An inexpert expert

ABSTRACT

We explore strategic information transmission when there is noise at the observation stage, when an expert observes signals, before he advises a policymaker. That is, the expert might be inexpert. We account for the fact that his signals might be totally uninformative, which is commonly known by players. We find that this inexpertise translates into a greater preference misalignment between players and that this yields a less informative equilibrium. We show that our results follow from the fact that the strategic effect of noise – the welfare change exclusive due to changes in the equilibrium partition – is always negative. Numerical simulations show that noise might be beneficial if the policymaker openly disagrees about noise chances. This makes the point that whether noise is beneficial or not crucially depends on how early in the game it arises, and also whether noise chances are commonly known by players or not.

KEYWORDS:

• Cheap talk
• bias
• informativeness
• noise

JEL CLASSIFICATION:

• D23
• D82

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ The uniform-quadratic case is the most commonly used set of assumptions in applications of the CS model (see Blume, Board, and Kawamura 2007; Ivanov 2010; Agastya, Bag, and Chakraborty 2014).

² The sender ex-ante expected utility is

${\mathcal{W}}_p^S(\mathit{b})=(1-\mathit{p})\sum _{\mathit{n}=1}^{\mathcal{N}(b)}{\int }_{{\mathit{x}}_{\mathit{n}-1}}^{x_n}{U}^S(a_n^{\star },\tilde{\theta },\mathit{b})\mathit{d}\tilde{\theta }+\mathit{p}\sum _{\mathit{n}=1}^{\mathcal{N}(b)}(x_n-x_{\mathit{n}-1})\int U^S(a_n^{\star },\mathit{\theta },\mathit{b})\mathit{d\theta }$

$\mathrm{As}-(a_n^{\star }-\tilde{\theta }-\mathit{b}{)}^2=-(a_n^{\star }-\tilde{\theta }{)}^2-b^2+2\mathit{b}(a_n^{\star }-\tilde{\theta }),\mathrm{then}$$-{\int }_{{\mathit{x}}_{\mathit{n}-1}}^{x_n}(a_n^{\star }-\tilde{\theta }-\mathit{b}{)}^2\mathit{d}\tilde{\theta }=-{\int }_{{\mathit{x}}_{\mathit{n}-1}}^{x_n}(a_n^{\star }-\tilde{\theta }{)}^2\mathit{d}\tilde{\theta }-b^2(x_n-x_{\mathit{n}-1})+2\mathit{b}(a_n^{\star }(x_n-x_{\mathit{n}-1})-{\int }_{{\mathit{x}}_{\mathit{n}-1}}^{x_n}\tilde{\theta }\mathit{d}\tilde{\theta })$. Using Equation 2 yields $-{\sum }_{n=1}^{\mathcal{N}(b)}{\int }_{{\mathit{x}}_{\mathit{n}-1}}^{x_n}(a_n^{\star }-\tilde{\theta }-\mathit{b}{)}^2\mathit{d}\tilde{\theta }=-{\sum }_{n=1}^{\mathcal{N}(b)}{\int }_{{\mathit{x}}_{\mathit{n}-1}}^{x_n}(a_n^{\star }-\tilde{\theta }{)}^2\mathit{d}\tilde{\theta }-b^2$ and ${\mathcal{W}}_p^S(\mathit{b})={\mathcal{W}}_p^R(\mathit{b})-b^2$, as in CS.

³ $\mathit{DE}=-(1-\mathit{p}){\sum }_{n=1}^{\mathcal{N}(b)}{\int }_{{\mathit{x}}_{\mathit{n}-1}}^{x_n}(a_n^{CS}-\mathit{\theta }{)}^2\mathit{d\theta }-\mathit{p}\int (a_0^{\star }-\mathit{\theta }-\mathit{b}{)}^2\mathit{d\theta }+{\sum }_{n=1}^{\mathcal{N}(b)}{\int }_{{\mathit{x}}_{\mathit{n}-1}}^{x_n}(a_n^{CS}-\mathit{\theta }{)}^2\mathit{d\theta }$.:

Additional information

Funding

José Antonio acknowledges financial support from FONDECYT #1221816.