IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v9y2019i2d10.1007_s13235-018-0270-x.html
   My bibliography  Save this article

Heterogeneous Society in Binary Choices with Externalities

Author

Listed:
  • Arianna Dal Forno

    (University of Molise)

  • Ugo Merlone

    (University of Torino)

Abstract

We study a two-strategy model with negative externalities proposed by Schelling, in a dynamical setting where a society consists of two interacting populations with different behaviors derived from experiments with human participants. The resulting dynamics is a three-dimensional piecewise smooth map with one discontinuity, which inherits some of the characteristics of each homogeneous population dynamics, while others are lost and new ones emerge. We propose a technique to represent the dynamics on a bidimensional space and prove that the heterogeneous society dynamics can be obtained as a linear combination of the dynamics of the two homogeneous populations. As expected, complexity arises with respect to some aspects. Firstly, the number of equilibria expands to infinity and we were able to determine possible focal equilibria in the sense of Schelling. Secondly, when heterogeneity is introduced, the period adding structure of cycles is replaced by a period incrementing structure. Thirdly, the phenomenon of overreaction and cyclic oscillations can be mitigated even if it never completely disappears. We also derive the orbits of cycles of period two and provide numerical evidences of coexistence of cycles with different periods. It is worth noticing that with the heterogeneous society, the dynamics does not depend on the society aggregate choices only, rather on each population choice; neglecting it will make impossible to determine the future evolution of the system. The implications are important as heterogeneity makes the system path-dependent and a policy maker, considering aggregate society choice only, would be unable to make the proper decisions, unless further information is considered.

Suggested Citation

  • Arianna Dal Forno & Ugo Merlone, 2019. "Heterogeneous Society in Binary Choices with Externalities," Dynamic Games and Applications, Springer, vol. 9(2), pages 433-457, June.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:2:d:10.1007_s13235-018-0270-x
    DOI: 10.1007/s13235-018-0270-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-018-0270-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13235-018-0270-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Agiza, H.N. & Elsadany, A.A., 2003. "Nonlinear dynamics in the Cournot duopoly game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 512-524.
    2. Colman, Andrew M., 2006. "Thomas C. Schelling's psychological decision theory: Introduction to a special issue," Journal of Economic Psychology, Elsevier, vol. 27(5), pages 603-608, October.
    3. Denis Phan, 2007. "Heterogeneous Agents with Local Social Influence Networks: Path Dependence and Plurality of Equilibria in the ACE Noiseless Case," Lecture Notes in Economics and Mathematical Systems, in: Andrea Consiglio (ed.), Artificial Markets Modeling, chapter 13, pages 181-194, Springer.
    4. Alos-Ferrer, Carlos, 1999. "Dynamical Systems with a Continuum of Randomly Matched Agents," Journal of Economic Theory, Elsevier, vol. 86(2), pages 245-267, June.
    5. Jean-Philippe Platteau & Tomasz Strzalecki, 2004. "Collective Action, Heterogeneous Loyalties and Path Dependence: Micro-evidence from Senegal," Journal of African Economies, Centre for the Study of African Economies, vol. 13(3), pages 417-445, September.
    6. Tesfatsion, Leigh & Judd, Kenneth L., 2006. "Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics," Staff General Research Papers Archive 10368, Iowa State University, Department of Economics.
    7. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 719-733, November.
    8. Leigh Tesfatsion & Kenneth L. Judd (ed.), 2006. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 2, number 2.
    9. Dal Forno, Arianna & Merlone, Ugo, 2013. "Border-collision bifurcations in a model of Braess paradox," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 1-18.
    10. repec:hhs:iuiwop:487 is not listed on IDEAS
    11. Patrick Kline, 2010. "Place Based Policies, Heterogeneity, and Agglomeration," American Economic Review, American Economic Association, vol. 100(2), pages 383-387, May.
    12. Cavalli, Fausto & Naimzada, Ahmad & Pireddu, Marina, 2016. "A family of models for Schelling binary choices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 276-296.
    13. Thomas C. Schelling, 1973. "Hockey Helmets, Concealed Weapons, and Daylight Saving," Journal of Conflict Resolution, Peace Science Society (International), vol. 17(3), pages 381-428, September.
    14. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    15. Andrea Consiglio (ed.), 2007. "Artificial Markets Modeling," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-73135-1, December.
    16. Antonio Ciccone & James Costain, 2004. "On payoff heterogeneity in games with strategic complementarities," Oxford Economic Papers, Oxford University Press, vol. 56(4), pages 701-713, October.
    17. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    18. Jonathan P. Caulkins & Gustav Feichtinger & Dieter Grass & Richard F. Hartl & Peter M. Kort & Andreas J. Novak & Andrea Seidl & Franz Wirl, 2014. "A Dynamic Analysis of Schelling’s Binary Corruption Model: A Competitive Equilibrium Approach," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 608-625, May.
    19. Dal Forno, Arianna & Gardini, Laura & Merlone, Ugo, 2012. "Ternary choices in repeated games and border collision bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 294-305.
    20. Pennings, Joost M. E. & Garcia, Philip, 2004. "Hedging behavior in small and medium-sized enterprises: The role of unobserved heterogeneity," Journal of Banking & Finance, Elsevier, vol. 28(5), pages 951-978, May.
    21. Alan Kirman, 2006. "Heterogeneity in Economics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 1(1), pages 89-117, May.
    22. Gian Italo Bischi & Ugo Merlone, 2017. "Evolutionary minority games with memory," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 859-875, November.
    23. J. Michael Harrison & David M. Kreps, 1978. "Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 92(2), pages 323-336.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Irene Alfarone & Ugo Merlone, 2024. "Should I stay or should I go: A dynamical model of musicians’ agglomeration and migration," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(1), pages 97-116, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Russell Golman, 2011. "Why learning doesn’t add up: equilibrium selection with a composition of learning rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 719-733, November.
    2. Golman, Russell, 2012. "Homogeneity bias in models of discrete choice with bounded rationality," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 1-11.
    3. Waters, George A., 2009. "Chaos in the cobweb model with a new learning dynamic," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1201-1216, June.
    4. Serena Brianzoni & Roy Cerqueti & Elisabetta Michetti, 2010. "A Dynamic Stochastic Model of Asset Pricing with Heterogeneous Beliefs," Computational Economics, Springer;Society for Computational Economics, vol. 35(2), pages 165-188, February.
    5. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    6. Hommes, Cars & Lux, Thomas, 2013. "Individual Expectations And Aggregate Behavior In Learning-To-Forecast Experiments," Macroeconomic Dynamics, Cambridge University Press, vol. 17(2), pages 373-401, March.
    7. Anufriev, Mikhail & Tuinstra, Jan, 2013. "The impact of short-selling constraints on financial market stability in a heterogeneous agents model," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1523-1543.
    8. Georges SARAFOPOULOS & Kosmas PAPADOPOULOS, 2017. "On A Cournot Duopoly Game With Differentiated Goods, Heterogeneous Expectations And A Cost Function Including Emission Costs," Scientific Bulletin - Economic Sciences, University of Pitesti, vol. 16(1), pages 11-22.
    9. Anufriev Mikhail & Bottazzi Giulio, 2012. "Asset Pricing with Heterogeneous Investment Horizons," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(4), pages 1-38, October.
    10. Dziubiński, Marcin & Roy, Jaideep, 2012. "Popularity of reinforcement-based and belief-based learning models: An evolutionary approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 433-454.
    11. Russell, Golman, 2011. "Quantal response equilibria with heterogeneous agents," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2013-2028, September.
    12. PAPADOPOULOS Kosmas & SARAFOPOULOS Georges, 2019. "Dynamics of a Cournot Game with Differentiated Goods and Asymmetric Cost Functions based on Relative Profit Maximization," European Journal of Interdisciplinary Studies, Bucharest Economic Academy, issue 02, June.
    13. Naimzada, Ahmad K. & Ricchiuti, Giorgio, 2009. "Dynamic effects of increasing heterogeneity in financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1764-1772.
    14. Ahmad Naimzada & Giorgio Ricchiuti, 2006. "Heterogeneous Fundamentalists and Imitative Processes," Working Papers 104, University of Milano-Bicocca, Department of Economics, revised Nov 2006.
    15. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
    16. Roy Cerqueti & Giulia Rotundo, 2015. "A review of aggregation techniques for agent-based models: understanding the presence of long-term memory," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(4), pages 1693-1717, July.
    17. Carl Chiarella & Roberto Dieci & Laura Gardini & Lucia Sbragia, 2008. "A Model of Financial Market Dynamics with Heterogeneous Beliefs and State-Dependent Confidence," Computational Economics, Springer;Society for Computational Economics, vol. 32(1), pages 55-72, September.
    18. Deniz Erdemlioglu & Nikola Gradojevic, 2021. "Heterogeneous investment horizons, risk regimes, and realized jumps," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(1), pages 617-643, January.
    19. Kubin, Ingrid & Zörner, Thomas O. & Gardini, Laura & Commendatore, Pasquale, 2019. "A credit cycle model with market sentiments," Structural Change and Economic Dynamics, Elsevier, vol. 50(C), pages 159-174.
    20. Westerhoff Frank H., 2008. "The Use of Agent-Based Financial Market Models to Test the Effectiveness of Regulatory Policies," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 228(2-3), pages 195-227, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:dyngam:v:9:y:2019:i:2:d:10.1007_s13235-018-0270-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.