<p>Following the literature of information asymmetry (see in Kyle among others), we have seen that many papers introduce a private signal, that is</p>

<p><span class="math-container">$$S=\tilde{v}+\tilde{e}$$</span>
where, <span class="math-container">$(\tilde{v},\tilde{e})$</span> are uncorrelated, <span class="math-container">$\tilde{v}\sim N(\bar{v},\sigma_{v}^2)$</span> denotes the payoff of the risky security that is traded among the traders in the market and <span class="math-container">$\tilde{e}\sim N(0,\sigma_{e}^2)$</span> is an error term (white noise if i am not mistaken). My question is, does this noisy signal increase or decrease the variance that the infroemd trader learns privately?</p>

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2020-06-13T16:07:25.397Z
$\sigma_{v}^2$ is the uninformed trader's prior variance (or, what is the same thing, the informed trader's "signal intensity"). If both traders are risk neutral, as in Kyle, $\sigma_{e}^2$ should play no role. In comparison, Grossman-Stiglitz starts with a similar set up for asset payoff but with CARA traders, and in that case $\sigma_{e}^2$ would enter into the endogenous constants determined in equilibrium.
Michael
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Private signals
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# Private signals

(Asked by: username_0 on 2020-06-13)

Following the literature of information asymmetry (see in Kyle among others), we have seen that many papers introduce a private signal, that is

$$S=\tilde{v}+\tilde{e}$$
where, $(\tilde{v},\tilde{e})$ are uncorrelated, $\tilde{v}\sim N(\bar{v},\sigma\_{v}^2)$ denotes the payoff of the risky security that is traded among the traders in the market and $\tilde{e}\sim N(0,\sigma\_{e}^2)$ is an error term (white noise if i am not mistaken). My question is, does this noisy signal increase or decrease the variance that the infroemd trader learns privately?

**Tags:** microeconomics, game-theory, mathematical-economics
> **Comments:**
> **username_1**: $\sigma_{v}^2$ is the uninformed trader's prior variance (or, what is the same thing, the informed trader's "signal intensity"). If both traders are risk neutral, as in Kyle, $\sigma_{e}^2$ should play no role. In comparison, Grossman-Stiglitz starts with a similar set up for asset payoff but with CARA traders, and in that case $\sigma_{e}^2$ would enter into the endogenous constants determined in equilibrium.  

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