Linguistic Indirectness in Public Cheap-Talk Games

TL;DR

This paper models social ties as graphs to analyze linguistic indirectness in public cheap-talk games, revealing how graph structure influences equilibrium message partitions and informativeness.

Contribution

It introduces a graph-based model of social ties affecting cheap-talk equilibria, deriving explicit results for trees and star graphs, and analyzing the impact of network structure on communication.

Findings

Stars maximize worth among trees, reducing equilibrium partitions.

Closed-form effective biases are derived for stars, with a critical threshold at 0.6.

Two-star configurations exhibit a precision flip at 8/15, affecting informativeness.

Abstract

We study linguistic indirectness when speakers attend to social ties. Social ties are modeled by a graph, and conferences are the sets of nodes that hear a message. Conference worth is a distance polynomial on the graph; allocations are given by the Myerson value of the conference-restricted worth, which yields the bargaining-power components for each participant. Aggregating these components gives an effective bias that, via a Partition-Threshold rule, pins down the number of equilibrium message partitions in a cheap talk game. Results: (i) among trees, stars maximize worth, leading to weakly fewer equilibrium partitions; (ii) on stars, we derive closed-form effective biases, with a witness-hub marginal effect of adding leaves changing sign at $\delta^{\ast}=0.6$; (iii) for two stars joined by one link, two-star (hub-hub) vs big-star (hub-leaf) precision flips at 8/15 for the same number of nodes; private leaf-leaf conferences are most informative.