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The Law of Proportionate Growth and Its Siblings: Applications in Agent-Based Modeling of Socio-Economic Systems

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Complexity, Heterogeneity, and the Methods of Statistical Physics in Economics

Part of the book series: Evolutionary Economics and Social Complexity Science ((EESCS,volume 22))

Abstract

The law of proportionate growth simply states that the time-dependent change of a quantity x is proportional to x. Its applicability to a wide range of dynamic phenomena is based on various assumptions for the proportionality factor, which can be random or deterministic, constant or time dependent. Further, the dynamics can be combined with additional additive growth terms, which can be constants, aggregated quantities, or interaction terms. This allows to extent the core dynamics into an agent-based modeling framework with vast applications in social and economic systems. The chapter adopts this overarching perspective to discuss phenomena as diverse as saturated growth, competition, stochastic growth, investments in random environments, wealth redistribution, opinion dynamics and the wisdom of crowds, reputation dynamics, knowledge growth, and the combination with network dynamics.

In memory of Masanao Aoki

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References

  • Aoki M (1973) On decentralized linear stochastic control problems with quadratic cost. IEEE Trans Autom Control 18(3):243–250

    Google Scholar 

  • Aoki M (2002) Modeling aggregate behavior and fluctuations in economics: stochastic views of interacting agents. Cambridge University Press, Cambridge

    Google Scholar 

  • Aoki M, Yoshikawa H (2011) Reconstructing macroeconomics: a perspective from statistical physics and combinatorial stochastic processes. Cambridge University Press, Cambridge

    Google Scholar 

  • Aoyama H, Fujiwara Y, Ikeda Y, Iyetomi H, Souma W, Yoshikawa H (2017) Macro-econophysics: new studies on economic networks and synchronization. Cambridge University Press, Cambridge

    Google Scholar 

  • Battiston S, Puliga M, Kaushik R, Tasca P, Caldarelli G (2012) DebtRank: too central to fail? Financial networks, the FED and systemic risk. Sci Rep 2:541

    Google Scholar 

  • Bechinger C, Di Leonardo R, Löwen H, Reichhardt C, Volpe G, Volpe G (2016) Active particles in complex and crowded environments. Rev Mod Phys 88(4):045006

    Google Scholar 

  • Bonabeau E, Theraulaz G, Deneubourg JL (1999) Dominance orders in animal societies: the self-organization hypothesis revisited. Bull Math Biol 61(4):727–757

    Google Scholar 

  • Bonacich P (1987) Power and centrality: a family of measures. Am J Sociol 92(5):1170–1182

    Google Scholar 

  • Casiraghi G, Schweitzer F (2020) Improving the robustness of online social networks: a simulation approach of network interventions. Front Robot AI 7:57

    Google Scholar 

  • Deffuant G, Neau D, Amblard F, Weisbuch G (2000) Mixing beliefs among interacting agents. ACS Adv Complex Syst 3:87–98

    Google Scholar 

  • Ebeling W, Schweitzer F (2003) Self-organization, active brownian dynamics, and biological applications. Nova Acta Leopold 88:169–188

    Google Scholar 

  • Ebeling W, Schweitzer F, Tilch B (1999) Active Brownian particles with energy depots modeling animal mobility. Biosystems 49(1):17–29

    Google Scholar 

  • Feistel R, Ebeling W (2011) Physics of self-organization and evolution. Wiley, New York

    Google Scholar 

  • Garcia V, Birbaumer M, Schweitzer F (2011) Testing an agent-based model of bacterial cell motility: how nutrient concentration affects speed distribution. Eur Phys J B 82(3–4):235–244

    Google Scholar 

  • Garcia D, Garas A, Schweitzer F (2014) Modeling collective emotions in online social systems. In: von Scheve C, Salmela M (eds) Collective emotions. Oxford University Press, Oxford, pp 389–406

    Google Scholar 

  • Garcia D, Kappas A, Kuster D, Schweitzer F (2016) The dynamics of emotions in online interaction. R Soc Open Sci 3:160059

    Google Scholar 

  • Garcia D, Mavrodiev P, Casati D, Schweitzer F (2017) Understanding popularity, reputation, and social influence in the Twitter society. Policy Internet 9(3):343–364

    Google Scholar 

  • Garas A, Garcia D, Skowron M, Schweitzer F (2012) Emotional persistence in online chatting communities. Sci Rep 2:402

    Google Scholar 

  • Grochulski B, Piskorski T (2010) Risky human capital and deferred capital income taxation. J Econ Theory 145(3):908–943

    Google Scholar 

  • Groeber P, Schweitzer F, Press K (2009) How groups can foster consensus: the case of local cultures. J Aritif Soc Soc Simul 12(2):1–22

    Google Scholar 

  • Hegselmann R, Krause U et al (2002) Opinion dynamics and bounded confidence models, analysis, and simulation. J Artif Soc Soc Simul 5(3):2

    Google Scholar 

  • Helbing D, Schweitzer F, Keltsch J, Molnár P (1997) Active Walker model for the formation of human and animal trail systems. Phys Rev E 56(3):2527–2539

    Google Scholar 

  • Koenig MD, Battiston S, Napoletano M, Schweitzer F (2008) On algebraic graph theory and the dynamics of innovation networks. Netw Heterog Media 3(2):201–219

    Google Scholar 

  • Koenig MD, Battiston S, Schweitzer F (2009) Modeling evolving innovation networks. In: Pyka A, Scharnhorst A (eds) Innovation networks: new approaches in modelling and analyzing. Springer, Berlin, pp 187–267

    Google Scholar 

  • Koenig MD, Battiston S, Napoletano M, Schweitzer F (2011) Recombinant knowledge and the evolution of innovation networks. J Econ Behav Organ 79(3):145–164

    Google Scholar 

  • Koenig MD, Battiston S, Napoletano M, Schweitzer F (2012) The efficiency and stability of R&D networks. Games Econ Behav 75(2):694–713

    Google Scholar 

  • Lorenz J (2007) Continuous opinion dynamics under bounded confidence: a survey. Int J Mod Phys C 18(12):1819–1838

    Google Scholar 

  • Lorenz J, Rauhut H, Schweitzer F, Helbing D (2011) How social influence can undermine the wisdom of crowd effect. Proc Natl Acad Sci (PNAS) 108(22):9020–9025

    Google Scholar 

  • Lorenz J, Paetzel F, Schweitzer F (2013) Redistribution spurs growth by using a portfolio effect on risky human capital. PLoS One 8(2):e54904

    Google Scholar 

  • Malevergne Y, Pisarenko V, Sornette D (2011) Testing the Pareto against the lognormal distributions with the uniformly most powerful unbiased test applied to the distribution of cities. Phys Rev E 83(3):036111

    Google Scholar 

  • Marsili M, Maslov S, Zhang Y-C (1998) Dynamical optimization theory of a diversified portfolio. Phys A 253(1–4):403–418

    Google Scholar 

  • Mavrodiev P, Tessone CJ, Schweitzer F (2012) Effects of social influence on the wisdom of crowds. In: Proceedings of the conference on collective intelligence CI-2012. https://arxiv.org/html/1204.2991

  • Mavrodiev P, Tessone CJ, Schweitzer F (2013) Quantifying the effects of social influence. Sci Rep 3:1360

    Google Scholar 

  • Nanumyan V, Garas A, Schweitzer F (2015) The network of counterparty risk: analysing correlations in OTC derivatives. PLoS One 10:e0136638

    Google Scholar 

  • Navarro E, Cantero R, Rodrigues JAF, Schweitzer F (2008a) Investments in random environments. Phys A 387(8–9):2035–2046

    Google Scholar 

  • Navarro JE, Walter FE, Schweitzer F (2008b) Risk-seeking versus risk-avoiding investments in noisy periodic environments. Int J Mod Phys C 19(6):971–994

    Google Scholar 

  • Perony N, Pfitzner R, Scholtes I, Schweitzer F, Tessone CJ (2012) Hierarchical consensus formation reduces the influence of opinion bias. In: Proceedings of the 26th European conference on modelling and simulation – ECMS 2012, pp 662–668

    Google Scholar 

  • Perony N, Pfitzner R, Scholtes I, Tessone CJ, Schweitzer F (2013) Enhancing consensus under opinion bias by means of hierarchical decision making. ACS Adv Complex Syst 16:1350020

    Google Scholar 

  • Rauhut H, Lorenz J, Schweitzer F, Helbing D (2011) Reply to Farrell: improved individual estimation success can imply collective tunnel vision. Proc Natl Acad Sci 108(36):E626

    Google Scholar 

  • Richmond P (2001) Power law distributions and dynamic behaviour of stock markets. Eur Phys J B 20(4):523–526

    Google Scholar 

  • Sarigol E, Pfitzner R, Scholtes I, Garas A, Schweitzer F (2014) Predicting scientific success based on coauthorship networks. EPJ Data Sci 3:9

    Google Scholar 

  • Schweitzer F (1998) Modelling migration and economic agglomeration with active Brownian particles. ACS Adv Complex Syst 1(1):11–37

    Google Scholar 

  • Schweitzer F (2003) Brownian agents and active particles: collective dynamics in the natural and social sciences. Springer, Berlin

    Google Scholar 

  • Schweitzer F (2018a) An agent-based framework of active matter with applications in biological and social systems. Eur J Phys 40(1):014003

    Google Scholar 

  • Schweitzer F (2018b) Sociophysics. Phys Today 71(2):40–46

    Google Scholar 

  • Schweitzer F, Behera L (2009) Nonlinear voter models: the transition from invasion to coexistence. Eur Phys J B 67(3):301–318

    Google Scholar 

  • Schweitzer F, Garcia D (2010) An agent-based model of collective emotions in online communities. Eur Phys J B 77(4):533–545

    Google Scholar 

  • Schweitzer F, Mach R (2008) The epidemics of donations: logistic growth and power-laws. PloS One 3(1):e1458

    Google Scholar 

  • Schweitzer F, Schimansky-Geier L (1994) Clustering of active Walkers in a two-component system. Phys A 206(3–4):359–379

    Google Scholar 

  • Schweitzer F, Tilch B (2002) Self-assembling of networks in an agent-based model. Phys Rev E 66(2):1–10

    Google Scholar 

  • Schweitzer F, Lao K, Family F (1997) Active random walkers simulate trunk trail formation by ants. Biosystems 41(3):153–166

    Google Scholar 

  • Schweitzer F, Mavrodiev P, Tessone CJ (2013) How can social herding enhance cooperation? ACS Adv Complex Syst 16:1350017

    Google Scholar 

  • Schweitzer F, Nanumyan V, Tessone CJ, Xia X (2014) How do OSS projects change in number and size? A large-scale analysis to test a model of project growth. ACS Adv Complex Syst 17:1550008

    Google Scholar 

  • Schweitzer F, Mavrodiev P, Seufert AM, Garcia D (2020, submitted) Modeling user reputation in online social networks: the role of costs, benefits, and reciprocity. Comput Math Organ Theory

    Google Scholar 

  • Schweitzer F, Casiraghi G, Perony N (2020, submitted) Modeling the emergence of hierarchies from dominance interactions. Bull Math Biol

    Google Scholar 

  • Seufert AM, Schweitzer F (2007) Aggregate dynamics in an evolutionary network model. Int J Mod Phys C 18(10):1659–1674

    Google Scholar 

  • Slanina F (1999) On the possibility of optimal investment. Phys A Stat Mech Appl 269(2–4):554–56

    Google Scholar 

  • Slanina F (2004) Inelastically scattering particles and wealth distribution in an open economy. Phys Rev E 69(4):046102

    Google Scholar 

  • Sutton J (1997) Gibrat’s legacy. J Econ Lit 35(1):40–59

    Google Scholar 

  • Tadic B, Suvakov M, Garcia D, Schweitzer F (2017) Agent-based simulations of emotional dialogs in the online social network MySpace. In: Holyst JA (ed) Cyberemotions: collective emotions in cyberspace. Springer, Cham, pp 207–229

    Google Scholar 

  • Tomasello MV, Napoletano M, Garas A, Schweitzer F (2016) The rise and fall of R&D networks. ICC Ind Corp Chang 26(4):617–646

    Google Scholar 

  • Yaari G, Solomon S (2010) Cooperation evolution in random multiplicative environments. Eur Phys J B 73(4):625–632

    Google Scholar 

  • Yakovenko VM, Rosser JB Jr (2009) Colloquium: statistical mechanics of money, wealth, and income. Rev Mod Phys 81(4):1703

    Google Scholar 

  • Zhang Y, Schweitzer F (2019) The interdependence of corporate reputation and ownership: a network approach to quantify reputation. R Soc Open Sci 6:190570

    Google Scholar 

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Acknowledgements

The author thanks Nicola Perony for providing Figs. 8.2, 8.3, 8.7, and 8.9.

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Authors and Affiliations

  1. Chair of Systems Design, ETH Zurich, Zurich, Switzerland

    Frank Schweitzer

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  1. Frank Schweitzer
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Correspondence to Frank Schweitzer .

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Editors and Affiliations

  1. Research Institute of Economy, Trade and Industry, Kyoto University, Kyoto, Japan

    Hideaki Aoyama

  2. Institute of Economic Research, Chuo University, Hachioji-shi, Japan

    Yuji Aruka

  3. Faculty of Economics, Rissho University, Tokyo, Japan

    Hiroshi Yoshikawa

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Schweitzer, F. (2020). The Law of Proportionate Growth and Its Siblings: Applications in Agent-Based Modeling of Socio-Economic Systems. In: Aoyama, H., Aruka, Y., Yoshikawa, H. (eds) Complexity, Heterogeneity, and the Methods of Statistical Physics in Economics. Evolutionary Economics and Social Complexity Science, vol 22. Springer, Singapore. https://doi.org/10.1007/978-981-15-4806-2_8

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