity or the context’ (Ponsard, 1994, p.171). Every agent is viewed as an ‘acting’ subject in the sense that he constructs his own objectives in an intentional and contingent manner. The evolutio- nary approach is freed, therefore, from the fiction of the representative agent by replacing the notion of limited rationality with the notion of situated rationality (Vriend, 2000). Viewed from this evolutionary perspective, the biocluster can be un- derstood as a complex, evolving system (Nicolis and Prigonine, 1994; Janszen and Degenaars, 1998). The interesting factor in this approach is that it takes account of internal mechanisms of adaptation and deci- sion-making, concerning both their emergence and their reversal. However, the co-evolution models arising from this approach, even a ter numerous refinements, deal little with the appropriation strategies of public and private agents. The literature offers many models of network externalities, such as that of David et al. (1998), which summons up the neighbourliness of interactions to show the emergence of niche technologies, or the works of Steyer and Zimmermann (2004), who use a relational structure model to show how ‘leader’ agents influence the evolutionary trajectories of the cluster. Other models show how altruis- tic behaviours can emerge in a cluster. Mitteldorf and Wilson (2000), for example, argue that dense links are important to the emergence of altruism. Nevertheless, while these models make a big contribution to cluster analysis, they have difficulty in dealing in a linked way with the ques- tions of mutual adaptation of strategies and of cluster viability in si- tuations of behavioural uncertainty. This remains, therefore, a path to explore. In distinguishing firms’ motivations, which satisfy their private interests, and also the motivations of the local authorities, which sa- tisfy the general interest, the question of the co-evolution of strategies aimed at appropriating resources is posed here. What opportunistic strategies are put into action by public and private actors in uncertain situations? How do these strategies evolve over time according to their impact on cluster performance? Here it is necessary to open up a ne line of research into the strategic dynamics of bioclusters, and to ex- tend the analysis to public decision-makers who are subject to firms’ influences. research methodology Artificial life3 simulations are enjoying growing popularity in organisatio- nal science, as reported by the special editions of the American Journal of Sociology in 2005 and the Academy of Management Review in 2007 attest (Cartier and Forgues, 2006 ; Brabazon and O’Neill, 2006; Davis et al., 2007). The advantage of a simulation is that it enables resear- chers to study systematically the behavioural patterns to be integrated adaptively into their « world model » (Marney and Tarber, 2000; Vriend, 2000). It consists of a simplified representation of reality which aims to establish links between start and end variables, and which can be used to explain a real situation or to predict outcomes (Gilbert and Troitzch, 1999). The simulation has a triple advantage (Cartier and For- 3. Artificial life was defined by Langton in 1989 as the study of man-made systems which pres- ent behaviours characteristic of natural living systems. An artificial life system can reproduce itself ; an artificial life system is capable of ad- aptation. 45 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 gues, 2006; Davis et al., 2007); it allows the simple formalisation of a complex reality and proves to be a powerful tool for the development of theory ; it allows proximity to the experimental conditions, and the study of different cause and effect relationships, by varying the model’s outset conditions; it is heuristic, and helps to generate findings by pro- ducing artefacts. Artificial life heuristics stage interacting agents, whose actions are based on the rules of autonomous behaviour. Natural se- lection then acts on these agents’ characteristics. The notion of emer- gence is at the core of the analysis, understood as the spontaneous appearance of a micro-regularity emerging from the interaction (Arthur et al., 1997). Artificial life assigns centrality to the interaction’s cognitive element, and more particularly to inductive learning. The agents are involved as individuals in a problem-solving process. They learn and adapt through a variety of cognitive processes which aim to convert the information – resulting from the experiment in a complex and changing environment – into action. Simulations are constructed based on different methods. The most frequently used are cellular robots, multi-agent systems and genetic algorithms. Cellular robots were born of Von Neumann’s (1966) work on self-replicating systems. Today, they are widely used in research on neighbourly interactions, and are particularly suited to the study of local phenomena or competitive market situations (Roehrich, 2006). Multi- agent systems are physical or virtual entities which act in communi- cation with other agents. Each agent optimises individual objectives according to available resources and to his perception of the environ- ment (Ferber, 1995; Wilensky, 2000). This kind of method is applied to concrete problems such as search engines in electronic commerce (Cartier and Forgues, 2006). Genetic algorithms (Holland, 1975) are also much used in management science for modelling emerging com- plex phenomena. Considered the most standard tools, they consist of the instrumentalisation of an optimising function (Goldberg, 1989) and are based on mutation and crossover operators. From a technical point of view, the principle of the genetic algorithm is to set up an initial popu- lation of individuals which then have to evolve and reproduce according to a natural selection process leading to progressively better adapted individuals. In management, they are used to represent the organisa- tion, each gene representing a characteristic of the organisation or of its constituent agents. The internal validity of the results of these different methods has been tested in numerous studies. According to Masuch and Lapotin (1989), the simulation enables the certain identification of causal relations. External validity is harder to determine with this type of method. As Cartier and Forgues (2006) observe, it is necessary to ensure beforehand that the results are not dependent on the model’s principal parameters. Moreover, it is necessary to be sure of the repre- sentativeness of the simulated reality, aligning significantly with field observations (Cartier and Forgues, 2006). 46 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 design of the simulation model The simulation model presented here is the simplified metaphor of a biocluster. It is a schematic model (Thietart, 2003) in the sense that relationship notions are here restricted only to firms’ and local autho- rities’ strategies. It does not attempt to recognise the totality of the research object, which is the cluster, but simply the public/private stra- tegic interactions and their co-evolution. The preferred method within this research is an artificial life simulation based on a genetic algorithm involving mutating and crossover operators (Holland, 1975; Goldberg, 1989). The advantage of the algorithm is that it enables agents sys- tematically to research behavioural coherence to be integrated adap- tively into their world model, so that they can pick up any emerging micro-regularities (Marney and Tarber, 2000; Vriend, 2000). Here, the behaviour of the firms and institutions is formalised through a games theory approach. There are two reasons for this choice of theoretical model. First, the internal validity of game theory models has been widely tested (Ellingsen, 1997). It constitutes a robust mathem ti- cal approach for strategy problems in operational research and econo- mics. Second, it contributes to the study of the behaviour of individuals facing antagonistic situations. It demonstrates more precisely the va- riety of rational strategies possible in situations where an actor’s gains depend not only on his behaviour and the rules of the game but also on that of the other participants, who may pursue different or contradictory objectives (Schelling, 1960). The model is described here according to the narrative method, which consists of deconstructing every action of the agents and reconstituting each one of them in the global adap- tive process. According to Goldspink (2002), it is the most appropriate method for presenting the design of simulation models specifying rigo- rously the nature of the interactions between agents. Strategic interactions within a biocluster or ‘world model’ In the model offered here, the actors negotiate for a share of a qua- si-rent, represented by a cake. It is artificial life modelling of a game of demand under ultimatum, making players interact and negotiate in pairs (Ellingsen, 1997). Thus, when the players respectively want to get a large portion of the cake, by more or less opportunistic means, the negotiation fails. In the opposite case, everyone goes away with the requested portion. The firms are modelled as ‘obstinate’ agents (Obs), whose demands are independent of those of their adversaries. As they participate in the performance of the cluster, they want to get a share of the cake that they decide themselves according to their profitability objectives and their opportunistic tendencies. Some of them ask for a major part of the cake (more than 50%), while others ask for a portion less than or equal to 50%. The local authorities are modelled as ‘sophisticated’ agents (Soph) which adapt their demands to the expectations of their adversaries ra- ther than meeting with failure. As guarantors of the general interest they choose to adapt to the firms’ demands in situations of uncertain- ty over the future of the latter. They have a tendency, then, to make ‘concessions’, their objective being to encourage the implantation of 47 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 these firms on their territory, to stimulate local research partnerships and thus to support territorial performance. Nevertheless, they remain under the ultimatum of the firms who, when they want to influence the local authorities, threaten to disengage. Furthermore, when two local authorities negotiate together, they share the cake 50-50. This equal share is in keeping with their wish to preserve the general interest and avoid any conflict. Determining the demand Each firm’s demand di is based on two constituents, the expected size of the cake, and the portion requested : The strategy consisting of demanding di with i = 0.5 is called the fair strategy which a portion such as i > 0.5 is demanded is called a greedy strategy. Other strategies, such as i < 0.5, they are called modest strategies. Local institutions, whose strategy is marked r, are able to observe the adversary’s demand strategy and to adapt their demand to the expec- ted demand of this adversary rather than endure a failure. Consequent- ly, when an institution meets a firm demanding di, it makes the following demand dr : dr = tegr - di avec dr ≥ 0 As with the firms, the institutions can also be led to failure if they ove- restimate the size of the cake. The payment function If firm i demands di and firm j demands dj, then player i gets the fol- lowing payment : Пij = di if di + dj ≤ T, 0 otherwise If the sum of di and dj exceeds the real size of the cake T, the nego- tiation fails, and the two players win nothing. In the opposite case the surpluses are lost, and thus a badly judged negotiation thus contributes the waste of collective gains within the cluster. When an institution ne- gotiates with a firm it obtains Пri = tegr – di if tegr ≤ T and di ≤ T 48 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 And when two institutions negotiate, they obtain : Пr1r2 = tegr1/2 si (tegr1+tegr2)/2 ≤ T The payment matrix is shown below. Table 1. Payment matrix Obstinate di Sophisticated r1 Obstinate dj Sophisticated r2 di dj di tegr2-di tegr1-dj dj tegr1/2 tegr2/2 Implementation of the genetic algorithm and model validity Internal validity of the model was sought through the use of three means: the choice of the algorithm and its sequentiality; the robus- tness of the chosen parameters; the behavioural structure of the game. The genetic algorithm, whose sequentiality is described in appendix I, consists of an optimising function (Goldberg, 1989) into which three evolution operators, selection / crossover / mutation are introduced. These operators have a double function (Schoenauer et al., 1996): the genetic process exploits the already-known neighbouring zones and simultaneously explores all the unknown zones beyond this proxi- mity (EVE dilemma – Exploitation versus Exploration). The choice of a genetic algorithm suits this research work’s objective, to be able to analyse the adaptive dynamic of different populations of agents, and to identify the mechanisms affecting this adaptation process and the emergence of micro-regularities (Bruderer and Singh, 1996; Davis et al., 2007)4 . Thus each agent is determined by its genotype (appendix 1), which consists of both the expected size of the cake and its sharing strategy. In the model, the population of firms and institutions amounts to 1000 agents, which corresponds to a real, medium-sized cluster5. The initial size of the cake is T = 1 and the variation interval is [0.1; 2.0]. This finite interval is intended to reinforce the model’s realism, since a cluster cannot grow exponentially. The population of firms and obstina- te agents (Obs) is divided into seven profiles represented by discrete intervals (table 2) between 0 and 100. The choice of seven profiles is large enough to ensure technically the representativeness of possible demands, while guaranteeing the legibility of the results on a histo- gram. Strength tests carried out on fifteen profiles produced identical results (figure 6 appendix 3) but reduced the legibility of the graphs. Each profile was arbitrarily fixed and corresponds to the portion of cake demanded. Table 2. The seven profiles of firms profile name explanation profile type Obs 7 Obs 21 Obs 35 Obs 50 Obs 64 Obs 78 Obs 92 Firms whose demand is 7 % Firms whose demand is 21 % Firms whose demand is 35 % Firms whose demand is 50 % Firms whose demand is 64 % Firms whose demand is 78 % Firms whose demand is 92 % Modest Fair Greedy 4. We invite the reader to refer to these two key articles presenting in-depth analyses of the validity of different tools used in artificial life. 5. Table 3 in annexe 2 offers a synthesis of the parameters used in the different simulations. 49 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 The simulations were based on the following evolutionary parameters : a rate of mutation of 10% ; a crossover rate of 50% ; the initial distri- bution of each profile (Obs and Soph) was 12,5% at the game’s out- set. According to Schoenauer et al.’s internal validity tests (1996), the choice of these parameters allows the maintenance of both of selective pressure on the population so as to ensure the convergence of the algorithm, and also of the genetic diversity of the population so as to avoid too a rapid convergence, because every algorithm risks gene- rating an excessive duplication of certain individuals which generate high gains. In this way, the loss of genetic diversity can bias the evolu- tionary process. The technical solution is to introduce, exogenously, a continuous rate of mutation. The ideal mutation rate is fixed at 10% for this technical reason, which is well identified in computer science re- search (Schoenauer et al., 1996). As for robustness, different mutation rates were tested, from 5% to 12,5%, which brought about no change to these results (figure 7, annexe 3). At 2,5% the results were distor- ted by early convergences ; from 15% the mutation rate disturbed the convergence of the algorithm and, furthermore, rendered the graphs illegible (figure 7, annexe 3). The crossover rate was fixed at 50%, in keeping with classic robustness references (Schoenauer et al., 1996). It corresponds to a so-called ‘sexual’ reproduction of the population of agents: pairs of individuals – ‘parents’ – generate ‘child’ individuals by a genetic process focused on teg. A rate of 50% is usually chosen to maintain the diversity of the population while allowing the convergence of the algorithm: too weak a reproduction rate for the agents prevents the learning process from happening; on the other hand, a crossover parameter of more than 50% contributes to precocious convergence of the algorithm. Even if there are numerous interconnections, the agents do not sys- tematically negotiate with the whole population, but only with certain partners when this proves to be necessary. Consequently, at each ne- gotiating round, the agents negotiate with a representative sample of 10% of the total population. Then every agent is assessed according to the gains he is capable of generating. In this artificial world, certain agents are linked by a so-called relatio- nal proximity (Grossetti, 1998). As Porter (1998) shows, the cluster is based on interconnected networks of firms and institutions. The hy- pothesis that certain agents have more direct relationships with each other informs the integration of this characteristic into the simulation model. Thus, although firms and institutions negotiate with all the mem- bers of the cluster (notation phase), they only exchange information about the size of the cake with partners they have noticed adopting the same strategy as them during the negotiation phase (crossover phase). Consequently, while some agents are unable to recognise their adversary’s strategy at the beginning, they can, nevertheless, learn it from experience during the negotiation process through trial and error. This relational proximity established between agents who opt for similar strategies enables them selectively to exchange information and places them in a single strategic approach. 50 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 The model’s internal validity is also reinforced by the structure of the ul- timatum game. This enables the clear and systematic identification of the links between agents’ behaviour and the gains that they generate, that is, the causal relations during an algorithmic sequence (Goldspink, 2002). In this ultimatum game, every instance of strategic interaction and all gains generated by agents negotiating two by two are explicit and readily identifiable in the payment matrix (table 1). In terms of external validity, great importance is attributed to the repr sentativeness of the model, which depends on the stylised facts descri- bed earlier (Rausser et al., 2000; Chataway et al., 2004; Leroux, 2004) and aims to be as close to reality as possible. However, it is quite ob- vious that this type of model, as is currently being debated, would be unable to create an identical reproduction of reality since, as stated at the beginning of this section, it is a schematic model. Nevertheless, its strength is its ability to restrict the analysis to modes of interaction that can be isolated to facilitate the identification of evolution and to observe endogenously generated artefacts. As argued in the works of Axelrod (1997), any simulation integrating non-linear evolution processes poses the problem of path depende cy. Thus, a simulation can be found to be conditioned by sensitivity to the initial conditions, the system’s response to an endogenous distu bance being dependent on the model’s structure and the sequential adap- tation process. No one simulation, then, will be identical to another. A research work based on this methodology generally reveals a wea- ker generalisation property than classic statistical analysis (Goldspink, 2002). Its external validity should therefore be moderated according to this sensitivity. However, and this is a significant subject of debate in the social sciences, the authors support the view of Axelrod (1997) according to which a simulation’s interest is not in its ability to develop exact predictions, which are valid in all circumstances. The strength of a simulation such as the one used here is that it enables the identifica- tion of typical behaviours within a system of agents which constitutes a metaphorical world and whose results are a valuable example of behavioural analysis. It provides elements to identify the emergence conditions of microb havioural regularities in a system of co-evolving actors, thus building up analytical elements that the researcher can use in the reality of a cluster. It remains true that the external validity of a simulation can be improved. According to Axelrod (1997) and Goldspink (2002), it is im- perative to relaunch the simulations and to develop statistical an lyses of the results in order to have the most exact identification possible of the different emerging micro-regularities. From this viewpoint, every si- mulation should be systematically repeated a thousand times, in such a manner as to be sure of the emerging results. For each simulation, the equilibria between the different populations of agents can be identi- fied using a statistical recognition technique (described in appendix 1), thus avoiding any error in the interpretation of the results. 51 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 RESULTS As Cartier and Forgues (2006) assert, the advantage of a simulation is that it enables the variation of the starting conditions, or of the exoge- nous rules of the game, in order to analyse the effect on the final re- sult. Consequently, the results presented here are those that emerged from three simulations which were gradually increased in complexity. In a cordance with the initial questions being examined, these three simulations aim to find out the mechanisms of firm-institution strategic co-evolution in uncertain situations: (1) the aim of the first simulation (S1) was to study the strategic co-evolution of the firms and institu- tions in the absence of uncertainty over the size of the cake, in such a way as to be able to compare this certain situation with situations characterised by uncertainty; (2) the aim of the second simulation was to study the strategic co-evolution of the firms and institutions when uncertainty about the size of the cake was introduced; (3) the aim of the third simulation was to study the strategic co-evolution of the firms and institutions in the presence of both uncertainty about the size of the cake and of opportunistic behaviours contributing to a reduction in cluster performance. simulation s1: the size of the cake is known and inva- riable The size of the cake is T = 1 and does not change during the nego- tiation process. The simulation enables observation of the strategies adopted by the agents, their co-evolution and possible changes of di- rection, stage by stage, over 500 periods or generations. The simula- tions were relaunched a thousand times and turned out the same way in 100% of cases. The results show that the negotiation strategies evolve in two distinct phases (figure 1). First, the local institutions constituted the majority of the total population during the first 20 periods. These negotiations ended in equal shares of the cake, that is 50/50. Then, this very large presence of concession-making institutions contributed to the emergence of the greediest strategies (92% of the cake) which constituted, in the end, the majority of the population represented, besi- des a small proportion of firms whose demand was 78%. With no uncertainty about the size of the cake, then, it can be seen that the most opportunistic strategies take the lead in the negotiations. The local institutions are not unfamiliar with this, and unintentionally play a distributive: in making concessions they contribute to the increase in the most opportunistic strategies to the detriment of fair or modest strategies. S1 outcome results: When the quasi-rents are known and stable over time, the firms tend to opt for very opportunistic strategies. In this, they rely on the concession-making institutions which involuntarily play a distributive role. 52 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 Figure 1. Example of the evolution of negotiation strategies adopted by the agents in simulation S1 simulation s2: the size of the cake is unknown which leads to uncertainty The size of the cake is unknown and the agents have to estimate it. Any overestimation will be damaging to them, this being an ultimatum game. Here the firms and the institutions have an endogenous capa- city to modify their respective demands d. They estimate the size of the cake according to a learning process focused on teg and made possi- ble through recourse to mutating and crossover operators. In this way, each agent has the capacity to assess teg, and every new assessment leads to a modification of demand d. The chance of failure is high, the- refore, since the agents can overestimate or underestimate the size of the cake. This, however, is fixed at T = 1. The launching of 1000 simulations produced the following resulting va- riations (figure 2): i) In 46,2% of cases the negotiation process stabilised around the most opportunistic firms, whose demand was 92%, and the local institutions. As in simulation 1, the most opportunistic stra- tegies were made possible due to the strength of the presence of local institutions during the first phases of the process. ii) In 29,6% of cases, the negotiation process stabilised around the firms whose demands amounted to either 78% or 64% on one side, and the local institutions on the other. 53 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 iii) In 22,4% of cases, the negotiation stabilised around the firms whose demands are described as fair, that is 50% of the cake, and the local institutions. iv) In 1% of cases, the negotiation process stabilised around the firms whose demand amounted to 35% of the cake. In these very rare cases, the local institutions disappeared, to the benefit of the firms making the most modest or fair demands. v) In 0,8% of cases, an evolutionary process accident can be seen, which makes it impossible to interpret the results of the si- mulation, and which constitutes an incompressible error margin. Figure 2. Percentage of equilibria obtained between sophisticated and obstinate over 1 000 simulations S2 When the size of the cake is unknown and the agents have to estimate it, the results vary and depend on the endogenous capacity of these agents to find it as quickly as possible. The winners are those who make the nearest assessment as quickly as possible, while also exchanging this information with the partners who have the lowest failure record in the evaluation process. In 46.2% of these simulated cases, the most opportunistic firms very rapidly drew benefit from the large presence of local institutions in the first 40 periods (figure 3). In the other cases, the majority, the development of much more cautious strategies can be seen. In the absence of precise knowledge about the real size of the cake, the firms made less opportunistic demands. The role of the local institutions remained just as important in this simulation because they reduced the possibility of failure in the phase of assessment of the size of the cake. In this way, when the size of the cake was unknown, the institutions also played a distributive role. In very rare cases (1%), the firms whose strategies were the most modest were able to survive without the local institutions, as they themselves played a distributive role. S2 outcome results: Generally, the firms develop less opportunistic strategies in situations of uncertainty about future collective benefits, while taking advantage of «the concession-making» institutions. 54 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 Figure 3. Example of a negotiation process stabilising around the most opportunistic sophisticated and obstinate profiles, S2 simulation simulation s3: the size of the cake varies according to the strategies adopted The size of the cake, which here is analogous to the cluster’s perfor- mance, becomes variable. The suggested is that when a firm opts for opportunistic strategies leading to the failure of the negotiation, this contributes to the reduction of the size of this cake. Conversely, when the agents choose strategies which are less opportunistic, or only sli- ghtly opportunistic, this contributes to the augmentation of the size of the cake. It is therefore necessary to observe how the strategies co- evolve in these conditions, which of these strategies will be developed, and what the role of the institutions is going to be. In technical terms, a parameter called influence k was applied to T. If in the previous round (n - 1) the number of successful negotiations was greater than the number of failures, then T increased from 0.01. In the opposite case, it reduced from 0.01. The choice of this parameter k = 0.01 was arbitrarily fixed at a low level. The objective was to establish a causal link between the agents’ behaviour and the modification of the size of the cake, without provoking a radical collapse of the system. The un- derlying hypothesis is that coordination flaws can cause a disturbance in the system, but cannot cause its total collapse as may be the case at the time of a major economic crisis (buyers backing out, etc.). The results show that the agents adapted their behaviour according to its impact on the size of the cake. Because of this, the negotiation pro- 55 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 cess did not stabilise over time and evolved according to different pha- ses (figure 4). The firms modified their behaviour in such a way as to maintain the size of the cake or make it grow. They opted for cautious, fair or modest behaviours when this outcome was threatened (when it shrank dramatically) and opted for the most opportunistic strategies when the cake reached a size close to the upper limit. Figure 4. Example of the evolution of negotiation strategies, simulation S3 For example, period [275; 375] is marked out by a considerable pre- sence of cautious firms whose demand was 64% (figure 5). These cau- tious behaviours contribute significantly to the growth of the cake to the upper limit. Once this was achieved, a change from cautious strategies of 64% to highly optimistic strategies of 92% could be seen. However, this was made possible by the presence of the local institutions which contributed to the reduction of negotiation failures, consequently avoi- ding any radical reduction in cluster performance. Thus, when the latter was threatened by behaviours which were largely too opportunistic, the local institutions emerged and played a regulatory role, allowing the cake to grow again. In this simulation, the performance of the cluster was maintained thanks to the local institutions. S3 outcome results: When there is uncertainty about the gains that may be generated, and the cluster performance is threatened, the local authorities help to compensate for the effects of the most opportunistic behaviours. 56 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 Figure 5. Evolution during period [275 ; 375], simulation S3 DISCUSSION These simulations provide some factors upon which to reflect concer- ning firm-institution strategic co-evolution within a biocluster. Broadly speaking, the co-evolution approach contributes to an initial conside- ration of the phasing dynamics of negotiation strategies within a bio- cluster. The agents adjust their strategies according to the effects of their own behaviour on the performance of the system. This type of simulation model could be very useful for further investigation into the coordination relations intrinsic to bioclusters, which until now have been difficult to grasp (Chataway et al., 2004; Saviotti, 1998). Whereas the model’s internal validity hinges on the adoption of crossed validation factors, its external validity needs to be dealt with in a particular way because of the path dependency phenomenon inherent in all non-linear simulations. More precisely, the representativeness of the model was understood on two levels. At the micro-behavioural level, conformity of the modelled behaviour of the firms and institutions to reality was ensu- red by drawing on stylised facts developed by Chataway et al., (2004), Leroux (2004) and Rausser et al. (2000). At the level of emerging re- gularities, the results correspond to the real behaviours resulting from interaction within clusters: behavioural phase dynamics and strategy reversal and collective management of uncertainty and its possible op- 57 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 portunistic exploitation. As Axelrod (1997) points out, the systematic statistical analysis of results contributes to a very precise identification of the situated behavioural micro-regularities. These micro-regularities constitute as many new analytical elements as the researcher in mana- gement could find in the real situation of a cluster. The results moderate the hypothesis according to which the principle of cooperation-competition systematically produces emulation (Teece, 1989) and they raise the question of the vulnerability of clusters. The artificial life paradigm thus allows stage by stage observation of how the agents instrumentalise their relations (Owen-Smith and Powell, 2003) and modify their strategies in a complex and changing environment. At any moment, a system accident, seen as an artefact, may considerably challenge the cluster’s evolution dynamic. Here we are opening up a line of thought on the link between the nature of inter-organisational strategic relations and the cluster’s potential vulnerability. These simulations also enable an exploration of the very complex rela- tions linking the firms and the local public institutions while also casting light on their regulatory role. Implicitly, it appears that the latter have a power that one could associate with the power of the weak presented by Schelling (1960) and underlined by Dockès (1999). This is because, without the institutions, the durability of the cluster could not have been assured in simulation S3. They are the key figures in strategic coordi- nation, even if the situation (withdrawal threats and concessions) is not in their favour at the outset. Later, the model confirms one of the major ambiguities which can be found in stylised facts, and which concerns the public/private relationships in a biocluster (Leroux, 2004). On the one hand, the local institutions bring the firms their aid, particularly fi- nancial aid, so as to encourage their establishment locally. On the other hand, this support frequently contributes to the emergence of oppor- tunistic strategies, the firms gaining the most benefit being those with great negotiation power due to their credible threat strategies. This then opens a line of research devoted to questions of territorial governance and strategic management in uncertain situations (Powell et al., 2005; Gulati et al., 2000). From a management point of view, particularly whe- re public-sector management is concerned, the task of the researchers is to engage in reflection on the nature of systemic risks with the aim of offering local authorities a better understanding of the strategic rela- tions in clusters. However, while the studies conducted thus far emphasise the importan- ce of uncertainty to the behaviour of firms in a cooperation-competition context (Argyres and Liebeskind, 2002) and heterogeneity (Saviotti, 1998; Powell et al., 2005; Roijakkers et al., 2005), these simulations assist in refining their role in the coordinations. When the firms are in a situation of uncertainty concerning the gains that might be generated, they tend to opt for less opportunistic appropriation behaviours. If the public actor does not want to be subject to pressure by the more power- ful groups (Bonardi et al., 2005), it could be in his interest to withold some information on the gains which may be collectively produced and redistributed. A line of thought opens up here: should the public actor 58 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 maintain a certain level of uncertainty to reduce the risk that opportunis- tic behaviours might emerge? However, these simulations can be refined technically. The first refine- ment would be to include more heterogeneous agents (e.g.research laboratories) and interactions in order to reinforce the model’s realism. The second refinement is the integration of geographic proximity to allow the study of the impact of distance on actors’ strategies. Fur- thermore, this simulation model paves the way to new explorations of the nature of public/private conflicts within the bioclusters. A suitable approach would be to develop longitudinal empirical analyses from a sample of several clusters, so as to achieve a deeper analysis of those conflicts, the resolution processes adopted, and the impacts on the evolution of the system. CONCLUSION The objective of this article was to use the results of artificial life simu- lations to understand the strategic co-evolution of the firms and institu- tions in a biocluster, when there is behavioural uncertainty. Considering the research trails developed and the refinements possible, the analysis and discussion of the results consist of three principal classes of impli- cations: theoretical, methodological and practical. From the theoretical viewpoint, this research contributes to reflections on the vulnerability of clusters, approaching the subject not from a structural perspective fo- cused on the phenomena of technological diffusion, but in the context of the strategic paradigm. The simulations enable a better understanding of the public/private actors’ games by adopting an innovative approach to the role of behavioural uncertainty in strategic decisions. Moreover, they help in the analysis of conflict, power and the definition of the stra- tegic rules of the game which are endogenous to a complex evolving system. This approach allows, for example, a glimpse of possible new ways of understanding the alliances, particularly for explaining compe- tition phenomena or to shed new light on asymmetric alliances and their co-evolution. From the methodological viewpoint, the simulation proved to be a powerful and original research method, even though it is still underused in management science. Genetic algorithms are particularly suited to the analysis of emerging strategic phenomena, as is argued in the work of Lee et al. (2002) on the maintenance of strategic groups, or studies from marketing (Roehrich, 2006) mentioned previously. A promising line of research is opened up for researchers in manage- ment who want to involve themselves more in research on the strate- gies of actors within clusters in general. From the practical viewpoint, this simulation continues the work carried out on the relations between firms and institutions and the strategies for the sharing of gains. For this reason, it allows a better understanding of the way local authorities manage resources and how it may be possible to exploit uncertainty to reduce the risks of opportunism. The trains of thought which follow from this fit naturally into the current question of the management of 59 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 competitive poles / French clusters (OECD Summary, 2007), that is, the role of public actors in the creation of conditions that are favourable to cooperation and innovation. Isabelle Leroux is a lecturer in industrial economics at Angers University in France. Her research, at the intersection of economics and management, deals with the analysis of territory governance as well as the strategic analysis of firms and local governments’ behaviour. More specifically, she works on strate- gic alliances, coalitions and bargaining games in local networks. The applica- tion of her work is mainly in competitive clustering; however, she also works on strategic networks in social economics. Alain Berro is a lecturer in computer science at Toulouse Capitole University in France. His main research interests are multi-objective optimisations and optimisations in dynamic environments. His analyses are focused on the study of robustness tests and on the improvement of the different existing methods of optimisation. His research lead to new heuristics based on evolutionary techni- ques applied to economic and managerial problems. Acknowledgements : First, we would like to thank Alain Desreumaux and the reviewers and sub-editors of M@n@gement, who contributed to many improve- ments since the initial paper and simulation. We are also keen to thank Frédé- rique Chédotel from Tours University, Paul Muller from Haute Alsace University, Camille Baulant from Angers University and Eric Rigamonti from ESSCA An- gers Business School for the precious advice they gave us at the various stages of writing and reviewing. 60 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 REFERENCES . Argyres, N., and Liebeskind J. (2002). Governance inseparability and the evo- lution of US biotechnology industry, Journal of Economic Behavior and Or- ganization, 47, 197-219. . Arthur, B. (1994). Increasing returns and path dependen- ce in the economy. Ann Arbor; Univer- sity of Michigan Press. . Arthur, W. B., Durlauf, S. N., and Lane, D. (1997). 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Present at the biotechnology revolution : transformation of technological identity for a large incumbent pharmaceutical firm, Research Policy, 26, 429-446. 64 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 APPENDIX 1 : SIMULATION PROCESS ALGORITHM The diagram below shows the operation of the genetic algorithm used. 1. The initialisation phase attributed to each agent in the popu- lation, in a random or a guided way, a value which related to its genetic characteristics, in other words its profile (its negotiation strategy) and the expected size of the cake. 2. The notation phase determined a mark for each agent, repre- senting the agent’s gain expectation in a negotiation. This phase allowed the evaluation of the quality of each agent’s strategy. In order to do this: a. A 10% sample of the population was randomly selec- ted. b. Then, one by one, every agent in the population nego- tiated with every agent in the sample and thus obtained some gains (see paragraph entitled The payment func- tion). c. By dividing the sum of an agent’s gains by the number of negotiations effected, we calculated the agent’s expec- tation of gains. 3. The goal of the selection phase was to choose the most hi- ghly performing agents, in other words those who have a high expectation of gain, and therefore had a good strategy. A ranking selection was used because this ensured that the probability of 65 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 selecting an agent was close to said agent’s mark ratio, and to the total of the marks of all the agents in the population. The se- lection by rank first sorted the population by fitness; next, each agent was ascribed a rank according to a positioning relative to the others. In this way all the agents had a chance of being se- lected. 4. The modification phase effected a genetic intermixing of the selected agents by means of the crossover operator, and main- tained the genetic diversity by means of the mutating operator. a. Crossover only operated between two agents with the same profile. The children resulting from this inherited the profile of the parents. The value of the expected size of the cake then either equalled that of one of the parents or was a different value. To calculate this different value, a number x between -0.25 and 1.25 was randomly selected, then tegchild = x * tegparent1 + (1-x) * tegparent2 was calculated. b. Mutation randomly modified one or several genetic cha- racteristics of an agent. Following a mutation, then, an agent could change strategy or the expected size of the cake. In this case it was an exogenous mutation. 5. Return to phase 2. Language used The model was implemented in Java. The specification of the Math. Random function [specification java.util.random], which enables the ge- neration of random numbers between [0; 1] guarantees that the seed of the pseudo-random number generator is new and unique at each launch of the program (Knuth, 1998). Equilibrium detection technique In the cases of simulations S1 and S2, the evolution in the proportions of each strategy can be seen for each generation, for 500 generations. To detect equilibrium, the average and the interval of its proportion in the population for the last 100 generations was calculated for each stra- tegy. Next, the two highest averages were identified to find the esta- blished equilibrium. But this equilibrium was only confirmed definitively if the following two conditions were fulfilled: 1) the standard deviations associated with the two strategies participating in the equilibrium situa- tion were less than 0,25; 2) the smallest proportion of strategies partici- pating in the equilibrium was over 5%. Regarding the first condition, this is because too large a standard deviation can lead to the supposition that a change of equilibrium occurred in the last 100 generations. In this case, as the equilibrium had not been stable for long enough, it could not be confirmed. The second condition was established so as to eliminate the cases of very early convergence linked to a loss of genetic diversity. 66 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 APPENDIX 2 : THE SIMULATION PARAMETERS Table 3. Common parameters, rates of mutation and crossover. APPENDIX 3 : ROBUSTNESS TESTS 1. Number of profiles The choice of 7 profiles is sufficiently large to ensure the representa- tiveness of the possible demands while guaranteeing the legibility of the results on a histogram. The simulation was tested with 15 profiles, obtaining identical results; using 15 profiles provided no additional ele- ments of analysis and rendered the graphs barely legible. Figure 6. Percentage of equilibrium obtained between sophisticated and obstinate over 1 000 S2 simulations with 15 profiles Simulation S1 Simulation S2 Simulation S3 Common parameters Initial size of the cake : 1 Variation interval of the size of the cake : [0.1 ; 2.0] Number of agents in the population : 1 000 Initial distribution of each profile : 12.5 % Ranking selection Mutation rate Crossover rate 10 % Modification of agent’s profile. 0 % All the individuals know the size of the cake so they are not seeking its expected size. 10 % Modification of agent’s profile or of the expected size of the cake. 50 % There is only crossover between two « parents » with the same profile. The « children » take after them. The value of expected size of the cake therefore equals one of the expected sizes of the cake of the « parents » or a different value. 67 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69 2. Mutation rates The following graphs show the equilibrium percentages between so- phisticated and obstinate obtained with 1000 S2 simulations. For each graph, the mutation rate used is indicated. As can be seen, from 5% to 12,5% the graphs give similar results. When the mutation rate is 2,5%, the errors (left-hand column) are essentially due to cases of early convergence. With a mutation rate of 15%, it can be seen that the pro- portion of equilibrium between the Obs 92% population and the Soph population becomes very high. Too high a mutation rate which is too high disturbs the evolution by modifying the genetic characteristics of too many individuals and artificially favouring the individuals with an elevated expectation of gains. Therefore, below 5% and above 15% the results cannot be used, for purely technical reasons. Figure 7. Graphs obtained with modification of the mutation rates 2,5 % 5 % 7,5 % 10 % 68 Public/private negotiation and strategic co-evolution in a biocluster M@n@gement vol. 13 no. 1, 2010, 38 - 69 12,5 % 15 % 69 Isabelle LEROUX and Alain BERROM@n@gement vol. 13 no. 1, 2010, 38 - 69