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Pragmatic languages with universal grammars


  • Hernández, Penélope
  • Urbano, Amparo
  • Vila, José E.


This paper constructs the equilibrium for a specific code that can be seen as a “universal grammar” in a class of common interest Sender–Receiver games where players communicate through a noisy channel. We propose a Senderʼs signaling strategy which does not depend on either the game payoffs or the initial probability distribution. The Receiverʼs strategy partitions the set of possible sequences into subsets, with a single action assignment to each of them. The Senderʼs signaling strategy is a Nash equilibrium, i.e. when the Receiver responds best to the Senderʼs strategy, the Sender has no incentive to deviate. An example shows that a tie-breaking decoding is crucial for the block-coding strategy to be an equilibrium. Efficiency is analyzed by comparing how close ex-ante expected payoffs are to those of noiseless communication. Moreover, we study how long communication should be to achieve a given payoff-approximation.

Suggested Citation

  • Hernández, Penélope & Urbano, Amparo & Vila, José E., 2012. "Pragmatic languages with universal grammars," Games and Economic Behavior, Elsevier, vol. 76(2), pages 738-752.
  • Handle: RePEc:eee:gamebe:v:76:y:2012:i:2:p:738-752
    DOI: 10.1016/j.geb.2012.08.009

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    References listed on IDEAS

    1. Ariel Rubinstein, 2000. "Economics and Language," Online economics textbooks, SUNY-Oswego, Department of Economics, number lang1, March.
    2. Michel Balinski & Rida Laraki, 2007. "Election by Majority Judgement: Experimental Evidence," Working Papers hal-00243076, HAL.
    3. Yaron Azrieli & Ehud Lehrer, 2004. "Categorization generated by prototypes -- an axiomatic approach," Game Theory and Information 0405003, EconWPA.
    4. Board, Oliver J. & Blume, Andreas & Kawamura, Kohei, 2007. "Noisy talk," Theoretical Economics, Econometric Society, vol. 2(4), December.
    5. Rubinstein, Ariel, 1996. "Why Are Certain Properties of Binary Relations Relatively More Common in Natural Language?," Econometrica, Econometric Society, vol. 64(2), pages 343-355, March.
    6. Jacques Crémer & Luis Garicano & Andrea Prat, 2007. "Language and the Theory of the Firm," The Quarterly Journal of Economics, Oxford University Press, vol. 122(1), pages 373-407.
    7. Lipman Barton L. & Seppi Duane J., 1995. "Robust Inference in Communication Games with Partial Provability," Journal of Economic Theory, Elsevier, vol. 66(2), pages 370-405, August.
    8. Stefano Demichelis & Jorgen W. Weibull, 2008. "Language, Meaning, and Games: A Model of Communication, Coordination, and Evolution," American Economic Review, American Economic Association, vol. 98(4), pages 1292-1311, September.
    9. repec:pit:wpaper:365 is not listed on IDEAS
    10. Koessler, Frederic, 2001. "Common knowledge and consensus with noisy communication," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 139-159, September.
    11. Koessler, Frederic, 2004. "Strategic knowledge sharing in Bayesian games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 292-320, August.
    12. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
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    Cited by:

    1. Penélope Hernández & Bernhard von Stengel, 2014. "Nash Codes for Noisy Channels," Operations Research, INFORMS, vol. 62(6), pages 1221-1235, December.

    More about this item


    Signaling game; Block-coding strategy; Separating equilibria;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design


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