Abstract
The paper studies how common codes of artificial language in communication are developed in the laboratory. We find that codes emerging from an environment with more variable spatial positions tend to use a limited set of symbols to represent positions, whereas codes emerging from an environment with more variable geometric shapes tend to discriminate among shapes. The paper also experimentally shows that “language” affects the way its “speakers” share the view about a novel figure.
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06 July 2017
An erratum to this article has been published.
Notes
See Sect. 5 for a review of the literature on some language differences relevant for this paper.
Blume (2000, 2005) is the first to theoretically study optimal languages in sender–receiver games and coin the notions of learning and learning efficiency in such games. He shows that the structure of language facilitates learning and that the learning-efficient language may use the structure of the state space.
We also conducted several experimental sessions in the Hong Kong University of Science and Technology (HKUST) and the Shanghai University of Finance and Economics (SHUFE), involving 46 subjects. The results from these sessions are qualitatively the same as those reported in the current paper.
The exact question we used in the bonus round was “Here is a new figure that has never appeared in the previous rounds. Which of the following figures below describes this new figure better?”
We assume \(p_{\beta b}=0\) in order to investigate how players describe a novel state \(\beta b\) in our experimental study in the simplest way.
As discussed in the introduction, this assumption captures the limitation of human expressive power. Alternatively, Selten and Warglien (2007) and Hong et al. (2017) design laboratory experiments of communication games with unlimited messages, attempting to explore grammatical structures of artificial codes.
To see it, let \(q(\omega )\in M\) for all \(\omega \in \Omega\) denote the sender’s strategy, and \(y(m)\in \Omega\) for all \(m\in M\) denote the receiver’s strategy. Given any q, the receiver’s posterior belief becomes
$$\begin{aligned} \mu (\omega |m)=\frac{p_{\omega }1_{\{m\}}(q(\omega ))}{\sum _{\omega ^{\prime } \in \Omega }p_{\omega ^{\prime }}1_{\{m\}}(q(\omega ^{\prime }))} \end{aligned}$$where \(1_{\{m\}}\) is an indicator function. Let \({\overline{\Omega }}_{m} \equiv \{\omega :\forall \omega ^{\prime }\in \Omega ,\) \(\mu (\omega |m)\ge \mu (\omega ^{\prime }|m)\}\). The receiver’s best response is \(y(m)\in {\overline{\Omega }}_{m}\). The receiver indicates the state (or, one of the states) that maximize(s) the likelihood of successful communication. With appropriately chosen out-of-equilibrium beliefs (whenever they matter), for any \(\omega\), there can be no message \(m^{\prime }\ne m\) such that \(y(m^{\prime })=\omega \ne y(m)\), so that the sender has no incentive to deviate from this q.
Relatedly, in a Sender–Receiver coordination game, Cremer et al. (2007) derive efficient organizational codes that use precise words for frequent events and vague words for unusual ones.
In discussing our experimental findings on this issue, the last paragraph of Sect. 4 reviews the relevant literature.
For each player and in each round, the positions of these figures are randomly determined.
Participants are told that the order in which the two choices appear at the bottom of their screen is randomly determined.
Although the average payment is smaller than the standard amount paid to subjects in developed countries, the amount is sufficient to motivate participants from Wuhan University. A regular meal in the university canteen costs approximately US$ 1 only.
Periods \({-}1\) and 0 are the two practice rounds before the official rounds. While the time trends in Fig. 2 include the practice rounds, in the analysis below we focus on official rounds in which the subjects were incentivized.
The 100% success rate for non-rare figures in those groups suggests that the players learnt very fast in the beginning and developed stable common codes at the later stage. After 2 practice rounds, they quickly converged to the optimal languages.
The frequency of successful coordination in this bonus stage is 0.6.
The interpretation here is motivated by the following example from Nisbett (2003): Suppose that at a dinner, one asks another if he or she wants to drink more tea. In Chinese the question is usually “drink more?”, while in English the question would be “more tea?”
Experimental and empirical research on the Sapir–Whorf hypothesis has mainly examined the following two issues: the metaphorical relationship between space and time, and color perception (see, e.g., Boroditsky 2011 for a discussion of the literature).
Verbs in Korean, which are also salient, tend to come at the end of the sentences. See Tardif (1996).
See Footnote 20.
Cities in pre-modern China were not units of cooperation, and urbanization rate was constantly low. In Medieval Europe, rural settlements were organized as cities which are neither composed nor governed by kinship lines (Greif and Tabellini 2012).
For instance, jià and qŭ in Chinese correspond to different relations in marriage. The statements that A jià B and that C qŭ D, roughly speaking, imply that B and C are more dominant in the marriage relationships. For another example, while there is only one term “uncle” in English, there are so many different terms in corresponding Chinese, representing different kinship relations of uncles.
In this respect, closest to our work is Dessi and Zhao (2015) who theoretically study how differences in the social and economic environment can give rise to differences in psychological traits such as overconfidence, supported by evidence from 38 countries.
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Acknowledgements
We are grateful to the editor and two anonymous referees for thoughtful and constructive comments. We would also like to thank Te Bao, Andreas Blume, Keith Chen, Liang Guo, Wei Huang, Jaimie Lien, Eric van Damme, Songfa Zhong, and participants in many seminars and conferences for helpful comments. We thank financial support from the Hong Kong University of Science and Technology and Shanghai University of Finance and Economics. The paper builds on an earlier version of the working paper titled “An Economic Investigation of Linguistic Differences” as a joint effort with Wooyoung Lim, and still reflects our earlier collaboration.
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Funding was provided by Shanghai University of Finance and Economics (start-up grant).
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An erratum to this article is available at https://doi.org/10.1007/s10683-017-9534-3.
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Hong, F., Zhao, X. The emergence of language differences in artificial codes. Exp Econ 20, 924–945 (2017). https://doi.org/10.1007/s10683-017-9518-3
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DOI: https://doi.org/10.1007/s10683-017-9518-3