Structure of the most informative asymmetric equilibrium and bounded number of truthful senders

Determine whether, in the cheap-talk model with one receiver and N senders defined in Section 2 (three states with a disagreement state θ2, binary private signals s∈{ℓ,h}, and binary messages approve/reject), the asymmetric perfect Bayesian equilibria that transmit the most information to the receiver have the following structure: a subset of senders report truthfully (approve on signal h and reject on signal ℓ) while the remaining senders disregard their signals; and prove that the number of senders who report truthfully is bounded by a finite constant independent of N.

Background

The paper studies a cheap-talk communication model with a single receiver and multiple senders, each receiving i.i.d. noisy binary signals about an unknown state with three possible values, including a disagreement state where senders and the receiver have misaligned preferences. The main analysis and results focus on symmetric equilibria, establishing that with a large number of senders, each sender’s message must be almost uninformative and the receiver cannot fully learn the state.

In the concluding remarks, the authors raise the issue of asymmetric equilibria, where senders may adopt different strategies. Leveraging insights from their results and related literature on sequential voting and common-interest voting, they conjecture a particular structure for the asymmetric equilibrium that maximizes information transmission: some senders tell the truth while others ignore their signals, with the number of truthful senders bounded independently of N. Formalizing and proving this conjecture would extend the paper’s core insights beyond symmetric equilibria.