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\begin{cases}a_e=\phi,\Omega_{\phi} =1 \\mbox{ or } a_e=p,a_m=\sim f, \Omega_{\sim f} =1 \\mbox{ or } a_e=w\end{cases}\
\begin{cases}a_e=\phi,\Omega_{\phi} =1 \\mbox{ or } a_e=p,a_m=\sim f, \Omega_{\sim f} =1 \\mbox{ or } a_e=w \\\end{cases}
Austensmith Feddersen (2008) - Public Disclosure Private Revelation Or Silence (view source)
Revision as of 22:41, 24 May 2010
, 22:41, 24 May 2010no edit summary
*Announce a whistleblowing policy <math>C(h,s) \ge 0\,</math> where <math>h\,</math> is the history of event, and <math>C(\cdot,\cdot)\,</math> is a schedule of penalities that will be imposed on the employee. These penalties are bounded <math>\overline(c) \ge C(h,s) \ge 0\,</math>, and costless to implement for the manager.
*The ability to make credible threats - they can commit to the penalty schedule above.
*A history consists of the action by an employee, the response by the manager, and <math>v \,</math> if it becomes known to the manager.
*<math>v, t, s\,</math> are drawn by nature
*<math>v,t\,</math> are revealed to the employee, <math>s\,</math> is revealed to the manager
*The manager announces <math>C(h,s)\,</math>
*A type <math>t\,</math> employee chooses from <math>a_e(v,t) \in \{\phi,p.w\}\,</math>
**If <math>\phi\,</math> then nature reveals the violation with probability <math>q_{\phi}v\,</math>, where <math>q_{\phi} \in \left [0,1\right)\,</math>. The revelation of the information by nature is modelled as <math>\Omega_{\phi} \in \{0,1\}\,</math>
**If <math>p\,</math> then the manager chooses whether or not to fix the violation. Fixing costs the firm <math>\alpha v\,</math>, <math>\alpha >0\,</math>. Let <math>a_m(v,s) \in \{f,\sim f\}. If not fix (<math>\sim f\,</math>), then nature chooses to reveal the violation with probability <math>q_pv, where <math>q_p \in (q_{\phi},1)\,</math>, and again the revelation is modelled as <math>\Omega_{p} \in \{0,1\}\,</math>. If the violation is fixed it is never revealed.
**If <math>w\,</math>, then <math>v\,</math> becomes common knowledge (denoted <math>\Omega_{w} \equiv 1\,</math>).
0 & \mbox{ if } a_e=p,a_m=f \\
-\delta v & \mbox{ if }
-v & \mbox{ otherwise} \\
\end{cases}
-\alpha v & \mbox{ if } a_e=p,a_m=f \\
-(\alpha + \delta) v & \mbox{ if }
0 & \mbox{ otherwise} \\
\end{cases}
Thus, depending on the level of the violation and the manager's type there are two cutoffs, that are a function of the employees belief about a manager's type <math>\beta\,</math>: <math>T_{\phi p}\,</math> - the cutoff between keeping silent and reporting internally, and <math>T_{p w}\,</math> - the cutoff between reporting internally and whistleblowing.
**By <math>\dot{v}(0) > \hat{v}(0)\,</math> any type of manager will fix a violation that they are aware of
**Employees therefore prefer to report internally than whistleblow
**<math>T_{\phi p}(v,\beta) = 0 \,</math> and <math>T_{p w}(v,\beta) = 1\,</math>
*Medium violations: <math>v \in \left [\hat{v}, \dot{v} \right )\,</math>
**Any type of manager will fix the violation
**Therefore all employee prefer to report privately rather than blowing the whistle
**The employee will report rather than staying silent if their type is above the threshold: <math>t > T_{\phi p}(v,\beta)\,</math>
**<math>0 < T_{\phi p}(v,\beta) \,</math> and <math>T_{p w}(v,\beta) = 1\,</math>
*Minor violations: <math>v \in \left [0, \hat{v} \right )\,</math>
**Type 1 managers fix everything, and type 0 fix nothing. Likewise a type 1 manager wants to hear about everything a type 0 about nothing.
**Again the following only holds under the assumption of no penalties, so that the employees actions are indenpendent of the managers type.
**<math>T_{\phi p}(v,\beta)\,</math> is decreasiong in <math>\beta\,</math> in this range. Only employee types <math>t \,</math> greater than the threshold report, and as their belief about the type of the manager increases more violations are reported.
**<math>T_{p w}(v,\beta)\,</math> is increasing in both <math>v\,</math> and <math>\beta\,</math>. Only employee types <math>t\,</math> greater than the threshold whistleblow, and as the pertinent consideration is whether the violation is fixed, and the employee prefers to avoid the reputational cost.
