Modeling the Structural Dynamics of Industrial Networks ... - CiteSeerX

Modeling the Structural Dynamics of Industrial Networks

By

Ian F. Wilkinson School of Marketing, University of New South Wales, (Sydney, NSW, 2052, Australia) email: [email protected]

James B. Wiley, Faculty of Commerce, Victoria University of Wellington (PO Box 600, Wellington, New Zealand) email: [email protected]

Aizhong Lin, University of Technology Sydney

InterJournal Complex Systems, Manuscript Number 409 Status Accepted 2001 http://www.interjournal.org/ (Originally Presented at International Conference on Complex Systems (ICCS) May 21-26, 2000 in Nashua, NH, USA)

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Abstract

Economic institutions involved in creating and delivering products and services to end-users operate within networks of relations that “organize” the flows of activities. Historically, an implicit assumption underlying research into these networks is that the patterns of relations are controlled by the organizations involved -- the so-called top down view. More recently, we have come to recognize that the relations among organizations may be (possibly unintentional) consequences of the ongoing process of interaction. That is, network structure can emerge in a bottom up self-organizing way. The research we describe aims to develop a methodology for studying the • processes by which institutional and network structures evolve, • the factors driving these processes, • the impact of environmental conditions on outcomes, and • the ways in which the evolution of better performing institutional and network structures may be encouraged. The work uses the NK Models developed by Stuart Kauffman at the Santa Fe Institute (Kauffman 1992, 1995) to develop computer models that are capable of mimicking the evolutionary processes of industrial networks. This paper briefly describes the logic of the underlying the models being developed and presents the results of the simulation of a simple network situation using an NK Boolean Model. Introduction Market systems consist of locally interacting agents who continuously pursue advantageous opportunities. Since the time of Adam Smith, a fundamental task of economics has been to understand how market systems develop and to explain their operation. During the intervening years, theory largely has stressed comparative statics analysis. Based on the assumptions of rational, utility or profit-maximizing agents, and

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negative (diminishing returns) feedback process, traditional economic analysis seeks to describe the (generally) unique state of an economy corresponding to an initial set of assumptions. The analysis is static in the sense that it does not describe the process by which an economy might get from one state to another. In recent years, an alternative view has developed. Associated with this view are three major insights. One of these is that market processes are characterized by positive feedback as well as the negative returns stressed in classical economics (e.g. Arthur 1994). The second insight is that market systems may be studied in the framework of complex adaptive system theory. “A 'complex system' is a system consisting of many agents that interact with each other in various ways. Such a system is 'adaptive' if these agents change their actions as a result of the events in the process of interaction" (Vriend, 1995, p. 205). Viewed from the perspective of adaptive systems, market interactions depend in a crucial way on local knowledge of the identity of some potential trading partners. A market, then, is not a central place where a certain good is exchanged, nor is it the aggregate supply and demand of a good. In general, markets emerge as the result of locally interacting individual agents who are themselves actively pursuing those interactions that are the most advantageous ones, i.e., they are self-organized (Vriend, 1995, p. 205). How self-organized markets emerge in decentralized economies is a question that formal analysis of such systems seeks to answer. The third insight associated with the alternative view is that there are parallels of economic processes with biological evolution. This insight, in turn, suggests that ideas and tools of biological evolution may fruitfully be applied to the study of economics. Among the promising tools are computer-based algorithms that model the evolution of artificial life. If the tools used to model artificial life may be applied to institutions,

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industries, or entire economies, then their evolution and performance may be studied using computer simulation. Objectives The aim of our work is to apply the above insights to the study of Industrial market systems (IMS). IMS consist of interrelated organizations involved in creating and delivering products and services to end-users. The present paper describes computer models which are capable of mimicking the evolutionary process of IMS, drawing in particular on the NK Models developed by Stuart Kauffman at the Santa Fe Institute (Kauffman 1992, 1995). The modeling effort has two interrelated but distinct purposes. The first is to help us to better understand the processes that shape the creation and evolution of firms and networks in IMS. This will provide a base both for predicting, and perhaps influencing, the evolution of industrial marketing systems. Secondly, the models may be used for optimizing purposes, to help us designing better performing market structures. The specific objectives of this research are to examine: •

the processes by which structure evolves in IMS,

•

the factors driving these processes, and

•

the conditions under which better performing structures may evolve. Background It is typical of complex adaptive systems in general, and those that mimic life

processes in particular, that order emerges in a bottom up fashion through the interaction of many dispersed units acting in parallel. No central controlling agent organizes and directs behaviour. [T]he actions of each unit depend upon the states and actions of a limited number of other units, and the overall direction of the system is determined by competition and coordination among the units subject to structural

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constraints. The complexity of the system thus tends to arise more from the interactions among the units than from any complexity inherent in the individual units per se (Tesfatsion 1997, p. 534). IMS may be described in terms of four sets of interrelated elements or components, i.e. actors, activities, resources and ideas or schema (Hakansson and Snehota 1995, Welch and Wilkinson 2000). The actors consist of various types of firms that operate in industrial markets. A “type” of firm (such as, wholesalers, drop shippers, manufacture agent, rack jobber, broker, and so forth) may be described in terms of the activities that it is capable of performing as well as in terms of their schema or “theories in use” which underlying actor’s actions and reactions (Gell-Mann 1998). In IMS, business entities seldom perform all of the necessary activities or functions required for a transaction to take place. Rather, they perform some of them. The firm and other firms with complementary specialization collectively perform requisite activities for transactions to occur. One way to look at the evolution of firms in market systems is to conceive that they evolve to establish competitive niches – much as organisms do in natural environments. That is, firms retain, add, or drop activities and functions as part of an on-going process. The outcome of this process is (or is not) a set which gives the firm a competitive advantage. The resulting interdependence, however, makes the “fitness” of any firm’s pattern of specialization dependent on the specialization patterns of other firms in the market system. Each firm of a given type may be further described in terms of its resources (such as inventories, cost structures, wealth, and the relationships it has established with other actors in the market). Patterns of relationships may be complex, and they will themselves evolve. The pattern of relationships that determines firms’ interdependencies also establishes the fitness of a specific pattern of activities and functions. Firms with which a firm has relationships have themselves relationships with other firms. These other firms have relationships with yet other firms and so forth, including the

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possibility of relationships (perhaps of different types) with the original firm. Relationship patterns may shift and become unstable. For example, the merger of two advertising agencies may result in their having to give up one of two clients in the same industry. The forsaken client may hire a new agency that, in turn, must give up a client in the industry. “Avalanches” of changes may follow in an analogous way to Per Bak’s (1996) sand piles. Depending on the nature and degree of connectivity and responsiveness among firms and relationships, changes in one part of the network can bring forth “avalanches” of changes of different sizes (Hartvigsen et. al. 2000). Each agency that changes clients loses links to the suppliers and customers of the old client and gains links to the suppliers and customers of the new client. Relationships may be of different types. For example, two merging automobile firms may require management consulting services. The consulting company may be allied with, or even a subsidiary of, an accounting firm, which in turn gains links to the merged auto firm though its relationship with the consulting firm. The consulting firm in turn may gain links to the merged company’s public relations agency. Because of the services provided by the consulting and accounting firms, the auto firm may require the services of a computer service bureau. The service bureau in turn may gain links to the auto firm’s investment bank. However, the exclusionary restrictions described in the previous paragraph may result in changes in consulting, accounting, banking, and service bureau industries. A second objective of this research, and the primary objective of the present paper, is to gain understanding of what drives the formation of relationship patterns and to look at the patterns of stable and unstable relationships that may occur. Modeling A differentiating characteristic of this research is the way in which relationships are viewed. Typically, descriptions of relations among firms make the implicit assumption that

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it is organizations that “organize” and direct the flows of activities in IMS. As Resnik (1998) point out such centralist thinking tends to be common in business: “People seem to have strong attachments to centralized ways of thinking: they assume that a pattern can exist only if someone (or something) creates and orchestrates the pattern. When we see a flock of birds, they generally assume the bird in front is leading the others - when in fact it is not. And when people design new organizational structures, they tend to impose centralized control even when it is not needed.” (p. 27) Recent developments in the science of complex adaptive systems show how structure emerges in bottom-up, self-organizing ways. The observed behaviour of the system is the outcome of independent actions of entities that have imperfect understanding of each other’s activities and objectives and who interfere with and/or facilitate each others activities and outcomes. Structure emerges as a property of the system, rather than in a top-down, managed and directed fashion (Holland 1998). From the ongoing processes of interaction, actors’ bonds, resource ties, activity links and mutual understandings emerge and evolve and these constitute the structure of the IMS (Hakansson and Snehota 1995, Welch and Wilkinson 2000). This structure can be more or less stable. Over time, the structure of the IMS evolves and co-evolves as a result of interaction with other IMS. We make use of recent developments in computer-based simulation techniques to model the evolution of relationships in IMS. We adopt this approach for two reasons. First, the complex interacting processes that take place in such systems are beyond the scope of traditional analytical techniques. Second, the actual IMS we observe in the real world, no matter how diverse they may be, are only samples of those that could arise. They are the outcomes of particular historical circumstances and accidents. As Langton (1996) observes in a biological context:

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We trust implicitly that there are lawful regularities at work in the determination of this set [of realized entities], but it is unlikely that we will discover many of these regularities by restricting ourselves only to the set of biological entities that nature actually provided us with. Rather, such regularities will be found only by exploring the much larger set of possible biological entities” (p x). So it is with IMS. Recent developments in the modeling and simulation of complex adaptive systems suggest ways in which we may explore the range of possible networks in IMS’s that might arise. In the next section, we describe the models of IMS’s we have developed and are developing based on Kauffman’s NK Models. NK Models Kauffman (1992, 1995) has developed a way of representing a network of interacting elements in terms of a set of N elements (actors, chemicals, firms or whatever) each of whose behaviors is affected by the behaviour of K other elements. The model is a discrete time simulation model; what exists in time t+1 is determined by what existed in time t. Two versions of the NK model are relevant to our research: •

NK Boolean Models, used to model relationship interaction, and

•

NK Fitness Landscapes with Patch Formation, used to model the emergence of cooperating groups of entities, such as firms.

Only the first has so far been implemented in our research and it is the version described in the next section of the paper. A description of the approach we are taking using NK Fitness Landscapes follows this.

NK Boolean Models and Relationship Interaction An important question is how to characterize network structure in terms of NK Models. We chose to use relationships between firms as the unit of analysis. The pattern

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of relationships at time t+1 is determined by the pattern of relationships at time t and Boolean logic rules for transforming one to the other. Note that by choosing relationships we are effectively operating at a second order level compared with traditional industrial network models. Actors are defined by the relationships they have and not, ab initio, as network entities in their own right. A fuller account of the model is to be found in Wilkinson and Easton (1997). The behavior of relationships is modelled in binary terms; they either e xist (i.e., are active) and have the value 1 or they do not exist (i.e., are inactive) and take on the value 0. The behavior of a relationship at time t depends on the behavior of K other relationships (possibly including its own behavior) in the previous period. Boolean operators specify the behavior of a relation in period t+1 for each combination of behaviors of the K connected relations in the previous period. The focal relation is called the output or regulated relation and the K connected relations affecting its behavior are called input relations. Our contention is that Boolean operators may be constructed that have conventional economic/business interpretations such as complementary supply relations, competing relations, temporally connected relations, and so forth. If this is so, then both the type of relationships and the degree of interconnection K can be modelled, and the effect of both dimensions on the character of IMS attractors simulated. Our model is an autonomous Boolean network because there are no inputs from outside the network itself, although this can be added (see below). For the purposes of our analysis, we assume that the Boolean network is a synchronous, parallel processing network in which all elements compute their behavior in the next period at the same time. Our general methodology for examining the behavior of our NK Boolean models follows that of Kauffman: To analyze the typical behaviour of Boolean networks with N elements, each receiving K inputs, it is necessary to sample at random from the populations of

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all such networks, examine their behaviors, and accumulate statistics. Numerical simulations to accomplish this therefore construct exemplars of the ensemble entirely at random. Thus the K inputs to each element are first chosen at random and then fixed, and the Boolean function assigned to each element is also chosen at random and then fixed. The resulting network is a specific member of the ensemble of NK networks” (Kauffman 1992 p192). The role of K Kauffman has shown that K, the number of other entities to which an entity is linked, is a critical parameter in determining the pattern of behaviour of the network. For low values of K, say 0 or 1, each entity is essentially an isolated unit. Its state does not influence other elements and so the network consists of “frozen” relationships that do not change or regularly switch on and off. For high values of K, the interactions are very complex and destabilizing, resulting in chaotic behaviour. For values of around 3 to 6 self-organizing patterns emerge within the network that are stable with respect to small perturbations (i.e., random changes in the state of individual relationships do not change the state of the system as a whole). As K is increased, the isolated actors become isolated interacting groups. Gradually, as K increases, more of the elements are joined in the network. Attractors are the sequences of relatively stable states to which the system settles for protracted periods and, as Kauffman (1992) observes, attractors “literally are most of what the systems do” (p. 191). In the present context, attractors are interpreted as relatively stable patterns of relationships that may occur in IMS. The pattern of relationships that might be observed in an actual industrial market might correspond to the patterns on one such attractor, whereas IMS are likely to have many possible attractors depending on N, K, the mix of Boolean operators involved and system starting conditions. The patterns of relationship corresponding to other attractors might correspond to patterns observed in other market systems or, possibly, to feasible patterns that have never been observed in IMS.

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System behaviour is affected by a biasing or canalising factor, reflected in a p arameter p. This reflects how sensitive an element is to the behavior of the K other elements to which a given element is connected. The value of p depends on the character of the Boolean operator and is measured in terms of the proportion of situations an entity will take on the most modal value, 0 or 1. The lowest value for p is 0.5 , which occurs when an element will take on the value 1 in the next period in 50% of situations and 0 in the other 50%. If it will take on the value 1 in 90% of situations, p is 0.9. Higher K may lead to order with higher values of p because p acts as a kind of damping function that “prevents” chaos. The p value of networks constructed using different combinations of Boolean operators will be used to aid our analysis of the behaviour of the network. An Example of an NK Boolean Model of Network Relationships To keep things simple we will consider the network in terms of the N=8 possible output relationships between supplier and distributors, which can either be active (=1) in a period or inactive (=0) in any period. Figure 1 illustrates the network. The system comprises four suppliers (S0 to S3) and the main competitor of each supplier is the one to its left e.g. the main competitor of S0 is S1. For S3 the main competitor is S0.

Figure 1 A Four Supplier Two Distributor Network

S0

S1

S2

S3

Input Relation 2 Input Relation 1

Output Relation D0

D1

Figure 1 focuses on the output relation between S0 and D0 (RD0,S0 ) and R D0,S1 and R D1,S0 are the input relations. The state of R D0,S0 in period t+1 depends on the states of of RD0,S1 and R D1,S0 in the previous period. RD0,S1 and R D1,S0 are the input variables and we

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can say R D0,S0 is connected to RD0,S1 and R D1,S0 . For simple exposition, we will for the moment assume relation R D0,S0 is not an input variable i.e., the relation is not connected to itself. In this network K=2 and there are K 2 or 4 different combinations of the input variables (00, 01,10,11) and there are sixteen Boolean operators that may be defined on the combinations. These are shown in Table 1 in terms of the behavior of the output or regulated variable (relation RDOSO) in period t+1, for each of the four possible combinations of input variables (RDOS2 and RD1SO) in period t. For example, rule 1 should be read as follows: RDOSO is inactive in period t+1 for all four possible combinations of behavior RDOS1 RD1SO in period t. Wilkinson and Easton (1997) examine in greater detail the sixteen Boolean operators in the context of an IMS. In the next section, we briefly consider the logic of simulation. We then describe simulations of two situations where the existence of a relationship between a supplier and a distributor depends on the preferences each has for exclusive dealing. We identify two types of exclusive dealing: ”Supplier Exclusive Dealing” (Rule 10, Figure 1), and “Mutually Exclusive Dealing” (Rule 3, Figure 1). They are discussed in more detail below. Role of Simulations Simulations are particularly useful for discovering the variety of system states that could be observed, including ones that are rare or unobserved in nature. They are useful for exploring the conditions that produce the respective states and for evaluating the relative performance of the states. They also are useful for investigating the stability of the states. Stability may be explored by perturbing the system and following what happens, something that would be difficult, if ethical to do in natural environments. Perturbation may take many forms. The most obvious would be to induce the formation or extinction of a type of entity or relationship. It is useful to find out how such changes propagate through the

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system over time, determine what the final configuration(s) is (are), and observe how the process and outcome differ in relation to the type and scale of the perturbation.

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Table 1. Boolean Functions for two input variables (Source: Wilkinson and Easton, 1997) Conditions Rule in Boolean Form Input Relation: 1) RDOS1 in period t is inactive (=0) inactive (=0) active (=1) active (=1) 2) RD1SO in period t is inactive (=0) active (=1) inactive (=0) active (=1) ___________________________________________________________________________________ RDOSO(t+1) is 1=active 0 = inactive Rule 1 0 0 0 0 Insulation Rule 2 1 1 1 1 Insulation ....................................................................................................................................................................... Rule 3 1 0 0 0 Rac nor Rad Rule 4 Rule 5

0 0

1 0

0 1

0 0

Rad and not Rac Rac and not Rad

Rule 6 0 0 0 1 Rac and Rad ........................................................................................................................................................................ Or (two conditions) Rule 7 0 1 1 0 Rac exc.or Rad Rule 8

1

0

0

1

Rac nor Rad or Rac and Rad

Rule 9 Rule 10

1 1

1 0

0 1

0 0

Rac nor Rad or Rad and not Rac Rac nor Rad or Rac and not Rad

Rule 11

0

1

0

1

Rad and not Rac or Rac and Rac

Rule 12 0 0 1 1 Rac and not Rad or Rac and Rad .......................................................................................................................................................................... Or (three conditions) Rule 13 0 1 1 1 Rad or Rac Rule 14 1 1 1 0 Rac nand Rad Rule 15 or Rac and Rad Rule 16 Rad or Rac and Rad

1

1

0

1

Rac nor Rad or Rad and not Rac

1

0

1

1

Rac nor Rad or Rac and not

We have developed an NK simulation program to allow us to explore the dynamics of relationships in networks (Wilkinson, Hibbert, Easton and Lin 1999). The program is written in C++ and permits the analyst to design a particular network of connected relations and Boolean operators of interest, or to construct such networks randomly. Once the network is constructed, the input and output relations specified and the Boolean operators chosen the program computes the system states over time. The starting conditions can be specified, or randomly generated and the option exists to systematically examine the behaviour of the network for different starting conditions or alternative combinations of Boolean operators. To illustrate the program we examine the behaviour of a simple network of firms each wishing to follow exclusive dealing arrangements with other firms. Referring to the network depicted in Figure 1, we hypothsize that the existence of Wilkinson, Wiley & Lin 2000 page 14

relationships between suppliers and distributors depends on the preferences each has for exclusive dealing. These preferences may be represented in terms of Boolean operators governing the behaviour of a focal relationship in terms of the existence of other relationships. For example, •

condition (a) supplier exclusive dealing, a supplier only deals with the distributor if it is not dealing with its main competitor. This condition is operationalized by Rule 10 of Figure 1.

•

condition (b) mutual exclusive dealing, a distributor wants an exclusive dealing relationship as well as the supplier and hence the dealer will not deal with the supplier if it is also dealing with other distributors. This condition is operationalized by Rule 3 of Figure 1.

• a) supplier exclusive dealing . The Boolean operator here is read off the row labelled “Rule 10” in Figure 1. This shows the state of the output relation in period t+1 for each possible combination of states of the two input relations in period t. In this condition the state of Input Relation 2, i.e., the existence or not of a relationship between the focal distributor and the closest competitor of the supplier dominates the rule. If this relation is active in period t the output relation will not be active in period t+1. The distributor does not care if the supplier deals with the other distributor or not. This is the Boolean rule that neither Input Relation 1 nor Input Relation 2 is active or Input Relation 1 and not Input R-elation 2 is active. More simply the Boolean rule may be specified in terms of Input Relation 2 only i.e., not Input Relation 2. The Boolean operator for condition b is read off the row labelled Rule 3 of Figure 1. Here the Output Relation will be active in period t+1 only if both Input Relations are not active in period t. This is the "Nor" rule i.e., neither Input Relation 1 nor 2 can be active for the output Our simulations show that In condition (a), supplier exclusive dealing, one type of

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equilibrium state or attractor exists when the distributors deal with alternate suppliers e.g., D0 deals with S0 and S2 and D1 deals with S1 and S3, as depicted in Figure 2. In this situation the existing relations continue because the distributor is not also dealing with the suppliers closest competitor and the inactive relations will not change because the suppliers will not deal with distributors who are also dealing with their closest competitor.

Figure 2 An Attractor for the Four Supplier Two Distributor Network: Supplier Exclusive Dealing Condition S0

S1

D0

S2

S3

D1

An equivalent attractor is when D1 deals with S1 and S3 and D0 deals with S0 and S2. If we start the network in this position it will remain there. However, if we change one of the starting conditions at random we find that this attractor is not very stable and the network goes to another attractor involving various kinds of cyclical behaviour. Because there are eight output relations in our model the are 2 8 = 256 possible starting configurations. In order to examine the types of attractors that can emerge we used the program to systematically explore the behavior of the model for different starting conditions. The attractors that emerge from a sample of 108 of these starting conditions are shown in the appendix. Starting conditions are grouped according to the attractor that results and into broader types of attractors and in terms of the number of states on the attractor, as indicated by the percentage of periods a particular output relation is active. The results show that the situation depicted in Figure 2 rarely occurs and that any disturbance from that state will result in the emergence of another attractor. Note that

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there are no trails leading to the attractor in our “simple” model. In other words all states of the model are on an attractor. The most common attractors are cyclical patterns in which all the relations switch between active and inactive states. An example is given in Figure 3 for the starting condition 10110001. Here a four period attractor results in which two relations are active 50% of the time (2 of the 4 periods), one is always inactive and one active. This is classified as a type b attractor and three other attractors have this mix of behavior. The most common type of attractor is a four period attractor in which four relations are active half the time, two are active 1 out of 4 and two active 3 out of 4 period. b) Mutual Exclusive Dealing When the mutual exclusive dealing rule is used the number and type of attractors changes. The same static equilibrium state or attractor exists when the distributors deal with alternate suppliers but once again this attractor only occurs if the firms start in that situation. Any divergence from it results in other attractors emerging. Some of these attractors are shown in Appendix 2 for different starting conditions. An eight period cycle is a commonly occuring attractor in which 4 relations are active 6 out of 8 periods and four are active 1 out of 8. Furthermore not all state of the network are on an attractor; there are lead in tails of behavior that can be analysed in the ways developed by Weunsche (1999) to show the paths to different attractors. The foregoing demonstrates that even an apparently simple network can produce surprisingly complex behavior. Kauffman (1992) shows that the number of attractors of randomly connected Boolean nets depends on K and N. When K=2 the number of attractors is about equal to the square root of N. He also shows that the behavior of the network over time starting at any two different states will tend to converge (ibid. p200) i.e. the behaviour of the network is not highly sensitive to starting conditions. Lastly, the median number of states on the attractor cycle is about equal to the square root of N.

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Figure 3 A Four Period Attractor for Starting Condition 10110001

Period 0

Period 1

Period 2

Period 3

Period 4

Kauffman’s results are for randomly connected Boolean nets, whereas we are interested in the behaviour of Boolean networks that conform to conditions found in industrial networks. In order to explore the number and kind of attractors existing for our focal networks, we simulate the behaviour of the network over time, keeping the Boolean rules fixed, while varying the starting conditions in terms of which relations are active and which inactive in the first period.

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The following questions may be investigated using the current version of our simulation program. •

What happens to the behaviour of the network over time under various starting conditions and relevant Boolean Rules? In other words what are the attractors for the behaviour of the network?

•

Which patterns of relations being active are mutually compatible, and what other repeated cyclical patterns of behaviour can arise?

•

How likely is each attractor to arise i.e. how large is the basin of attraction for each attractor?

•

How stable are different attractors i.e., does a slight move away from the attractor result in its return to the same or another attractor?

We are particularly interested in the conditions under which emergence of “edge-ofchaos” attractors emerge. This is because attractors of this sort resemble that of a partially frozen pond in that they involve combinations of a “frozen” set of fixed on relations (i.e., longterm relations) or fixed off relations (i.e., no relation), interspersed with “islands” of relations that exhibit a pattern of behaviour over time. These islands are separated from each other by the frozen skeleton of relations such that innovations and mutations taking place in these islands do not necessarily interfere with behavior in other parts of the network. These kinds of attractors have been identified by Kauffman, Langton and others as central to the emergence and organisation of complex systems including molecules, cells, organisms, and economic and social organizations (e.g. Kauffman 1992, 1995, Langton 1992). Such network attractors also correspond to what others have observed in real network patterns, i.e., a mix of stability and change (e.g., Gadde and Mattsson 1987, Hakansson 1992) and this parallel in part motivates our research.

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Next Steps Further developments of the Boolean model involve introducing lagged operators and interactions between different industrial networks. The latter step leads to larger scale industrial and economic organisation. The extension is straightforward. For example, the behaviour of some relations (or actors) in one industrial network can be made to depend on the behavior of relations (or actors) in another network, as well as on those in their own network. Both the number of networks S and the extent of inter-coupling among networks C may be varied and may themselves evolve. Finally, an exogenous environment can introduce noise or other exogenous effects directly on some or all parts of the network(s).

NK Fitness Landscapes and Patches Another realization of the NK model is in terms of NK fitness landscapes. Here, an entities behavior is again usually modelled in binary form with 1 = on or active and 0 = off or inactive. The specific fitness or utility of an an entity at time t is determined by the entity’s state in the period and by the states of K other entities. In terms of IMS a firm’s (or relationships) fitness depends on its own behavior in the period as well as on the behavior of K other firms e.g. suppliers, complementors, customers and competitors (or connected relationships). An entity changes its behavior from one period to the next (0 to 1, or 1 to 0) if it “expects” to improve its fitness. Usually models assume that entities choose their behavior based on the assumption that other actors’ behavior will remain unchanged in the next period. Fitness values, usually between 0 and 1, are allocated randomly to each possible combination of behaviors of a focal entity and its K connected enetities. Here we do not plan to model the behavior of relationships directly, as for the NK Boolean model. Instead relations among actors emerge as a result of the formation of patches of cooperating actors.

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Kauffman (1995) has introduced the concept of “patches” to refer to groups of actors coordinating their actions to achieve better group fitness. We use the concepts of patches in two ways. The first focuses on the development of cooperative relations among actors in a network and the second focuses on activities as the primary unit of analysis and how groups of activities emerge to define firms. Modelling the Emergence of Patches of Cooperating Actors The first approach follows that of Kauffman, in the sense that patches define sets of cooperating elements. With a patch size of one, entities operate independently in deciding their behavior in the next period. Larger patch sizes correspond to multiple actors cooperating to jointly improve group fitness and it is assumed that gains and losses are distributed equally among groups members – therefore average fitness in the group is the driving force of behavior. Kauffman (1995) shows that patch size in this sense has a dramatic effect on the ability of a system to achieve higher performing structures. We plan to use NK fitness landscape type models to model the patch formation process endogenously and to explore the way network dynamics and evolution is impacted by patch formation. Previous modelling work has tended to focus on patch size as an externally imposed parameter, whereas the formation of patches in IMS is a central feature of structural change and evolution. Firms and inter firm alliances in an IMS are examples of patches formed in real networks in a self-organizing way. Modeling the way patches may form and reform over time and how this shapes network performance will yield important insights into the deep processes of industrial network evolution.

Four potentially fruitful approaches to modelling patch formation have been identified. The first uses payoff rules for patch formation, based on work by Kauffman and McCready. Here, an IMS may begin with individual behavior i.e. a patch size of 1, or some other starting configuration of interest, and each period actors join and leave patches

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according to certain rules. Actors try to join a patch (and thereby leave their existing patch) if the average payoff is greater in the other patch than their existing patch. But actors may or may not be accepted into a patch. New patch members are accepted only if the average patch payoff is expected to increase as a result of their joining. These expectations are determined by examining what the payoffs would have been if the actor was a member of the patch in the previous period. The evolution of patches can be modelled over time using different starting configurations, different values of K, different patch churning rules, as well as different types of fitness distributions (e.g. normal versus other distributions). The second approach is based on models of iterated prisoner’s dilemma games with choice and refusal of partners (IPD/CR) pioneered by researchers at Iowa State University (e.g. Tesfatsion 1997). These models allow actors to form links with other entities and learn from the experience interacting with them. Depending on the outcomes of interaction using a fixed number of IPD plays, links may be strengthened, extended, undermined, or broken. Over time actors form groups (patches) of interacting actors, that are more or less cooperative, or they remain isolated “wallflowers” i.e. patches of size 1. Actors can employ different strategies in their interactions with others, which will affect the outcomes of interaction and the types of groups of interacting actors that form. Strategies can also be modified over time depending on the performance of an actor and its awareness of the performance of others. The third approach models the probability of cooperating with other actors directly and can be viewed as a variant of the IPD/CR approach, except t that there is no modelling of interaction in terms of IPD games. This approach is based on the models developed by Hartvigsen et al (2000). Populations of actors are located on a two-dimensional aquare toroidal lattice and have a defined number of neighbours with whom they can interact. Each actor has a probability of cooperating, p i, and those that interact are considered cooperative

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and open to communication. Those with low p i interact infrequently and those with p i = 0 are pure defectors. A parameter ε specifies the amount each actor p i is changed in response to the interaction experience each period. Interactions in any period are governed by two random numbers generated for each actor that determine if they interact and whether a neighbour cooperates or defects. If the chosen neighbour cooperates, the target actors p i is increased by ε , otherwise it is decreased. By simulating the pattern of interaction over time, interacting groups (patches) emerge. The final approach is suggested by models of firm growth developed by Epstein and Axtell (1996) and Axtell (1999). In these models, actors join firms (patches) to gain economies of scale and the rewards are divided equally among members of a firm. Actors vary in terms of their work versus leisure trade offs and this affects their “cooperation” within a firm. Problems of shirking and free riders result from work-leisure tradeoffs and this leads to the breakup of firms and the formation of other firms. These models have been shown to be capable of mimicking the actual size distribution of firms in an economy. Modelling Activity interactions using NK Fitness Landscapes The standard NK fitness model represents the N elements as scalars (binary values of 1's and 0's). Fitness is computed for the K+1 vector describing the state of the firm and the states of K other firms that influence it. The firm’s state in period t+1 is determined to be the one that has the highest fitness. The NK fitness model can be adapted to model a firm in which the states are vector valued, rather than scalar valued. For a given set of activities A, A I is the vector of 0s and 1s indicating whether firm “i” does or does not perform each activity. Firms can perform different combinations of activities which are the equivalent of patches i.e. they can alter the combination of activities performed in the expectation of improving overall fitness or the vector. The fitness of performing or not an activity depends on the K other activities it is connected to that are performec within the firm or by other firms. Patches here are a

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natural descriptor of a firm in terms of the set of activities included in the vector. Patch sizes vary in terms of the number of activities firms consider in combination. Firms can add and drop activities in their vector (i.e. change patch size) as well as alter the state of each activity in their vector or patch. The approach is similar in some ways to that proposed by McKelvey (1999) in which he uses the activities specified in Porter’s value chain as the basis for representing firms in terms of NK models.

Summary, Managerial Implications, and Conclusions Traditionally, economics’ view of the economic process has focused on the actions of agents, rational actors who interact with each other and their environment to control scarce resources. An alternative view of the economic process has developed in recent years. Among the leading proponents of this view are those who note parallels between economic processes and biological evolution. These parallels suggest that ideas and tools of biological evolution may fruitfully be applied to the study of economic processes. Taking an evolutionary view profoundly changes the underlying metaphor of economic processes, from what might be called an engineering metaphor, to a biological one involving stochastic, dynamic processes, with myopic, “satisficing” agents. Formal representations of such processes can be difficult, if not impossible, to solve. There is an analytic approach based on evolutionary computer algorithms that avoids the need for a formal model. Among the promising tools are agent based computer models of complex adaptive systems and the emerging Science of Complexity. The relevance of the Science of Complexity to management is beginning to be appreciated by industry. One example of this is the Embracing Complexity Conferences run by Ernst and Young (e.g. 1996 1997), which bring together scientists from various disciplines working on aspects of complex systems behaviour with business. New types of

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models are being developed to better understand, sensitize managers and perhaps control the behaviour of complex intra and inter-organizational systems. An important insight of the new types of models is that firms are operating in complex adaptive systems in which control is distributed throughout the system. While there may be exceptions, in the main, no actor or entity coordinates or directs the behaviour of the network. Instead, a firm is participating, learning and responding to the local circumstances it encounters and tries to achieve its particular objectives. Coordinated action results from interrelated yet separate operations occurring in parallel. This leads to a different concept of management and strategy; one in which the firm participates and responds to the system in which it operates rather than tries to control and direct it (Wilkinson and Young forthcoming). Firms jointly create both their own destiny and the destiny of others. In this regard, firms act to preserve and create the ability to act through the futures they shape for other firms on whom they depend as well as themselves. Together, they co-create the winning games the winning actors play (Kauffman 1996). In the mainstream business academic literature, we are beginning to see the emergence of this type of thinking, as firms come to see themselves as parts of business ecosystems in which cooperative and competitive processes act to shape the dynamics and evolution of the ecosystem (Haeckel 1999, Moore 1995, Moore 1996). Of particular note is the 1999 special issue of Organization Science devoted to complexity and the important role played by NK models in the special issue (Anderson et al 1999). We must be on the right track!

References

Anderson, Philip, Meyer, Alan, Eisenhardt, Kathleen, Carley, Kathleen, Pettigrew, Andrew (1999) Introduction to the Special Issue: Applications of Complexity Theory to Organization Science. Organization Science. 10 (May-June 1999): 233–236. Arthur, Brian (1994) Increasing Returns and Path Dependence in the Economy, Ann Arbour, The University of Michigan Press

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Axtell, Robert (1999) The Emergence of Firms in a Population of Agents Center on Social and Economic Dynamics, Brookings Institution Washington, DC. Bak, Per (1996) How Nature Works, New York, Springer Verlag Easton, G. (1995) “Methodology and Industrial Networks” in Business Marketing : an Interaction and Network Perspective. K. Moller and D. T. Wilson eds. Norwell, Mass., Kluwer. Easton, Geoff, Wilkinson, Ian F. and Georgieva, Christina (1997) “On the Edge of Chaos: Towards Evolutionary Models of Industrial Networks” in Hans Georg Gemunden and Thomas Ritter eds. Relationships and Networks in International Markets, Elsevier 1997 pp273-294 Epstein, Joshua M. and Axtel, Robert (1996) Growing Artificial Societies, Cambridge, MA. MIT Press Ernst and Young ed.: Proceedings: Exploring Complexity Conference, Ernst and Young, California, August, 1997 ________________.: Proceedings: Embracing Complexity Conference, Ernst and Young, Cambridge: MA. August, 1998. Gadde, Lars-Eric and Mattsson, Lars-Gunnar (1987) “ Stability and Change in Network Relations” International Journal of Research in Marketing, 4, pp29-41 Gell-Mann, Murray (1995) “Complex Adaptive Systems” in The Mind, The Brain, and Complex Adaptive Systems, Morowitz, H.J. and Singer, J.L. Sante Fe Institute Studies in the Science of Complexity, Reading MA: Addison-Wesley Publishing Company, 11-24 Haeckel, Stephan H.(1999) Adaptive Enterprise Boston: Harvard Business School Press Hakansson, Hakan (1992) Evolution Processes in Industrial Networks”, in B Axelsson and G. Easton eds Industrial Networks: A New View of Reality, London Routledge, pp129-143 Hakansson, Hakan and Ivan Snehota (1995)Developing Relationships in Business Networks, Routledge, London,. Hartvigsen, G., Worden, L. and Levin, S.A. (2000) “Global Cooperation Achieved Through Small Behavioral Changes Among Strangers” Complexity 5: 3, 14-19 Holland, John H. (1998) Emergence, Addison-Wesley Publishing, Reading, MA. Kauffman, S. (1992) Origins of Order: Self Organisation and Selection in Evolution, New York: Oxford University Press Kauffman, S. (1995) At Home in the Universe, New York, Oxford University Press Kauffman, Stuart (1996) Investigations: The Nature of Autonomous Agents and the Worlds they mutually Create, Santa Fe Institute Working Paper 96-08-072, Santa Fe, NM. Langton, Chris (1992) “Adaptation to the Edge of Chaos” in Artificial Life II: Proceedings Volume in the Santa Fe Institute Studies in the Science of Complexity, C. G. Langton, J.D.Farmer, S, Rasmussen and C. Taylor, eds. Reading, MA, Addison Wesley. Langton, Chris ed. (1996) Artificial Life: An Overview. Cambridge MA, MIT Press Wilkinson, Wiley & Lin 2000 page 26

Levitan, Bennett, Lobo Jose, Kauffman, Stuart and Schuler, Richard (1999) “Optimal Organization Size in a Stochastic Environment with Externalities” Santa Fe Institute Working Paper 99-04-024 Moore, James (1996) The Death of Competition, John Wiley, Chichester, 1996. Moore, Geoffrey (1995) Inside the Tornado, Harper Collins, New York. McKelvey, Bill (1999) “Avoiding Complexity Catastrophe in Coevolutionary Pockets: Strategies for Rugged Landscapes” Organization Science. 10 (May-June) 294–321 Resnick, Mitchel (1998) “Unblocking the Traffic Jam in Corporate Thinking” Complexity 3 (4): 27-30. Tesfatsion, L. (1997) “How Economists Can Get Alife” in Arthur, W.B., S. Durlauf and D.A. Lane eds. The Economy as an Evolving Complex System II, Redwood City: Ca, Addison Wesley p534-564 Vriend, N. (1995) “Self Organization of Markets: An Example of a Computational Approach” Journal of Computational Economics 8 (3) 205-231 Welch, Catherine and Wilkinson, Ian F. (2000) “From AAR to AARI? Incorporating Idea Linkages into Network Theory” Industrial Marketing and Purchasing Conference, University of Bath, September. Wiley, James B. (1999) “Evolutionary Economics, Artificial Economies, and Market Simulations,” Working Paper, University of Western Sydney, School of Marketing, International Business and Asian Studies. Wilkinson, Ian F and G. Easton (1997) "Edge of Chaos II: Industrial Network Interpretation of Boolean Functions in NK Models," in F. Mazet, R. Salle and J-P Valla eds. Interaction Relationships and Networks in Business Markets : 13th IMP Conference Vol 2: Groupe ESC Lyon pp 687-702 Wilkinson, Ian F. and Young Louise C. (forthcoming) “On Cooperating: Firms, Relations and Networks” Journal of Business Research Wilkinson, Ian F., Hibbert , Bryn, Easton, Geoff and Lin, Aizhong (1999) Boollean NK Program Version 2.0 A C++ program to simulate the behaviour of NK Boolean Networks, School of Marketing International Business and Asian Studies, University of Western Sydney, Nepean. Wilkinson, I. F., Wiley, James B. and Easton, Geoff: Simulating Industrial Relationships with Evolutionary Models , Proceedings of the 28th European Marketing Academy Annual Conference, Humboldt University, Berlin, 1999.

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Appendix A Supplier Exclusive Dealing Attractors for 108 staring condition Type a 1 0 0 1 1 0 0 1 100% 0% 0% 100% 100% 0% 0% 100% 0 0 1 1 0 0 1 1 0% 0% 100% 100% 0% 0% 100% 100% Type b 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0 50% 0% 50% 0% 1 0 0 1 1 0 100% 100% 0 1 0 1 0 0 0% 0%

0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 50% 100% 50% 100%

0 1 1 1 1 1 50% 50%

1 0 0 1 1 0 1 0 0 50% 50%

0 1 0 1 0% 0%

50% 50%

0 1 1 1 1 1 1 1 1 100% 100%

50% 50%

Type c 1 1 0 1 1 0 1 0 0 1 1 1 100% 25% 100% 25% 0 0 0 1 0 1 0 0 1 25% 25%

1 0 1 0 1 1 0% 0%

0 1 0 1 0% 0%

75% 75%

0 1 1 0 1 1 0 1 1 75% 100% 75% 100%

1 1 0 0 1 1 0 1 100% 75% 0% 100% 75% 0%

25% 25%

0 0 0 1 0 0 0% 0%

75% 75%

1 0 0 1 1 0 1 1 0 25% 25%

0 1 1 0 1 1 1 1 1 100% 100%

0 1 1 0 0 1 1 1 0% 75% 100% 0% 75% 100% 1 0 1 1 0 0 75% 75%

1 1 1 1 0% 0%

25% 25%

0 0 1 0 1 1 25% 100% 25% 100%

Type d 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 50% 50% 50% 50% Type e 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 1 75% 75% 75% 75%

1 1 1 1 1 1 0 0 0 1 1 1 1 1 1

0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 50% 50% 50% 50%

1 1 1 1

0 1 0 1 0 1 1 1 25% 25% 25% 25%

0 1 1 0 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 25% 25%

0 0 0 1 0 0 0 0 0 0 0 0 1 0 75% 75%

1 1 1 1 1 1 1

0 1 1 1 1 1 1 1 1 0 1 0 1 0 75% 25% 75% 25%

0 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 25% 25%

1 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 25% 25%

1 0 0 0 0 0 0 1 1 1

0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 75% 75% 75% 75%

0 1 0 1 1 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 75% 75%

1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 25% 25%

0 0 1 1 1 0 0 1

0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 25% 75% 25% 75%

Type f 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 50% 25% 50% 25%

0 1 1 1 0 0 0 0 0 0 1 1

0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 50% 75% 50% 75%

1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 1 0 75% 75%

0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 50% 50%

1 1 1 1 1 1 0 1 1 0

0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 25% 50% 25% 50%

0 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 0 50% 50%

0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 75% 75%

1 1 1 1 1 1 1 1

0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 50% 25% 50% 25%

0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 25% 25%

0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 50% 50%

1 1 0 0 0 1 1 1 1 1

0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 75% 50% 75% 50%

Wilkinson, Wiley & Lin 2000 page 28

Appendix B

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