Structure and emergence in a nested logit model with social and spatial interactions

  • Elenna R. Dugundji
  • László Gulyás


Suppose you have the possibility to choose to adopt one of a number of different behaviors or to choose to buy one of a number of different products, and suppose your choice is influenced by your individual perception of the average choices made by others. Economists Brock and Durlauf (in Am. Econ. Rev. 92(2):298, 2002; The Economy as an Evolving Complex System III. Oxford University Press, New York, 2006) have derived seminal theoretical results for the equilibrium behavior of the multinomial discrete choice model with social interactions, assuming homogeneous decision-makers, global interactions and laws of large of numbers. The research presented in this paper extends Brock and Durlauf’s model to allow for unobserved preference heterogeneity between choice alternatives by studying the nested logit model. Next, by drawing on the computational possibilities permitted through social simulation of multi-agent systems (MAS), this paper relaxes the assumption of global interactions and considers instead local interactions within several hypothesized social and spatial network structures. Additional heterogeneity is thus hereby induced by the influence on a given decision-maker’s choice by the particular network connections he or she has and the particular perceived percentages, for example, of the agent’s neighbors or socio-economic peers making each choice. Discrete choice estimation results controlling these heterogeneous individual preferences are embedded in a multi-agent based simulation model in order to observe the evolution of choice behavior over time with socio-dynamic feedback due to the network effects. The MAS approach also gives us an additional advantage in the possibility to test size effects, and thus relax the assumption of large numbers, as well as test the effect of different initial conditions. Finally an extra benefit is gained via the MAS approach in that we are not confined to study only the equilibrium behavior, and have the possibility here to observe the time-varying trajectories of the choice behavior. This is important since smaller network sizes are revealed to be associated with higher volatility of the choice behavior in this model, and consequently stochastic cycling between equilibria. Averaged over time, the emergent behavior in such case yields a quite different picture than the theoretical results predicted by Brock and Durlauf. Furthermore being able to observe the emergent behavior allows us to see the subtle role of the unobserved heterogeneity in the nested logit model in breaking the symmetry of the multinomial logit model. We can see the temporal patterns by which theoretically predicted dominant equilibria emerge or not according to different social and spatial network scenarios. With an eye towards application in the context of transportation mode choice, we conclude highlighting limitations of our present study and recommendations for future work.


Discrete choice Multi-agent based social simulation Social networks Spatial interaction Transportation demand 



The authors would like to gratefully acknowledge discussion with Harry Timmermans, Theo Arentze, Cars Hommes, Frank le Clercq, Loek Kapoen, George Kampis, József Váncza and András Márkus, as well as the valuable and insightful comments from three anonymous reviewers which greatly improved the exposition in this paper. Very special thanks are also due to Guus Brohm and Nelly Kalfs at the Agency for Infrastructure, Traffic and Transport of the Municipality of Amsterdam, to Willem Vermin and the High Performance Computing support team at SARA Computing and Networking Services, Amsterdam and to David Sallach, Michael North, Charles Macal and the RePast development team. In addition we would like to express our appreciation more generally to a number of other committed scholars and out-of-the box thinkers that influenced our own thinking during formative years: Nigel Gilbert, keynote speaker at the first Lake Arrowhead Conference where the authors first met, and one of the team of visionary signatories of the European Social Simulation Association (ESSA); Axel Leijonhufvud, Robert Axtell and Masanao Aoki for eye-opening introduction to the world of adaptive economic processes; Kathleen Carley, a beacon for inspiration on the realm of possibilities of network analysis coupled with population scale social simulation; and Scott Page and John Miller, organizers of the Santa Fe Institute Graduate Workshop on Computational Economics, for pointing us to William Brock and Steven Durlauf’s work on multinomial choice with social interactions during an intensive two weeks of learning. Finally we would like to thank Clara Smith, Fred Amblard, Paul Chapron, Matthias Maillard and Samuel Thiriot for their wonderful initiative to bring together researchers in social network analysis and multi-agent systems at the lively SNAMAS workshop at ESSA 2011. The authors claim full responsibility for any errors.


  1. Aoki M (1995) Economic fluctuations with interactive agents: dynamic and stochastic externalities. Jpn Econ Rev 46(2):148–165 CrossRefGoogle Scholar
  2. Arentze TA, Timmermans HJP, Hofman F (2008) Creating synthetic household populations: problems and approach. Transp Res Rec 2014:85–91 CrossRefGoogle Scholar
  3. Arentze TA, van den Berg P, Timmermans HJP (2012) Modeling social networks in geographic space: approach and empirical application. Environ Plan A 44(5):1101–1120 CrossRefGoogle Scholar
  4. Barrett CL, Beckman RJ, Khan M, Marathe MV, Stretz PE, Dutta T, Lewis B (2009) Generation and analysis of large synthetic social contact networks. In: Rossetti MD, Hill RR, Johansson B, Dunkin A, Ingalls RG (eds) Proceedings of the 2009 winter simulation conference. IEEE Press, New York Google Scholar
  5. Ben-Akiva M (1973) Structure of passenger travel demand models. Dissertation, Massachusetts Institute of Technology, Cambridge Google Scholar
  6. Ben-Akiva M, Lerman SR (1985) Discrete choice analysis: theory and application to travel demand. MIT Press, Cambridge Google Scholar
  7. Berry S, Levinsohn J, Pakes A (1995) Automobile prices in market equilibrium. Econometrica 63:841–889 CrossRefGoogle Scholar
  8. Berry S, Levinsohn J, Pakes A (2004) Differentiated products demand systems from a combination of micro and macro data: the new vehicle market. J Polit Econ 112(1):68–105 CrossRefGoogle Scholar
  9. Bertolini L (2007) Evolutionary urban transportation planning: an exploration. Environ Plan A 39:1998–2019 CrossRefGoogle Scholar
  10. Bhat CR, Pendyala RM (2005) Modeling intra-household interactions and group decision-making. Transportation 32:443–448 CrossRefGoogle Scholar
  11. Bierlaire M (2003) BIOGEME: a free package for the estimation of discrete choice models. In: Proceedings of the 3rd Swiss transportation research conference, Ascona, Switzerland Google Scholar
  12. Blume LE, Durlauf SN (2003) Equilibrium concepts for social interaction models. Int Game Theory Rev 5(3):193–209 CrossRefGoogle Scholar
  13. Blume LE, Brock WA, Durlauf SN, Ioannides Y (2011) Identification of social interactions. In: Benhabib J, Bisin A, MO Jackson (eds) Handbook of social economics. Elsevier, North Holland Google Scholar
  14. Brock WA, Durlauf SN (2001) Discrete choice with social interactions. Rev Econ Stud 68:235–260 CrossRefGoogle Scholar
  15. Brock WA, Durlauf SN (2002) A multinomial choice model of neighborhood effects. Am Econ Rev 92(2):298–303 CrossRefGoogle Scholar
  16. Brock WA, Durlauf SN (2006) Multinomial choice with social interactions. In: Blume LE, Durlauf SN (eds) The economy as an evolving complex system III. Oxford University Press, New York Google Scholar
  17. Buehler R, Pucher J (2012) Demand for public transport in Germany and the USA: an analysis of rider characteristics. Transp Rev 32(5):541–567 CrossRefGoogle Scholar
  18. Butts CT, Acton RM (2011) Spatial modeling of social networks. In: Nyerges T, Couclelis H, McMaster R (eds) The Sage handbook of GIS and society research. SAGE, Thousand Oaks Google Scholar
  19. Butts CT, Acton RM, Hipp JR, Nagle NN (2012) Geographical variability and network structure. Soc Netw 34(1):82–100 CrossRefGoogle Scholar
  20. Domencich T, McFadden D (1975) Urban travel demand. North Holland, Amsterdam Google Scholar
  21. Dugundji ER (2006) Residential choice and the geography of family networks: some considerations. In: Proceedings of the 85th annual meeting of the transportation research board, Washington, DC Google Scholar
  22. Dugundji ER (2012) Socio-dynamic discrete choice: equilibrium behavior of the nested logit model with social interactions. In: Interdisciplinary workshop on information and decision in social networks. Massachusetts Institute of Technology, Cambridge Google Scholar
  23. Dugundji ER (2013) Socio-dynamic discrete choice: theory and application. Dissertation, Universiteit van Amsterdam, Amsterdam, Netherlands Google Scholar
  24. Dugundji ER, Gulyás L (2003) An exploration of the role of global versus local and social versus spatial networks in transportation mode choice behavior in the Netherlands. In: Proceedings of AGENT 2003: challenges in social simulation. Argonne National Laboratory and University of Chicago, Chicago. Google Scholar
  25. Dugundji ER, Gulyás L (2006) Emergent opinion dynamics on endogenous networks. In: Trajkovski GP, Collins SG (eds) Interaction and emergent phenomena in societies of agents. AAAI Press, Menlo Park. Technical Report FS-06-05 Google Scholar
  26. Dugundji ER, Gulyás L (2008) Socio-dynamic discrete choice on networks: impacts of agent heterogeneity on emergent equilibrium outcomes. Environ Plan B, Plan Des 35:1028–1054 CrossRefGoogle Scholar
  27. Dugundji ER, Gulyás L (2012a) Socio-dynamic discrete choice on networks in space: the role of utility parameters and connectivity. Proc Comput Sci 10:827–832 CrossRefGoogle Scholar
  28. Dugundji ER, Gulyás L (2012b) Socio-dynamic discrete choice applied to intercity travel demand: issues in estimation. In: Proceedings of the federated conference on computer science and information systems (FedCSIS), Wroclaw, Poland. IEEE Press, New York Google Scholar
  29. Dugundji ER, Walker JL (2005) Discrete choice with social and spatial network interdependencies: an empirical example using mixed generalized extreme value models with field and panel effects. Transp Res Rec 1921:70–78 CrossRefGoogle Scholar
  30. Dugundji ER, Kapoen LL, le Clercq F, Arentze TA, Timmermans HJP, Veldhuisen KJ (2001) The long-term effects of multi-modal transportation networks: the residential choice behavior of households. In: Proceedings of the 9th world conference on transportation research, Seoul, Korea Google Scholar
  31. Dugundji ER, Páez A, Arentze TA (2008) Social networks, choices, mobility and travel. Environ Plan B, Plan Des 35(6):956–960 CrossRefGoogle Scholar
  32. Dugundji ER, Páez A, Arentze TA, Walker JL, Carrasco JA, Marchal F, Nakanishi H (2011) Transportation and social interactions. Transp Res, Part A, Policy Pract 45(4):239–247 CrossRefGoogle Scholar
  33. Dugundji ER, Scott DM, Carrasco JA, Páez A (2012) Urban mobility and social-spatial contact—introduction. Environ Plan A 44(5):1011–1015 CrossRefGoogle Scholar
  34. Fischel WA (2006) The Tiebout model at 50. Lincoln Institute of Land Policy, Cambridge Google Scholar
  35. Fukuda D, Morichi S (2007) Incorporating aggregate behavior in an individual’s discrete choice: an application to analyzing illegal bicycle parking behavior. Transp Res, Part A, Policy Pract 41:313–325 CrossRefGoogle Scholar
  36. Goetzke F (2008) Network effects in public transit use: evidence from a spatially autoregressive mode choice model. Urban Stud 45(2):407–417 Google Scholar
  37. Goetzke F, Andrade PM (2009) Walkability as a summary measure in a spatially autoregressive mode choice model: an instrumental variable approach. In: Páez A, Buliung RN, Le Gallo J, Dall’erba S (eds) Progress in spatial analysis: methods and applications, advances in spatial science. Springer, Berlin, Heidelberg Google Scholar
  38. Goetzke F, Rave T (2011) Bicycle use in Germany: explaining differences between municipalities with social network effects. Urban Stud 48(2):427–437 CrossRefGoogle Scholar
  39. Goetzke F, Weinberger R (2012) Separating contextual from endogenous effects in automobile ownership models. Environ Plan A 44(5):1032–1046 CrossRefGoogle Scholar
  40. Hackney J, Kowald M (2011) Exponential random graph models of the Zurich snowball survey. In: Futurenet workshop: social network analysis in transport, Manchester, UK Google Scholar
  41. Ioannides Y (2006) Topologies of social interactions. Econ Theory 28:559–584 CrossRefGoogle Scholar
  42. Kenworthy J, Laube F (2005) An international comparative perspective on sustainable transport in European cities. Eur Spat Res Policy 12:11–50 Google Scholar
  43. Kollman K, Miller JH, Page SE (1997) Political institutions and sorting in a Tiebout model. Am Econ Rev 87(5):977–992 Google Scholar
  44. Kowald M, Axhausen KW (2012) Spatial distribution of connected leisure networks: selected results from a snowball sample. Environ Plan A 44(5):1085–1100 CrossRefGoogle Scholar
  45. Louviere J, Train KE, Ben-Akiva M, Bhat C, Brownstone D, Cameron TA, Carson RT, Deshazo JR, Fiebig D, Greene W, Hensher D (2006) Recent progress on endogeneity in choice modeling. Mark Lett 16(3–4):255–265 Google Scholar
  46. Macal CM, North MJ (2010) Tutorial on agent-based modeling and simulation. J Simul 4:151–162 CrossRefGoogle Scholar
  47. Manski C (1995) Identification problems in the social sciences. Harvard University Press, Cambridge Google Scholar
  48. Maxwell DT, Carley KM (2009) Principles for effectively representing heterogeneous populations in multi-agent simulations. In: Tolk A, Jain LC (eds) Comp sys in knowledge-based environments. SCI, vol 168. Springer, Berlin, Heidelberg, Google Scholar
  49. McFadden D (1978) Modelling the choice of residential location. In: Karlquist A et al (eds) Spatial interaction theory and residential location. North Holland Press, Amsterdam Google Scholar
  50. Musgrave RA (1959) The theory of public finance: a study in public economy. McGraw-Hill, New York Google Scholar
  51. Oates WE (1969) The effects of property taxes and local public spending on property values: an empirical study of tax capitalization and the Tiebout hypothesis. J Polit Econ 77:957–971 CrossRefGoogle Scholar
  52. Páez A, Scott DM (2007) Social influence on travel behavior: a simulation example of the decision to telecommute. Environ Plan A 39:647–665 CrossRefGoogle Scholar
  53. Páez A, Scott DM, Volz E (2008) A discrete-choice approach to modeling social influence on individual decision making. Environ Plan B, Plan Des 35(6):1055–1069 CrossRefGoogle Scholar
  54. Rivers D, Vuong Q (1988) Limited information estimators and exogeneity tests for simultaneous probit models. J Econom 39:347–366 CrossRefGoogle Scholar
  55. Samuelson PA (1954) The pure theory of public expenditures. Rev Econ Stat 36(4):387–389 CrossRefGoogle Scholar
  56. Samuelson PA (1955) Diagrammatic exposition of a pure theory of public expenditures. Rev Econ Stat 37(4):350–356 CrossRefGoogle Scholar
  57. Tiebout CM (1956) A pure theory of local expenditures. J Polit Econ 64:416–424 CrossRefGoogle Scholar
  58. Timmermans HJP, Zhang J (2009) Modeling household activity travel behavior. Transp Res, Part B, Methodol 43:187–190 CrossRefGoogle Scholar
  59. Train KE (2009) Discrete choice methods with simulation, 2nd edn. Cambridge University Press, Cambridge CrossRefGoogle Scholar
  60. Walker JL, Ehlers E, Banerjee I, Dugundji ER (2011) Correcting for endogeneity in behavioral choice models with social influence variables. Transp Res, Part A, Policy Pract 45:362–374 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Universiteit van AmsterdamAmsterdamThe Netherlands
  2. 2.AITIA International Inc.BudapestHungary

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