Changes

Suppose that targets can be either Hard or Soft, such that with probability <math>0 < p_H < p_S < 1p_j\,</math>of being responsive, and can send a message message where <math>m_H\,0 < p_H </math> or p_S <math>m_S1\,</math> to the activist . The prior probability that has a prior target is H is <math>\rho_0p_0\,</math> that the target is Hard. Hard types never concede.

The prior ex ante probability that a target will concede is:

:<math>\sigma_H(HS) < 1\,</math>

:<math>\rho(m_H) = \frac{\rho_0}{\rho_0 + (1-\rho_0)\sigma_H(S)'}\,</math>

This gives us the activists activist's belief that a target will concede given message : :<math>m_Hp(m_S) = p_S\,</math>:

*Is more aggressive when <math>m_S\,</math> is recievedreceived*Is less aggressive when <math>m_H\,</math> is recieved*But the <math>m_H\,</math> campaign is still more aggresive than it would have beenreceived

This leads to a signalling strategy by the Soft firms such that sending the Hard type message to avoid the more aggressive campaign is increasing in <math>\gamma\,</math> and <math>p_S\,</math>, and decreasing in <math>\eta\,</math> and <math>\beta\,</math>. Less aggressive campaign result for Soft firms if it sends <math>m_H\,</math> than if it sends <math>m_S\,</math>, but the campaign given <math>m_H\,</math> is more aggressive than it would have been based on prior information.