Higher-Order Uncertainty About Language∗

It has been frequently noted that successful language use depends on the interlocutors’ higher-order beliefs. David Lewis [21], for example, informally introduces common knowledge as part of his account of language as a convention. We, instead, formally model and study the effects of higher-order uncertainty about language. We find that in common-interest communication games higher-order uncertainty about language, while potentially resulting in suboptimal language use at any finite knowledge order, by itself has negligible ex ante payoff consequences. In contrast, with imperfect incentive alignment, higher-order uncertainty about language may lead to complete communication failure for any finite-order knowledge of language. ∗We have benefitted from comments by James Fisher, Sidartha Gordon, Kohei Kawamura, Anton Kolotilin, Shih En Lu, Ariel Rubinstein, Joel Sobel, Jonathan Weinstein and from seminar audiences at Simon Fraser University, University of Arizona, Universität Bielefeld, University of British Columbia, University of Southern California and Tel Aviv University. We owe special thanks to Stephen Morris for having urged us to examine the connection of our conception of uncertainty about language with David Lewis’s work.