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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
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    References listed on IDEAS

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    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. 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.
    7. 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.
    8. Patriarca, Marco & Leppänen, Teemu, 2004. "Modeling language competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 296-299.
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    Cited by:

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    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.

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    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

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