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How much ambiguity can persist? A complete characterization of neutrally stable states for an evolutionary proto-language game



In an evolutionary sender–receiver game that describes how signals become associated with objects (Hurford, 1989; Nowak and Krakauer, 1999), the set of evolutionarily stable states coincides with the set of strict Nash strategies—and a language is a strict Nash strategy if and only if it links each possible referent exclusively to 1 signal and vice versa (Trapa and Nowak, 2000). As a consequence, a language that displays homonymy (or synonymy)—the property that one signal is linked to more than one referent (or one referent to more than one signal)—cannot be an evolutionarily stable state. This seems to conflict with the results of the computer simulation reported in Nowak and Krakauer (1999) that lend support to the conjecture that a language in which the same signal is used for more than one object can be evolutionarily stable. This paper provides necessary and sucient conditions for a neutrally stable state of this game—and, importantly, these conditions directly characterize a single strategy—showing that a language displaying homonymy or synonymy, even though it fails to be evolutionarily stable (in the strict sense), may still satisfy neutral stability, explaining why an evolutionary process does not necessarily lead away from it.

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  • Christiane Pawlowitsch, 2005. "How much ambiguity can persist? A complete characterization of neutrally stable states for an evolutionary proto-language game," Vienna Economics Papers 0509, University of Vienna, Department of Economics.
  • Handle: RePEc:vie:viennp:0509

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    References listed on IDEAS

    1. Grossman, Sanford J & Hart, Oliver D, 1979. "A Theory of Competitive Equilibrium in Stock Market Economies," Econometrica, Econometric Society, vol. 47(2), pages 293-329, March.
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    4. Peter M. DeMarzo, 1993. "Majority Voting and Corporate Control: The Rule of the Dominant Shareholder," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 713-734.
    5. Dierker, Egbert & Dierker, Hildegard, 2010. "Welfare and efficiency in incomplete market economies with a single firm," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 652-665, September.
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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