Abstract
We study wealth accumulation dynamics in a population of heterogeneously mixed agents with a capacity for a certain primitive form of cooperation enabled by static network structures. Despite their simplicity, the stochastic dynamics generate inequalities in wealth reminiscent of real-world social systems even in a fully mixed population. A simple form of cooperation is introduced and is shown to enhance the viability of agents by embedding such dynamics in a network; the impact of social structures on the origins and persistence of inequality can be teased out easily. The models developed here complement traditional modeling approaches based on grid worlds.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The concept social structures [19] is more general than the widely held belief in computational social science that social structure is just a social network.
- 2.
The use of such analysis for studying wealth dynamics was presented by one of the authors at CSSA18 [32]. Unlike the finite interval dynamics used there, the dynamics here take place on a semi-infinite line.
- 3.
The discrete-time step \(\Delta t=1\). w in the discrete setting is a Gaussian distributed random variable \(\mathcal {N}(0,\sigma ^2) = \mathcal {N}(0,D\Delta t)\).
- 4.
These formulations make use measure theoretical probability to convert SDEs to partial differential equations known as Fokker-Planck equations. They provide numerical and closed-form estimates of probability density, survival time probabilities, and other quantities of importance.
- 5.
The result follows from the additivity properties of white noise.
- 6.
The two pictures: the particle perspective and the proto perspective, are equivalent. While it is easier to mathematically analyze the system in the proto perspective, the individual wealth of the particles carries meaning; it is just not useful for studying survival of the proto or the particles within it.
- 7.
Preliminary investigations suggest that for simple non-network ensembles, Gini either stays close to 0 or 1. We suspect that this is because of the constant wealth growth rate used in our models, Gini is a partially useful measure. This is unlike in macroeconomic models where exponential growth rate gives rise an appearance of non-trivial Gini coefficients.
- 8.
We define “Stage 1” as the period before the first proto is formed, “Stage 2” as the period during which protos are being formed.
- 9.
An isolate agent is one with no graph neighbors.
- 10.
Note that this “gain” could be negative, in which case the agent, and possibly its proto, may be subject to death exactly as in step (3).
References
Brian Arthur, W.: Chapter 32 out-of-equilibrium economics and agent-based modeling. In: Handbook of Computational Economics, vol. 2, pp. 1551–1564. Elsevier (2006)
Benhabib, J., Bisin, A.: Skewed wealth distributions: theory and empirics. J. Econ. Lit. 56(4), 1261–91 (2018)
Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59(1), 65–98 (2017)
Granovetter, M.: Soc. Econ. Harvard University Press (2017)
Granovetter, M.: The impact of social structure on economic outcomes. J. Econ. Perspect. 19(1), 33–50 (2005)
Greif, A.: Cultural beliefs and the organization of society: a historical and theoretical reflection on collectivist and individualist societies. J. Polit. Econ. Polit. 102(5), 912–950 (1994)
Hedström, P., Bearman, P.: The Oxford Handbook of Analytical Sociology. Oxford Handbooks, OUP Oxford (2011)
Hedström, P., Bearman, P.: What is analytical sociology all about? an introductory essay. In: Hedström, P., Bearman, P. (eds.) The Oxford Handbook of Analytical Sociology. Oxford Handbooks, chapter 1, pp. 3–24. OUP Oxford (2011)
Hedström, P., Udehn, L.: Analytical sociology and theories of the middle range. In Hedström, P., Bearman, P. (eds.) The Oxford Handbook of Analytical Sociology. Oxford Handbooks, chapter 2, pp. 25–47. OUP Oxford (2011)
Jackson, M.O., Rogers, B.W., Zenou, Y.: The economic consequences of social-network structure. J. Econ. Lit. 55(1), 49–95 (2017)
Kasper, C., Mulder, M.B.: Who helps and why?: cooperative networks in mpimbwe. Curr. Anthropol. 56(5), 701–732 (2015)
Katz, M.B.: The People of Hamilton, Canada West: Family and Class in a Mid-Nineteenth-Century City. Harvard Studies in Urban History Series. Harvard University Press (2013)
Keuschnigg, M., Lovsjö, N., Hedström, P.: Analytical sociology and computational social science. J. Comput. Soc. Sci. 1(1), 3–14 (2018)
Koster, J., Leckie, G., Miller, A., Hames, R.: Multilevel modeling analysis of dyadic network data with an application to Ye’kwana food sharing. Am. J. Phys. Anthropol. 157(3), 507–512 (2015)
Koster, J., Lukas, D., Nolin, D., Power, E.A., Alvergne, A., Mace, R., Ross, C.T., Kramer, K., Greaves, R., Caudell, M., et al.: Kinship ties across the lifespan in human communities (2019)
Koster, J.M., Leckie, G.: Food sharing networks in lowland Nicaragua: an application of the social relations model to count data. Soc. Netw. 38, 100–110 (2014)
Macy, M., Flache, A.: Social dynamics from the bottom up. In: Hedström, P., Bearman, P. (eds.) The Oxford Handbook of Analytical Sociology, Oxford Handbooks, chapter 11, pp. 245–268. OUP Oxford (2011)
Macy, M.W., Willer, R.: From factors to actors: computational sociology and agent-based modeling. Ann. Rev. Sociol. 28(1), 143–166 (2002)
Martin, J.L., Lee, M.: Social structure. In: Wright, J.D. (Ed) International Encyclopedia of the Social and Behavioral Sciences, vol. 22, 2nd edn., pp. 713–718. Elsevier (2015)
Mudigonda, S., Friesen, M.: Institutional emergence and the persistence of inequality. In: Proceedings of Computational Social Sciences Society of the Americas 2018 Annual Conference. Springer Press (2018)
Newman, M.: Networks. Oxford University Press, Oxford (2018)
Nolin, D.A.: Food-sharing networks in Lamalera, Indonesia: status, sharing, and signaling. Evol. Hum. Behav. 33(4), 334–345 (2012)
Piketty, T., Goldhammer, A.: Capital in the Twenty-First Century. Harvard University Press (2017)
Power, E.A., Ready, E.: Cooperation beyond consanguinity: post-marital residence, delineations of kin, and social support among south Indian Tamils (in press). Philos. Trans. Roy. Soc. Biol. Sci. (2019)
Ready, E., Power, E.A.: Why wage earners hunt: food sharing, social structure, and influence in an arctic mixed economy. Curr. Anthropol. 59(1), 74–97 (2018)
Redner, S.: A Guide to First-Passage Processes. Cambridge University Press, A Guide to First-passage Processes (2001)
Sampson, R.J., Wilson, W.J.: Great American City: Chicago and the Enduring Neighborhood Effect. University of Chicago Press (2012)
Sampson, R.J., Morenoff, J.D., Gannon-Rowley, T.: Assessing “neighborhood effects”: social processes and new directions in research. Ann. Rev. Sociol. 28(1), 443–478 (2002)
Smith, D., Dyble, M., Major, K., Page, A.E., Chaudhary, N., Salali, G.D., Thompson, J., Vinicius, L., Migliano, A.B., Mace, R.: A friend in need is a friend indeed: need-based sharing, rather than cooperative assortment, predicts experimental resource transfers among Agta hunter-gatherers. Evol. Hum. Behav. 40(1), 82–89 (2019)
Tesfatsion, L.: Chapter 16 agent-based computational economics: a constructive approach to economic theory. In: Handbook of Computational Economics, vol. 2, pp. 831–880. Elsevier (2006)
Tesfatsion, L.: Modeling economic systems as locally-constructive sequential games. J. Econ. Methodol. 24(4), 384–409 (2017)
Venkatachalapath, R.: Revisiting Markov models of intragenerational social mobility. In: Proceedings of Computational Social Sciences Society of the Americas 2018 Annual Conference. Springer Press (2018)
White, D.R.: Kinship, class and community. In: Scott, J.C., Carrington, P. (eds.) Sage Handbook of Social Networks. Sage Publications, New York, pp. 129–147 (2011)
Wilhite, A.: Chapter 20 economic activity on fixed networks. In: Handbook of Computational Economics, vol. 2, pp. 1013–1045. Elsevier (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Venkatachalapathy, R., Davies, S., Nehrboss, W. (2021). Wealth Dynamics in the Presence of Network Structure and Primitive Cooperation. In: Yang, Z., von Briesen, E. (eds) Proceedings of the 2019 International Conference of The Computational Social Science Society of the Americas. CSSSA 2020. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-77517-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-030-77517-9_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-77516-2
Online ISBN: 978-3-030-77517-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)