Template-type: ReDIF-Paper 1.0
Author-Name: Margaret Meyer
Author-Workplace-Name: Nuffield College and Dept. of Economics, Oxford University
Author-Email: margaret.meyer@nufield.ox.ac.uk
Author-Name: Inés Moreno de Barreda
Author-Workplace-Name: Dept of Economics, Oxford University
Author-Email: ines.morenodebarreda@economics.ox.ac.uk.
Author-Name: Julia Nafziger
Author-Workplace-Name: Dept. of Economics and Business, Aarhus University
Author-Email: jnafziger@econ.au.dk
Title: Robustness of Full Revelation in Multisender Cheap Talk

Abstract: This paper studies information transmission in a two-sender, multidimensional cheap
talk setting where there are exogenous restrictions on the feasible set of policies for the
receiver. Such restrictions, which are present in most applications, can, by limiting the
punishments available to the receiver, prevent the existence of fully revealing equilibria
(FRE). We focus on FRE that are i) robust to small mistakes by the senders, in that small
differences between the senders’ messages result in only small punishments by the receiver,
and ii) independent of the magnitudes of the senders’ bias vectors. For convex policy spaces
in an arbitrary number of dimensions, we prove that if there exists a FRE satisfying property
ii), then there exists one satisfying both i) and ii). Thus the requirement of robustness is,
under these assumptions, not restrictive. For convex policy spaces in two dimensions, we
provide a simple geometric condition, the Local Deterrence Condition, on the directions of
the senders’ biases relative to the frontier of the policy space, that is necessary and sufficient
for the existence of a FRE satisfying i) and ii). We also provide a specific policy rule, the
Min Rule, for the receiver that supports a FRE satisfying i) and ii) whenever one exists.
The Min Rule is the anonymous rule that punishes incompatible reports in the least severe
way, subject to maintaining the senders’ incentives for truthtelling, no matter how large
their biases. We characterize necessary and sufficient conditions for collusion-proofness of
a FRE supported by the receiver using the Min Rule and show that if such a FRE is not
collusion-proof, then no other FRE satisfying ii) can be collusion-proof. We extend our
existence results to convex policy spaces in more than two dimensions and to non-convex
two-dimensional spaces. Finally, our necessary and sufficient condition, as well as our
specific policy rule, can be easily adapted if the receiver is uncertain about the directions of
the biases and/or if the biases vary with the state of the world.
X-Classification-JEL: 
X-Keywords: 
Length: 51 pages
Creation-Date: 2016-06-22
Number: 2016-W02
File-URL: https://www.nuffield.ox.ac.uk/economics/papers/2016/MeyerMorenoNafziger23Mar2016.pdf
File-Format: application/pdf
Handle: RePEc:nuf:econwp:1602