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Heterogeneous Society in Binary Choices with Externalities

Author

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  • 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
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    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. Andrea Consiglio (ed.), 2007. "Artificial Markets Modeling," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-73135-1, July.
    5. 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.
    6. 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.
    7. 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.
    8. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Leigh Tesfatsion & Kenneth L. Judd (ed.), 2006. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 2, number 2.
    15. 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.
    16. 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.
    17. repec:hhs:iuiwop:487 is not listed on IDEAS
    18. Patrick Kline, 2010. "Place Based Policies, Heterogeneity, and Agglomeration," American Economic Review, American Economic Association, vol. 100(2), pages 383-387, May.
    19. 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.
    20. 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.
    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.
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