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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.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 76 (2012)
Issue (Month): 2 ()
Pages: 738-752

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Handle: RePEc:eee:gamebe:v:76:y:2012:i:2:p:738-752
DOI: 10.1016/j.geb.2012.08.009
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Rubinstein,Ariel, 2000. "Economics and Language," Cambridge Books, Cambridge University Press, number 9780521593069, September.
  2. Rubinstein, Ariel, 1996. "Why Are Certain Properties of Binary Relations Relatively More Common in Natural Language?," Econometrica, Econometric Society, vol. 64(2), pages 343-55, March.
  3. Frederic Koessler, 2000. "Common Knowledge and Consensus with Noisy Communication," Econometric Society World Congress 2000 Contributed Papers 0887, Econometric Society.
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  5. 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.
  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. Board, Oliver J. & Blume, Andreas & Kawamura, Kohei, 2007. "Noisy talk," Theoretical Economics, Econometric Society, vol. 2(4), December.
  8. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-51, November.
  9. Koessler, Frederic, 2004. "Strategic knowledge sharing in Bayesian games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 292-320, August.
  10. Stefano Demichelis & Jörgen Weibull, 2009. "Language, meaning and games A model of communication, coordination and evolution," Working Papers hal-00354224, HAL.
  11. Yaron Azrieli & Ehud Lehrer, 2004. "Categorization generated by prototypes -- an axiomatic approach," Game Theory and Information 0405003, EconWPA.
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