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# Topologies Of Social Interactions

## Author

Listed:
• Yannis M. Ioannides

## Abstract

We examine in this paper the role of an economy's social interaction structure, defined as a graph. Individuals care about the decisions of their neighbors. We extend the behavioral discrete-response rules along the lines of the interactive discrete choice model of Brock and Durlauf (2001) to static and dynamic settings and also explore properties of a richer class of {\em anisotropic} equilibria in the context of richer social interaction topologies, such as circular interaction and one-dimensional lattice. We examine the model where individuals make decisions on the basis of observations on the actual decisions of their neighbors in a static setting and explored some of the issues that come up in dynamic settings. In the static case, we accomplish this by exploiting the properties of Markov random fields as Gibbs states. We also link interactive discrete choice models with the econometric theory of simultaneous systems of equations modelling discrete decisions. We examine the role of closure in social structure. With local interaction either in the form of circular or of interaction along a line, synergistic effects lead to spatial oscillations and clustering, with the most unstable'' states pushing the economy away from the symmetric isotropic outcome, which is unstable. We obtain general results for the dynamics of adjustment towards isotropic equilibria and shows that they combine spectral properties of the adjacency matrix with those associated with the nonlinearity of the reaction functions that lead to multiplicity of steady states. When all agents have the same number of neighbors the dynamics of adjustment exhibit relative persistence. Cyclical interaction is associated with endogenous and generally transient spatial oscillations that take the form of islands of conformity. The paper also examines stochastic dynamics for general interaction topologies. Yannis M. Ioannides Department of Economics Tufts University Medford, MA 02155 Voice: 617 627 3294 Fax: 617 627 3917 yannis.ioannides@tufts.edu www.tufts.edu/~yioannid

## Suggested Citation

• Yannis M. Ioannides, 2004. "Topologies Of Social Interactions," Econometric Society 2004 North American Winter Meetings 287, Econometric Society.
• Handle: RePEc:ecm:nawm04:287
as

File URL: http://repec.org/esNAWM04/up.32053.1049081236.pdf

## References listed on IDEAS

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## Citations

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Cited by:

1. Evstigneev, Igor & Taksar, Michael, 2009. "Dynamic interaction models of economic equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 166-182, January.
2. Schütz, Gunter M. & de Almeida Prado, Fernando Pigeard & Harris, Rosemary J. & Belitsky, Vladimir, 2009. "Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4126-4144.
3. Chadha, R. & Brown, D.K. & Deardorff, A.V. & Stern, R.M., 2000. "Computational Analysis of the Impact on India of the Uruguay Round and the Forthcoming WTO Trade Negotiations," Working Papers 459, Research Seminar in International Economics, University of Michigan.
4. Opolot, Daniel & Azomahou, Theophile, 2012. "Learning and convergence in networks," MERIT Working Papers 074, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
5. Chincarini, Ludwig & Asherie, Neer, 2008. "An analytical model for the formation of economic clusters," Regional Science and Urban Economics, Elsevier, vol. 38(3), pages 252-270, May.
6. Antoine Billot, 2009. "How to shake the invisible hand (when Robinson meets Friday)," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(3), pages 257-270.
7. Hennessy, David A. & Lapan, Harvey E., 2009. "Harmonic symmetries of imperfect competition on circular city," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 124-146, January.
8. Grajzl, Peter & Baniak, Andrzej, 2012. "Mandating behavioral conformity in social groups with conformist members," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 479-493.
9. Glaser, Darrell J., 2009. "Teenage dropouts and drug use: Does the specification of peer group structure matter?," Economics of Education Review, Elsevier, vol. 28(4), pages 497-504, August.
10. Elpianna Emmanouilidi, 2012. "Estimation Of A Discrete-Choice Model With Spatial Interactions The Case Of Deforestation In Western Attica Between 1990 And 2000," Regional Science Inquiry, Hellenic Association of Regional Scientists, vol. 0(3), pages 69-83, December.
11. Horst, Ulrich, 2010. "Dynamic systems of social interactions," Journal of Economic Behavior & Organization, Elsevier, vol. 73(2), pages 158-170, February.
12. Ioannides, Yannis M., 2012. "Complexity and organizational architecture," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 193-202.
13. repec:spr:joecth:v:64:y:2017:i:3:d:10.1007_s00199-016-0990-3 is not listed on IDEAS
14. Zakaria Babutsidze & Robin Cowan, 2014. "Showing or telling? Local interaction and organization of behavior," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 9(2), pages 151-181, October.
15. Ballester, Coralio & Calvó-Armengol, Antoni & Zenou, Yves, 2004. "Who's Who in Crime Network. Wanted the Key Player," Working Paper Series 617, Research Institute of Industrial Economics.
16. George Norman & Lynne Pepall & Dan Richards, 2001. "Versioning, Brand-Stretching, and the Evolution of e-Commerce Markets," Discussion Papers Series, Department of Economics, Tufts University 0114, Department of Economics, Tufts University.
17. Jan K. Brueckner & Oleg Smirnov, 2008. "Social Networks And The Convergence Of Population Attributes: A Generalization," Journal of Regional Science, Wiley Blackwell, vol. 48(2), pages 359-365.
18. repec:hrs:journl::y:2012:v:4:i:3:p:69-83 is not listed on IDEAS
19. João Amaro de Matos & Pedro Barros, 2004. "Social Norms and the Paradox of Elections’ Turnout," Public Choice, Springer, vol. 121(1), pages 239-255, October.
20. Sumit Joshi & Poorvi Vora, 2013. "Weak and strong multimarket bidding rings," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 657-696, August.

### Keywords

Discrete regression and qualitative choice models;

### JEL classification:

• C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
• C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
• D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

### NEP fields

This paper has been announced in the following NEP Reports:

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