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A complex adaptive systems perspective of innovation diffusion: an integrated theory and validated virtual laboratory

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Abstract

In this paper we integrate the rich yet fragmented insights from the extensive literature on the diffusion of innovation into an elegant, coherent model. Using complex adaptive systems theory as the overarching framework, we integrate prior literature around three constructs: agents, interactions, and an environment. The integrated model is presented in both natural language and as an agent-based simulation model. A series of validation experiments instill confidence that our agent-based model (and similar others) can be used as a virtual research laboratory. We provide theoretical and methodological directions for future research.

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Notes

  1. We also repeated each simulation 30 times and found similar results.

References

  • Abrahamson E (1991) Managerial fads and fashions: the diffusion and rejection of innovations. Acad Manag Rev 16(3):586–612

    Google Scholar 

  • Abrahamson E (1996) Management fashion. Acad Manag Rev 21(1):254–285

    Google Scholar 

  • Abrahamson E, Rosenkopf L (1993) Institutional and competitive bandwagons: using mathematical modeling as a tool to explore innovation diffusion. Acad Manag Rev 18:487–517

    Google Scholar 

  • Abrahamson E, Rosenkopf L (1997) Social network effects on the extent of innovation diffusion: a computer simulation. Organ Sci, 289–309

  • Ahuja G (2000) Collaboration networks, structural holes, and innovation: a longitudinal study. Adm Sci Q 45(3):425–455

    Google Scholar 

  • Aiken M, Bacharach SB, French JL (1980) Organizational structure, work process, and proposal making in administrative bureaucracies. Acad Manag J 23(4):631–652

    Google Scholar 

  • Ajzen I (1991) The theory of planned behavior. Org Behav Hum Decis Process 50:179–211

    Google Scholar 

  • Anderson P (1999) Complexity theory and organization science. Organ Sci 10(3):216–232

    Google Scholar 

  • Angst CM, Agarwal R, Sambamurthy V, Kelley K (2010) Social contagion and information technology diffusion: the adoption of electronic medical records in US hospitals. Manag Sci 56(8):1219–1241

    Google Scholar 

  • Astley WG, Sachdeva PS (1984) Structural sources of intraorganizational power: a theoretical synthesis. Acad Manag Rev 9(1):104–113

    Google Scholar 

  • Attewell P (1992) Technology diffusion and organizational learning: the case of business computing. Organ Sci 3(1):1–19

    Google Scholar 

  • Bandura A (1997) Self-efficacy: the exercise of control. W.H. Freeman, New York

    Google Scholar 

  • Baum J, Calabrese T, Silverman B (2000) Don’t go it alone: alliance network composition and start-ups performance in Canadian biotechnology. Strateg Manag J 21(3):267–294

    Google Scholar 

  • Bell GG (2005) Clusters, networks, and firm innovativeness. Strateg Manag J 26(3):287–295

    Google Scholar 

  • Bercovitz J, Feldman MP (2008) Academic entrepreneurs: organizational change at the individual level. Organ Sci 19(1):69–89

    Google Scholar 

  • Bohlmann JD, Calantone RJ, Zhao M (2010) The effects of market network heterogeneity on innovation diffusion: an agent-based modeling approach. J Prod Innov Manag 27(5):741–760

    Google Scholar 

  • Bourdieu P (1986) The forms of capital. In: Richardson JG (ed) Hand-book of theory and research for the sociology of education. Greenwood, New York, pp 241–258

    Google Scholar 

  • Brass DJ, Galaskiewicz J, Greve HP, Tsai W (2004) Taking stock of networks and organizations: a multi-level perspective. Acad Manag J 47(6):795–817

    Google Scholar 

  • Brown SA, Venkatesh V (2005) Model of adoption of technology in households: a baseline model test and extension incorporating household life cycle. Manag Inf Syst Q 29(3):399–426

    Google Scholar 

  • Burt R (1977) Power in a social typology. Soc Sci Res 6:1–83

    Google Scholar 

  • Carley KM (1996) Validating computational models. Available at http://www.casos.cs.cmu.edu/publications/papers.php

  • Cavusoglu H, Hu N, Li Y, Ma D (2010) Information technology diffusion with influentials, imitators, and opponents. J Manag Inf Syst 27(2):305–334

    Google Scholar 

  • Chen M, Miller D (2012) Competitive dynamics: themes, trends, and a prospective research platform. Acad Manag Ann 6:1–89

    Google Scholar 

  • Choi H, Kim S, Lee J (2010) Role of network structure and network effects in diffusion of innovations. Ind Mark Manage 39(1):170–177

    Google Scholar 

  • Chua RYJ, Ingram P, Morris MW (2008) From the head and the heart: locating cognition- and affect-based trust in managers’ professional networks. Acad Manag J 51(3):436–452

    Google Scholar 

  • Cobb AT (1986) Political diagnosis: applications in organizational development. Acad Manag Rev 11(3):482–497

    Google Scholar 

  • Coleman JS (1988) Social capital in the creation of human capital. Am J Sociol 94:95–120

    Google Scholar 

  • Coleman JS (1990) Foundations of social theory. Harvard University Press, Cambridge

    Google Scholar 

  • Compeau DR, Higgins CA (1995) Application of social cognitive theory to training for computer skills. Inf Syst Res 6(2):118–142

    Google Scholar 

  • Czepiel J (1975) Patterns of interorganizational communications and the diffusion of a major technological innovation in a competitive industrial community. Acad Manag J 18(1):6–24

    Google Scholar 

  • Darr E, Argote L, Epple D (1995) The acquisition, transfer and depreciation of knowledge in service organizations: productivity in franchises. Manag Sci 41:1750–1762

    Google Scholar 

  • Davis FD, Bagozzi RP, Warshaw PR (1989) User acceptance of computer technology: a comparison of two theoretical models. Manag Sci 35(8):982–1003

    Google Scholar 

  • DeCanio SJ, Dibble C, Amir-Atefi K (2000) The importance of organizational structure for the adoption of innovations. Manag Sci 46(10):1285–1299

    Google Scholar 

  • Delmas MA, Toffel MW (2004) Institutional pressure and environmental management practices. Stakeholders, Environ Soc, 230–245

  • Delre SA, Jager W, Janssen MA (2007) Diffusion dynamics in small-world networks with heterogeneous consumers. Comput Math Organ Theory 13(2):185–202

    Google Scholar 

  • Delre SA, Jager W, Bijmolt THA, Janssen MA (2010) Will it spread or not? The effects of social influences and network topology on innovation diffusion. J Prod Innov Manag 27(2):267–282

    Google Scholar 

  • Dewar RD, Dutton JE (1986) The adoption of radical and incremental innovations: an empirical analysis. Manag Sci 32(11):1422–1433

    Google Scholar 

  • Dimaggio PJ, Powell MW (1983) The iron cage revisited: institutional isomorphism and collective rationality in organizational fields. Am Sociol Rev 48(2):147–160

    Google Scholar 

  • Dunne EJ, Stahl MJ, Melhart LJ (1978) Influence sources of project and functional managers in matrix organizations. Acad Manag J 21(1):135–140

    Google Scholar 

  • Epstein JM, Axtell R (1996) Growing artificial societies: social science from the bottom up. Brookings Institution Press, Washington

    Google Scholar 

  • Fichman RG (2004) Real options and it platform adoption: implications for theory and practice. Inf Syst Res 15:132–154

    Google Scholar 

  • Fidler LA, Johnson AD (1984) Communication and innovation implementation. Acad Manag Rev 9(4):704–711

    Google Scholar 

  • French JRP, Raven B (1959) The bases of social power. In: Cartwright D (ed) Studies in social power. University of Michigan Press, Ann Arbor

    Google Scholar 

  • Gaba V, Meyer A (2008) Crossing the organizational species barrier: how venture capital practices infiltrated the information technology sector. Acad Manag J 51(5):976–998

    Google Scholar 

  • Galaskiewicz J (1985) Social organization of an urban grants economy. Academic Press, New York

    Google Scholar 

  • Gallivan M, Spitler V, Koufaris M (2005) Does technology training really matter? A social information processing analysis of co-workersí influence on it usage in the workplace. J Manag Inf Syst 22(1):153–192

    Google Scholar 

  • Goes JB, Park SH (1997) Interorganizational links and innovation: the case of hospital services. Acad Manag J 40(3):673–696

    Google Scholar 

  • Greenwood R, Suddaby R, Hinings CR (2002) Theorizing change: the role of professional associations in the transformation of institutionalized fields. Acad Manag J 45(1):58–80

    Google Scholar 

  • Grimes AJ (1978) Authority, power, influence and social control: a theoretical synthesis. Acad Manag Rev 3:724–735

    Google Scholar 

  • Gunther M, Stummer C, Wakolbinger LM, Wildpaner M (2011) An agent-based simulation approach for the new product diffusion of a novel biomass fuel. J Oper Res Soc 62(1):12–20

    Google Scholar 

  • Haveman HA (1993) Follow the leader—mimetic isomorphism and entry into new markets. Adm Sci Q 38(4):593–627

    Google Scholar 

  • Hoffman AJ (1999) Institutional evolution and change: environmentalism and the US chemical industry. Acad Manag J 42(4):351–371

    Google Scholar 

  • Holland JH (1995) Hidden order: how adaptation builds complexity. Perseus Books, Reading

    Google Scholar 

  • Hong S-J, Tam KY (2006) Understanding the adoption of multipurpose information appliances: the case of mobile data services. Inf Syst Res 17:162–179

    Google Scholar 

  • Iacovou CL, Benbasat I, Dexter AS (1995) Electronic data interchange and small organisations: adoption and impact of technology. Manag Inf Syst Q 19(4):465–485

    Google Scholar 

  • Ibarra H (1993) Network centrality, power, and innovation involvement: determinants of technical and administrative roles. Acad Manag J 36(3):471–501

    Google Scholar 

  • Jasperson JS, Carter PE, Zmud RW (2005) A comprehensive conceptualization of post-adoptive behaviors associated with information technology enabled work systems. Manag Inf Syst Q 29(3):525–557

    Google Scholar 

  • Kane GC, Alavi M (2007) Information technology and organizational learning: an investigation of exploration and exploitation processes. Organ Sci 18(5):796–812

    Google Scholar 

  • Kauffman RJ, McAndrews J, Wang Y-M (2000) Opening the “black box” of network adoption. Inf Syst Res 11(1):61–82

    Google Scholar 

  • Kiesling E, Günther M, Stummer C, Wakolbinger LM (2012) Agent-based simulation of innovation diffusion: a review. Cent Eur J Oper Res 20(2):183–230

    Google Scholar 

  • Ko D, Kirsch LJ, King WR (2005) Antecedents of knowledge transfer from consultants to clients in enterprise system implementations. Manag Inf Syst Q 29(1):59–85

    Google Scholar 

  • Kraatz MS (1998) Learning by association: interorganizational networks and adaptation to environmental change. Acad Manag J 41(6):621–643

    Google Scholar 

  • Krackhardt D (1990) Assessing the political landscape: structure, cognition, and power in organizations. Adm Sci Q 35(2):342–369

    Google Scholar 

  • Laursen K, Salter A (2006) Open for innovation: the role of openness in explaining innovation performance among U.K. manufacturing firms. Strateg Manag J 27(2):131–150

    Google Scholar 

  • Leiponen A, Helfat C (2010) Innovation objectives, knowledge sources, and the benefits of breadth. Strateg Manag J 31(2):224–236

    Google Scholar 

  • Lazer D, Friedman A (2007) The network structure of exploration and exploitation. Adm Sci Q 52(4):667–694

    Google Scholar 

  • Macdonald S (1998) Information for innovation: managing change from an information perspective. Oxford University Press, New York

    Google Scholar 

  • Maienhofer D, Finholt T (2002) Finding optimal targets for change agents: a computer simulation of innovation diffusion. Comput Math Organ Theory 8(4):259–280

    Google Scholar 

  • Marcus AA (1988) Responses to externally induced innovation: their effects on organizational performance. Strateg Manag J 9:387–402

    Google Scholar 

  • Markus M (1987) Toward a “critical mass” theory of interactive media: universal access, interdependence, and diffusion. Commun Res 14:491–511

    Google Scholar 

  • Middleton B (2005) Achieving U.S. health information technology adoption: the need for a third hand. Health Aff 24(5):1269–1272

    Google Scholar 

  • Midgley D, Dowling GR (1978) Innovativeness: the concept and its measurement. J Consum Res 4:229–242

    Google Scholar 

  • Miller JH, Page SE (2007) Complex adaptive systems: an introduction to computational models of social life. Princeton University Press, Princeton

    Google Scholar 

  • Mishra AN, Agarwal R (2010) Technological frames, organizational capabilities, and IT use: an empirical investigation of electronic procurement. Inf Syst Res 21(2):249–270

    Google Scholar 

  • Moore GC, Benbasat I (1991) Development of an instrument to measure the perceptions of adopting an information technology innovation. Inf Syst Res 2(3):173–191

    Google Scholar 

  • Nagarajan A, Mitchell W (1998) Evolutionary diffusion: internal and external methods used to acquire encompassing, complementary, and incremental technological changes in the lithotripsy industry. Strateg Manag J 19(11):1063–1077

    Google Scholar 

  • Nan N (2011) Capturing bottom-up IT use processes: a complex adaptive systems model. Manag Inf Syst Q 35(2):505–532

    Google Scholar 

  • Naylor TH, Finger JM (1967) Verification of computer simulation models. Manag Sci 14(2):B92–B101

    Google Scholar 

  • Nidumolu SR, Goodman SE, Vogel DR, Danowitz AK (1996) Information technology for local administration support: the governorates project in Egypt. Manag Inf Syst Q 20(2):197–224

    Google Scholar 

  • Oliver C (1990) Determinants of interorganizational relationships: integration and future directions. Acad Manag Rev 15(2):241–265

    Google Scholar 

  • Parthasarathy M, Bhattacherjee A (1998) Understanding post-adoption behaviour in the context of online services. Inf Syst Res 9(4):362–379

    Google Scholar 

  • Paul DL, McDaniel RR Jr (2004) A field study of the effect of interpersonal trust on virtual collaborative relationship performance. Manag Inf Syst Q 28(2):183–227

    Google Scholar 

  • Pawlowski SD, Robey D (2004) Bridging user organizations: knowledge brokering and the work of information technology professionals. Manag Inf Syst Q 28(4):645–672

    Google Scholar 

  • Perry-Smith JE (2006) Social yet creative: the role of social relationships in facilitating individual creativity. Acad Manag J 49(1):85–101

    Google Scholar 

  • Phelps CP (2010) A longitudinal study of the influence of alliance network structure and composition on firm exploratory innovation. Acad Manag J 53(4):89–913

    Google Scholar 

  • Plouffe CR, Hulland JS, Vandenbosch M (2001) Research report: richness versus parsimony in modeling technology adoption decisions—understanding merchant adoption of a smart card-based payment system. Inf Syst Res 12(2):208–222

    Google Scholar 

  • Rai A, Patnayakuni R (1996) A structural model for case adoption behavior. J Manag Inf Syst 13(2):205–234

    Google Scholar 

  • Rice RE, Aydin C (1991) Attitudes toward new organizational technology: network proximity as a mechanism for social information processing. Adm Sci Q 36(2):219–244

    Google Scholar 

  • Robey D, Boudreau M-L, Rose GM (2000) Information technology and organizational learning: a review and assessment of research. Account Manag Inf Technol 10(2):125–155

    Google Scholar 

  • Rodan S, Galunic C (2004) More than network structure: how knowledge heterogeneity influences managerial performance and innovativeness. Strateg Manag J 25(6):541–562

    Google Scholar 

  • Rogers EM (2003) Diffusion of innovations, 5th edn. Free Press, New York

    Google Scholar 

  • Rosenkopf L, Abrahamson E (1999) Modeling reputational and informational influences in threshold models of bandwagon innovation diffusion. Comput Math Organ Theory 5(4):361–384

    Google Scholar 

  • Ryan B, Gross NC (1943) The diffusion of hybrid seed corn in two Iowa communities. Rural Sociol 8:15–24

    Google Scholar 

  • Sanders W, Tuschke A (2007) The adoption of institutionally contested organizational practices: the emergence of stock option pay in Germany. Acad Manag J 50(1):33–56

    Google Scholar 

  • Schilling MA (2002) Technology success and failure in winner-take-all markets: the impact of learning orientation, timing, and network externalities. Acad Manag J 45(2):387–398

    Google Scholar 

  • Scott WR (2008) Institutions and organizations: ideas and interests. Sage Publications, Thousand Oaks

    Google Scholar 

  • Singh J (2005) Collaborative networks as determinants of knowledge diffusion patterns. Manag Sci 51(5):756–770

    Google Scholar 

  • Spekman R (1979) Influence and information: an exploratory investigation of the boundary role person’s bases of power. Acad Manag J 22:104–117

    Google Scholar 

  • Still MC, Strang D (2009) Who does an elite organization emulate? Adm Sci Q 54(1):58–89

    Google Scholar 

  • Teo HH, Wei KK, Benbasat I (2003) Predicting intention to adopt interorganizational linkages: an institutional perspective. Manag Inf Syst Q 27(1):19–49

    Google Scholar 

  • Thong JYL, Yap CS, Raman K (1994) Engagement of external expertise in information systems implementation. J Manag Inf Syst 11(2):209–231

    Google Scholar 

  • Tornatzky LG, Klein KJ (1982) Innovation characteristics and innovation adoption-implementation: a meta-analysis of findings. IEEE Trans Eng Manag 29(1):28–45

    Google Scholar 

  • Turnbull PW, Meenaghan A (1980) Diffusion of innovation and opinion leadership. Eur J Mark 14:3–33

    Google Scholar 

  • Tushman ML (1977) Special boundary roles in the innovation process. Adm Sci Q 22(4):587–605

    Google Scholar 

  • Van Eck PS, Jager W, Leeflang PSH (2011) Opinion leaders’ role in innovation diffusion: a simulation study. J Prod Innov Manag 28:187–203

    Google Scholar 

  • Van Horn R (1971) Validation of simulation results. Manag Sci 17(5):247–258

    Google Scholar 

  • Venkatesh V, Morris MG, Davis GB, Davis FD (2003) User acceptance of information technology: toward a unified view. Manag Inf Syst Q 27(3):425–478

    Google Scholar 

  • Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, Cambridge and New York

    Google Scholar 

  • Weigelt C, Sarkar MB (2009) Learning from supply-side agents: the impact of technology solution providers’ experiential diversity on clients’ innovation adoption. Acad Manag J 52(1):37–60

    Google Scholar 

  • Weitzel T, Beimborn D, König W (2006) A unified economic model of standard diffusion: the impact of standardization, cost, network effects, and network topology. Manag Inf Syst Q 30(1):489–514

    Google Scholar 

  • Westphal JD, Gulati R, Shortell SM (1997) Customization or conformity? An institutional and network perspective on the content and consequences of TQM adoption. Adm Sci Q 42(2):366–394

    Google Scholar 

  • Wilensky U (1999) “NetLogo,” center for connected learning and computer-based modeling. Northwestern University, Evanston. Available at http://ccl.northwestern.edu/netlogo

    Google Scholar 

  • Zhang T, Nuttall WJ (2011) Evaluating government’s policies on promoting smart metering diffusion in retail electricity markets via agent-based simulation. J Prod Innov Manag 28(2):169–186

    Google Scholar 

  • Zhang T, Gensler S, Garcia R (2011) A study of the diffusion of alternative fuel vehicles: an agent-based modeling approach. J Prod Innov Manag 28(2):152–168

    Google Scholar 

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Authors and Affiliations

  1. Management Information Systems, Sauder School of Business, The University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Ning Nan

  2. Management Information Systems, Price College of Business, University of Oklahoma, 307 West Brooks, Norman, OK, 73019, USA

    Robert Zmud & Emre Yetgin

Authors
  1. Ning Nan
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  2. Robert Zmud
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Correspondence to Ning Nan.

Appendices

Appendix A: Behavioral rules

1.1 A.1 Behavioral rules affecting both the adopter role and influencer role

  • Awareness stock update rule:

    Incremental awareness = (neighbor awareness − awareness ∗ neighbor tie strength) ∗ (1 − innovation arduousness) ∗ adoption history multiplier

    Awareness = awareness ∗ awareness forgetting factor + incremental awareness ∗ other-learning rate

    An agent’s awareness stock level is increased if this agent’s contacts hold higher awareness stock levels. Contacts’ awareness stock levels are adjusted by the tie strength of their relationships with the agent. The amount of awareness stock level increase for the agent is adjusted by innovation arduousness, and the agent’s adoption history, learning-through-others rate, and awareness forgetting rate.

  • Capability stock update rule:

    Incremental capability = random number ∗ the capability difference between the agent and the signaling neighbors that have higher capabilities

    Capability = capability ∗ adoption-history-multiplier + incremental capability ∗ other-learning rate

    An agent’s capability stock level is increased if this agent’s contacts hold higher capability stock levels. Contacts’ capability stock levels are adjusted by the tie strength of their relationships with the agent. The amount of capability stock level increase for the agent is adjusted by the agent’s learning-through-others rate, self-learning rate, and capability forgetting rate.

  • Motivation stock update rule:

    Incremental motivation = incremental value gained from adoption + (neighbor motivation − motivation ∗ neighbor tie strength)

    Motivation = motivation ∗ motivation forgetting factor + incremental motivation ∗ other-learning rate

    An agent’s motivation stock level is increased when the agent gains value from the innovation (if the agent is already an adopter), or if this agent’s contacts hold higher motivation stock levels. Contacts’ motivation values are adjusted by the tie strength of their relationships with the agent. The amount of motivation stock level increase for the agent is adjusted by the agent’s learning-through-others rate and motivation forgetting rate.

1.2 A.2 Adopter role behavioral rules

  • Adoption rule (for agents who currently have not adopted an innovation):

    Adoption is set to one IF awareness ≥ awareness threshold AND capability ≥ capability threshold AND motivation ≥ motivation threshold.

    Incremental value gained from adoption = random number ∗ adoption history multiplier ∗ (1 + proportion of adopters among contacts ∗ externality multiplier)

    Value gained from adoption = value gained from adoption + incremental value gained from adoption

    When an agent’s awareness, capability, and motivation stock levels are simultaneously above their respective thresholds, the agent adopts the innovation. This agent’s value gained from adoption is incremented. The amount of value gain increment is determined by the value gained by prior adopters, the agent’s capability, the innovation’s arduousness, and, if network externality effects are present, the proportion of the agent’s contacts who have adopted the innovation.

  • Disadoption rule (for agents who have currently adopted an innovation):

    Adoption is set to zero IF capability < capability threshold OR motivation < motivation threshold.

    Incremental value gained from adoption = 0

    If an agent’s awareness stock level is above the awareness threshold but the agent’s capability or motivation stock levels drop below their respective thresholds, the agent disadopts the innovation, and no longer accrues value from the innovation.

1.3 A.3 Influencer role behavioral rules

  • Signaling rule:

    Value gained from signaling = motivation ∗ adoption history multiplier ∗ (1 + proportion of adopters among contacts ∗ externality multiplier) IF awareness ≥ awareness threshold

    Agent signals IF value gained from signaling ≥ signaling threshold

    When an agent’s awareness of the innovation is above the awareness threshold, this agent’s value gained from signaling is determined by the agent’s motivation stock level, whether the agent has adopted the innovation and the time since such adoption, and, if network effects are present, the proportion of the agent’s contacts who have adopted the innovation. If this agent’s value gained from signaling is above the signaling threshold, this agent will transmit a signal to all of the agent’s contacts.

  • Signal amplifying rule:

    Specialist is set to one IF capability > the average capability of the agents within the same innovativeness category + 1.2 standard deviations

    Incremental stock = incremental stock ∗ exemplar multiplier IF influencer is an exemplar

    If an influencer’s capability stock level is sufficiently large (relatively to all other agents within the same innovativeness category), the influencer becomes a specialist and the influencer’s signals are amplified. If an influencer is randomly identified as an exemplar, the influencer’s signals are amplified. If an influencer holds a high dominance value, the agent is more likely to serve as a central node within the population, and to possess relatively higher tie strengths with contacts—both of which serve to amplify the agent’s signal strength.

Appendix B: Network structure

  • Setting up focal links:

    Number of focal links = number of focal agents ∗ (number of focal agents − 1)/ 2 ∗ focal network density

    The number of focal links is calculated as a function of the focal network density. For example, if the focal population is 50 and network density is 0.5, the number of focal links is set at 612 by using the formula specified above. To create a link, an agent is randomly selected to be the first node. This first node then selectively builds a link with a second node by biasing toward more dominant agents. The link creation procedure is repeated 612 times in order to build the necessary number of links in the focal population. The existence of links between focal agents therefore accounts for focal network centrality with more dominant agents serving as central nodes, as well as network density specified by the model user.

  • Setting up external links:

    Number of other links = number of other agents ∗ (number of other agents − 1)/ 2 ∗ other network density

    The number of external (other) links is calculated according to the external network density. Then, this existence of links between external agents is specified the same way as that of focal agents.

  • Setting up inter-population links:

    Number of inter-links = proportion of inter-links ∗ minimum (number of focal agents, number of other agents)

    The number of inter-population links is calculated according to the proportion of inter-links that exist between the focal and external populations. Then, the existence of inter-population links is specified, accounting for the innovativeness of the focal agents with more innovative focal agents being more likely to have links with external agents. The innovativeness of focal agents is defined based on Rogers’ (2003) five adopter categories: innovators, early adopters, early majority, late majority, and laggards. We randomly assigned a focal agent into an adopter category so that the distribution of these five adopter categories follows the distribution found by Rogers (2003). The more innovative a focal agent is, the more likely it would build a tie with an agent in the external population.

  • Calculating the tie strength:

    The strength of a tie between two agents is calculated according to their spatial proximity; the closer two agents are, the stronger tie they have. Then, the tie strength is adjusted depending on the distribution of the spatial distances between the agent pairs with the same innovativeness category.

Appendix C: Model variables

3.1 C.1 Global variables

L::

The number of clock ticks (i.e., iterations) in a simulation.

N::

The adoption duration of an agent, in terms of the number of clock ticks. 0 means that the agent has never adopted the innovation.

Number of focal links::

The number of links in the focal population.

Number of inter-links::

The number of links between the focal and external populations.

Number of other links::

The number of links in the external population.

3.2 C.2 Exogenous variables

Awareness forgetting factor::

A multiplier that refers to the rate at which agents’ awareness decreases with each iteration, increasing continuously from 0 to 1. 1 means that an agent’s awareness does not decrease at all. 0 means that an agent’s awareness is completely diminished.

Capability forgetting factor::

A multiplier that refers to the rate at which agents’ capability decreases with each iteration, increasing continuously from 0 to 1. 1 means that an agent’s capability does not decrease at all. 0 means that an agent’s capability is completely diminished.

Exemplar multiplier::

A multiplier that is used to amplify the influence of exemplars on agents that favor exemplars, increasing continuously from 1 to 2. 1 means that exemplars’ influence is not amplified at all, whereas 2 means that exemplars’ influence is doubled.

Externality multiplier::

A multiplier that is used to amplify the value gained from adoption due to network externalities, increasing continuously from 1 without an upper bound. 1 means that the innovation does not have any network externality effects.

Focal network centrality::

The centrality of the focal network, increasing continuously from 0 to 1.

Focal network density::

The density of the focal network, increasing continuously from 0 to 1.

Initial other adopters::

The proportion of initial adopters in the external population, increasing continuously from 0 to 1. 0 means that there are no initial adopters in the external population. 1 means that every agent in the external population is initially an adopter.

Innovation arduousness::

The arduousness of the innovation, increasing continuously from 0 to 1.

Motivation forgetting factor::

A multiplier that refers to the rate at which agents’ motivation decreases with each iteration, increasing continuously from 0 to 1. 1 means that an agent’s motivation does not decrease at all. 0 means that an agent’s motivation is completely diminished.

Number of clusters::

The total number of clusters in the focal and external populations.

Number of focal agents::

The number of agents in the focal population.

Number of other agents::

The number of agents in the external population.

Other network centrality::

The centrality of the external network, increasing continuously from 0 to 1.

Other network density::

The density of the external network, increasing continuously from 0 to 1.

Proportion of inter-links::

The proportion of the inter-population links, increasing continuously from 0 to 1. 0 means that there are no inter-population links. 1 means every agent in the focal or external population, depending on whichever is fewer, has an inter-population link.

3.3 C.3 Endogenous variables

Adoption history multiplier::

A multiplier that is used to dampen the impacts of the innovation, depending on how long an agent has been an adopter. It is calculated as (N+1)/N (see Appendix C.1).

Adoption::

The binary adoption state of an agent. 0 means that the agent is a non-adopter during the current tick of the clock, whereas 1 means that the agent is an adopter during the current clock tick.

Attentiveness::

The tendency of an agent to pay attention to its contacts’ signals. It ranges continuously from 0.1 to 0.8, depending on an agent’s innovativeness category. Agents that are more innovative have higher attentiveness values.

Awareness threshold::

The minimum awareness value of an agent for it to consider adopting the innovation. Once an agent’s awareness stock exceeds the awareness threshold, awareness of the innovation is maintained throughout the remainder of a simulation run.

Awareness::

The awareness stock of an agent, increasing continuously from 0 to 150. 0 means the state of unaware. 150 is an upper bound we found through sensitivity analyses; awareness values greater than 150 did not produce noticeable impact on the diffusion processes and outcomes. We therefore use 150 to represent the state of being fully aware.

Capability threshold::

The minimum capability value of an agent for it to adopt or keep the innovation.

Capability::

The capability stock of an agent, increasing continuously from 0 to 200. 0 means the state of no capability. 200 is an upper bound we found through sensitivity analyses; capability values greater than 200 did not produce noticeable impact on the diffusion processes and outcomes. We therefore use 200 to represent the state of being fully capable.

Dominance::

The relative dominance of an agent. It is calculated randomly from a gamma distribution with alpha and lambda values of 1.

Exemplar::

An agent’s binary state of being an exemplar. 0 means that an agent is not an exemplar, whereas 1 means that the agent is an exemplar.

Favor exemplar::

The extent to which an agent favors exemplars. It is calculated randomly from a normal distribution with a standard deviation of 1, in which the mean is shifted depending on an agent’s innovativeness category. The more innovative an agent is, the less likely it favors exemplars.

Gain::

A multiplier that is used to adjust the impacts of the innovation. It is calculated randomly from a normal distribution, in which the mean is shifted depending on the innovation’s arduousness.

Incremental awareness::

The incremental change in an agent’s awareness stock over each iteration.

Incremental capability::

The incremental change in an agent’s capability stock over each iteration.

Incremental motivation::

The incremental change in an agent’s motivation stock over each iteration.

Incremental value gained from adoption::

The value an agent gains from the innovation over each iteration (see Appendix A.2 for its calculation).

Innovativeness::

The innovativeness category (Rogers 2003) of an agent. It is an integer between 1 and 5, where 1 is the most innovative category (i.e., innovator) and 5 is the least innovative category (i.e., laggard).

Motivation threshold::

The minimum awareness value of an agent for it to adopt or keep the innovation.

Motivation::

The motivation stock of an agent, increasing continuously from 0 to 300. 0 means the state of no motivation. 300 is an upper bound we found through sensitivity analyses; motivation values greater than 300 did not produce noticeable impact on the diffusion processes and outcomes. We therefore use 300 to represent the state of being fully motivated.

Neighbor awareness::

The average awareness stock of an agent’s contacts that are signaling about the innovation.

Neighbor motivation::

The average motivation stock of an agent’s contacts that are signaling about the innovation.

Neighbor tie strength::

The average strength of an agent’s relationships with its contacts that are signaling about the innovation.

Other-learning rate::

A multiplier that is used to adjust the awareness, capability, and motivation that an agent gains from its contacts. It increases continuously from 0.05 to 0.8, depending on an agent’s innovativeness category. Agents that are more innovative have higher other-learning rates.

Proportion of adopters among contacts::

The proportion of adopters among an agent’s contacts. 0 means that none of an agent’s contacts is an adopter, while 1 means that all contacts of an agent are adopters.

Self-learning rate::

A multiplier that is used to adjust the capability that an agent gains from its own experience with the innovation. It increases continuously from 1.0 to 1.3, depending on an agent’s innovativeness category. Agents that are more innovative have higher self-learning rates.

Signaling threshold::

The minimum value an agent needs to gain from signaling, in order for the agent to start or keep signaling about the innovation.

Specialist::

An agent’s binary state of being a specialist. 0 means that an agent is not a specialist, whereas 1 means that the agent is a specialist.

Tie strength multiplier::

The strength of the relationship between two agents (see Appendix B for its calculation).

Value gained from adoption::

The cumulative value an agent gains from the innovation (see incremental value gained from adoption).

Value gained from signaling::

The value an agent gains from signaling about the innovation (see Appendix A.3 for its calculation).

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Nan, N., Zmud, R. & Yetgin, E. A complex adaptive systems perspective of innovation diffusion: an integrated theory and validated virtual laboratory. Comput Math Organ Theory 20, 52–88 (2014). https://doi.org/10.1007/s10588-013-9159-9

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