IDEAS home Printed from https://ideas.repec.org/a/sae/ratsoc/v24y2012i4p442-462.html
   My bibliography  Save this article

Minority language and the stability of bilingual equilibria

Author

Listed:
  • Nagore Iriberri

    (Universitat Pompeu Fabra, Catalonia-Spain)

  • José-Ramón Uriarte

    (University of the Basque Country, Basque Country-Spain)

Abstract

We investigate a society with two official languages: A , shared by all individuals, and B , spoken by a bilingual minority. A model is developed in which the bilingual agents must make strategic decisions about the language to be used in a conversation. The decisions are taken under imperfect information about the linguistic type of the participants. We show that the bilingual population is optimally partitioned into two groups, one composed of agents who strategically hide their bilingual nature and the other composed of those who reveal it. As a consequence, in the interactions between members of the former group the language used is A , having therefore coordination failures on the minority language. We show that this mixed strategy Nash equilibrium has strong stability properties: it is evolutionarily stable and, dynamically, asymptotically stable for the one-population replicator dynamics. These properties might explain the difficulties encountered by language policies directed at promoting the use of minority languages. JEL Classification Numbers: C72, D81.

Suggested Citation

  • Nagore Iriberri & José-Ramón Uriarte, 2012. "Minority language and the stability of bilingual equilibria," Rationality and Society, , vol. 24(4), pages 442-462, November.
    • Handle: RePEc:sae:ratsoc:v:24:y:2012:i:4:p:442-462
    DOI: 10.1177/1043463112453556
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/1043463112453556
    Download Restriction: no
    File URL: https://libkey.io/10.1177/1043463112453556?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
    ---><---

    References listed on IDEAS

    as
    1. Daniel M. Abrams & Steven H. Strogatz, 2003. "Modelling the dynamics of language death," Nature, Nature, vol. 424(6951), pages 900-900, August.
    2. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    3. Cabrales, Antonio, 2000. "Stochastic Replicator Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 451-481, May.
    4. Pinasco, J.P. & Romanelli, L., 2006. "Coexistence of Languages is possible," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 355-360.
    5. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
    6. Stauffer, Dietrich & Castelló, Xavier & Eguíluz, Víctor M. & San Miguel, Maxi, 2007. "Microscopic Abrams–Strogatz model of language competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 835-842.
    7. Patriarca, Marco & Leppänen, Teemu, 2004. "Modeling language competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 296-299.
    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. Juan Pablo Pinasco & Mauro Rodríguez Cartabia & Nicolas Saintier, 2018. "A Game Theoretic Model of Wealth Distribution," Dynamic Games and Applications, Springer, vol. 8(4), pages 874-890, December.
    2. Torsten Templin, 2019. "A language competition model for new minorities," Rationality and Society, , vol. 31(1), pages 40-69, February.
    3. Michael Boissonneault & Paul Vogt, 2021. "A systematic and interdisciplinary review of mathematical models of language competition," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-12, December.
    4. Kentaro Hatsumi, 2023. "Second‐language acquisition behavior and hegemonic language," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(1), pages 3-20, March.
    5. Antonio Cabrales & Esther Hauk, 2022. "Norms and the Evolution of Leaders' Followership," CESifo Working Paper Series 9845, CESifo.
    6. Stefan Sperlich & Jose-Ramon Uriarte, 2019. "The economics of minority language use: theory and empirical evidence for a language game model," Papers 1908.11604, arXiv.org.
    7. Ramon Caminal, 2013. "The economic value of reciprocal bilingualism," UFAE and IAE Working Papers 933.13, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    8. José Ramón Uriarte & Stefan Sperlich, 2021. "A behavioural model of minority language shift: Theory and empirical evidence," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-17, June.

    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. Juan Carlos Bárcena‐Ruiz & Máximo Sedano, 2011. "Endogenous Timing In A Mixed Duopoly: Weighted Welfare And Price Competition," The Japanese Economic Review, Japanese Economic Association, vol. 62(4), pages 485-503, December.
    2. Iriberri Etxebeste, Nagore & Uriarte Ayo, José Ramón, 2011. "Minority Language and the Stability of Bilingual Equilibria," IKERLANAK info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    3. Patriarca, Marco & Heinsalu, Els, 2009. "Influence of geography on language competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 174-186.
    4. Templin, Torsten & Seidl, Andrea & Wickström, Bengt-Arne & Feichtinger, Gustav, 2016. "Optimal language policy for the preservation of a minority language," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 8-21.
    5. Michael Boissonneault & Paul Vogt, 2021. "A systematic and interdisciplinary review of mathematical models of language competition," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-12, December.
    6. Nie, Lin-Fei & Teng, Zhi-Dong & Nieto, Juan J. & Jung, Il Hyo, 2015. "State impulsive control strategies for a two-languages competitive model with bilingualism and interlinguistic similarity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 136-147.
    7. Torsten Templin, 2019. "A language competition model for new minorities," Rationality and Society, , vol. 31(1), pages 40-69, February.
    8. Bakalis, Evangelos & Galani, Alexandra, 2012. "Modeling language evolution: Aromanian, an endangered language in Greece," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4963-4969.
    9. Ponti, Giovanni, 2000. "Continuous-time evolutionary dynamics: theory and practice," Research in Economics, Elsevier, vol. 54(2), pages 187-214, June.
    10. Weibull, Jorgen W., 1998. "Evolution, rationality and equilibrium in games," European Economic Review, Elsevier, vol. 42(3-5), pages 641-649, May.
    11. Caridi, Inés & Nemiña, Francisco & Pinasco, Juan P. & Schiaffino, Pablo, 2013. "Schelling-voter model: An application to language competition," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 216-221.
    12. Antonio Cabrales & José-Ramón Uriarte, 2013. "Doubts and equilibria," Journal of Evolutionary Economics, Springer, vol. 23(4), pages 783-810, September.
    13. Cabrales, Antonio & Uriarte Ayo, José Ramón, 2008. "Doubts and Equilibria," IKERLANAK 2008-31, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    14. TANABE Yasuo, 2004. "A Result for Approximation of Imitational Behavior in Large Populations," ESRI Discussion paper series 084, Economic and Social Research Institute (ESRI).
    15. Stefan Sperlich & Jose-Ramon Uriarte, 2019. "The economics of minority language use: theory and empirical evidence for a language game model," Papers 1908.11604, arXiv.org.
    16. Uriarte, Jose Ramon, 2007. "A behavioural foundation for models of evolutionary drift," Journal of Economic Behavior & Organization, Elsevier, vol. 63(3), pages 497-513, July.
    17. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    18. repec:esj:esridp:84 is not listed on IDEAS
    19. Uriarte Ayo, José Ramón, 2005. "A Behavioral Foundation for Models of Evolutionary Drift," IKERLANAK 2005-19, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    20. Ponti, Giovanni, 2000. "Cycles of Learning in the Centipede Game," Games and Economic Behavior, Elsevier, vol. 30(1), pages 115-141, January.
    21. Noemi Schmitt & Jan Tuinstra & Frank Westerhoff, 2018. "Stability and welfare effects of profit taxes within an evolutionary market interaction model," Review of International Economics, Wiley Blackwell, vol. 26(3), pages 691-708, August.

    More about this item

    Keywords

    Imperfect information; language competition; majority/minority language; Nash equilibrium; replicator dynamics;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    Statistics

    Access and download statistics

    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:sae:ratsoc:v:24:y:2012:i:4:p:442-462. 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: SAGE Publications (email available below). General contact details of provider: .

    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.