Changes

===One Lobby - Three States===

Again there is no incentive for the SIG to misreport <math>\theta_H\,</math> when it is the true state. When <math>\theta_M\,</math> is the true state we can perform the bias restriction calculation as before to get:

If we were just distinguishing between all three states this would hold for <math>\theta_L\,</math> too:

However, the SIG now has the option of reporting <math>\theta_L\,</math> or not <math>\theta_L\,</math>, in the latter case expecting the policy maker to implement <math>\frac{(\theta_H-\theta_M)}{2}\,</math>. In this case of partial information transmission we have to recalculate the bias restriction for when the real state of the world is <math>\theta_L\,</math> (For <math>\theta_M\,</math> the bias restriction is less binding). Here the SIG's ideal point is <math>\theta_L+\delta\,</math> so the SIG will not report falsely iff:

:<math>(\theta_L+\delta) - \theta_L \ge \frac{(\theta_H + \theta_M)}{2} - (\theta_L + \delta)\,</math>

This allows for an equilibrium with partial transmission of information - this can be possible when the bias conditions for full transmission are violated.

:<math>\,</math>