Coordination through ambiguous language

TL;DR

This paper models how players coordinate in finite games using ambiguous natural language signals, showing that ambiguity leads to subjective correlated equilibria, extending traditional coordination models.

Contribution

It introduces a formal framework for understanding coordination via ambiguous language signals and demonstrates how ambiguity results in subjective correlated equilibria.

Findings

Ambiguity in language leads to subjective correlated equilibria.

Self-enforcing strategies induce correlated equilibria without ambiguity.

Language ambiguity affects players' perceptions and coordination outcomes.

Abstract

We provide a syntactic construction of correlated equilibrium. For any finite game, we study how players coordinate their play on a signal by means of a public strategy whose instructions are expressed in some natural language. Language can be ambiguous in that different players may assign different truth values to the very same formula in the same state of the world. We model ambiguity using the player-dependent logic of Halpern and Kets (2015). We show that, absent any ambiguity, self-enforcing coordination always induces a correlated equilibrium of the underlying game. When language ambiguity is allowed, self-enforcing coordination strategies induce subjective correlated equilibria.