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With strategic interactions, a competition in pro-active measures ensues. The result is equivalent to the activist conducting a second-price auction for the opportunity to avoid a campaign. A sufficient condition (but not necessary) for this is that harm is emphasized over rewards. The race to the top leads to greater aggregate change than targeting a single firm.
 
 
===Target Reputation===
 
Suppose that targets can be either Hard or Soft, such that <math>0 < p_H < p_S < 1\,</math>, and can send a message message <math>m_H\,</math> or <math>m_S\,</math> to the activist that has a prior <math>\rho_0\,</math> that the target is Hard. Hard types never concede.
 
The prior probability that a target will concede is:
 
:<math>p_0 = \rho_0 p_H + (1-\rho_0)p_S\,</math>
 
 
Let <math>\sigma_H(j)\,</math> be the probability that type <math>j\,</math> sends a hard message, and assume that:
 
:<math>\sigma_H(H) = 1\,</math>
 
:<math>\sigma_H(H) < 1\,</math>
 
 
The posterior probability that the target is Hard given a signal <math>m_H\,</math> is:
 
:<math>\rho(m_H) = \frac{\rho_0}{\rho_0 + (1-\rho_0)\sigma_H(S)}\,</math>
 
 
 
and likewise:
 
:<math>\rho(m_S) = 0\,</math>
 
 
 
This gives us the activists belief that a target will concede given message <math>m_H\,</math>:
 
:<math>p(m_H) = \rho(m_H)p_H + (1-\rho(m_H))p_S \in [p_H, p_S]\,</math>
 
 
This results in the activist pursuing a campaign that:
*Is more aggressive when <math>m_S\,</math> is recieved
*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 been
 
This leads to a signalling strategy by the Soft firms such that sending the Hard type message is increasing in <math>\gamma and <math>p_S\,</math>, and decreasing in <math>\eta\,</math> and <math>\beta\,</math>.
 
 
===Contesting the Campaign===
 
Suppose that the firm can fight back with intensity <math>f \ge 0\,</math>, where <math>k(f)\,</math> is the cost of fighting (increasing and convex), and that <math>\theta \in (0,\infty)\,</math> is the public's support for the firm. Then the probability of success is defined as:
 
:<math>q = \frac{\theta h}{\theta h + f}\,</math>
 
 
The campaign lasts for a duration 1, and the target chooses to fight or not at time 0, A fight lasts for <math>\delta in \left[0,1\right)\,</math>.
 
 
====Extenstion to this Sub-Model====
 
Extentions include:
*Opportunistic Behavior - the activist makes the most aggressive demand it can if it wins
*Committment not to act opportunistically - the activist commits to get the firm to yield by choosing a campaign that avoids fighting
 
===Reputation===
 
There is a section on credibility and commitment that shows that reputation on behalf of the activist can sustain both credibility and commitment. At least I assume it does, I couldn't take anymore of this model.
 
==Summary==
 
The following is taken directly from the paper, but is a very useful summary of principal results:
#When its campaign is credible, an activist prefers an issue with high value and strong public support and a target that is responsive to a campaign, for which the cost of a campaign is low, and the cost of fighting is high.
#The campaign is more aggressive and more negative the weaker (more responsive) the target. For the example, the activist’s demand is more aggressive the more important is the issue, the more responsive is the target, and the lower the marginal costs of conducting the campaign.
#An activist prefers harm to reward because harm decreases investment in the targeted activity, whereas rewards alone can increase investment. Selection among potential targets leads to more negative campaigns, and harm is emphasized when rewards are costly to deliver.
#Activists that only provide rewards, only provide harm, and provide both can be present in the market for activism.
#An activist has an incentive through repetition to follow through on its campaign promises of reward and harm and for not exploiting targets that accept its demands.
#A potential target can forestall a campaign through self-regulation by changing its practices proactively but only if the activist can commit not to subsequently launch a campaign or if the proactive change shifts the activist to an alternative target. Self-regulation is plagued by a hold-up problem.
#With multiple potential targets the activist can generate a race to the top in proactive measures. This creates an incentive for an industry to act collectively. A potential target may develop a reputation for toughness to forestall a campaign, and the incentive to do so is strengthened by a moral hazard problem associated with revelation of its type. Conversely, a potential target that reveals itself as responsive or soft will be a more attractive target and campaigns will be more aggressive in their demands and threats. Potential targets thus have an incentive to signal that they are tough using both public and private politics strategies.
#In an infinitely-repeated game the activist can implement the optimal single-period campaign and has no incentive to shirk on the delivery of rewards and harm if its horizon is sufficiently long. For any given discount factor, however, the activist has an incentive to shirk on the delivery of harm in the optimal single period campaign if the probability of responsiveness is sufficiently high. Consequently, firms that are highly likely to be targets will not incur the single-period optimal campaign.
#If a campaign can be contested and the activist cannot commit to exploit a successful campaign, the target fights on the equilibrium path of play. If the activist can commit not to exploit a successful campaign,a responsive target concedes immediately and a recalcitrant target fights. When the cost of fighting is linear, the campaign is less aggressive when the activist can commit not to exploit a successful campaign.
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