# An Extended Framework for Recovering From Trust Breakdowns in Online Community Settings
## Extended Framework
### Incentive Mechanism  
In order to encourage a victim and members of victim community to cooperate with a transgressor in future transactions, we propose two types of incentives:  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Positive Motivations** & **Victim** & **Victim Community** & **Transgressor Community** \\ (**PM**) & (\(F_{v}\)) & (\(F_{vc}\)) & (\(F_{tc}\)) \\ \hline \hline Intent (\(PM_{in}\)) & \(\bullet\) & & \\ History (\(PM_{hi}\)) & \(\bullet\) & \(\bullet\) & \\ Apology (\(PM_{ap}\)) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ Severity (\(PM_{se}\)) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ Importance (\(PM_{im}\)) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Positive motivations for evaluating forgiveness from the viewpoints of different forgiveness sources [19].  
* **Financial incentive**. A reparative action in the form of monetary compensation provided by the transgressor can be a primary response of functional recovery effort in business environment [34]. In addition, reducing the product or service price can make the transgressor more attractive and more competitive [35]. In this study, financial incentive is in the form of a one-time product's discount price offered by the transgressor to the victim and the victim community members. The value of the discount price is different depending on the value of forgiveness contributed by the the victim and the victim community members. For the victim, the value of the discount price can be calculated as follows: \[Disc_{v}=\omega_{v}F_{v}(x,y,Y)\times P_{t}(y),\] (4) where \(F_{v}(x,y,Y)\) is the forgiveness value evaluated by the victim \(x\) for the violation committed by the transgressor \(y\) who is a member of the community \(Y\). \(\omega_{v}\) is a weight factor of forgiveness value provided by the victim \(x\). \(P_{t}(y)\) is the product or service price offered by the transgressor \(y\). We calculate the value of discount price for members of victim community by assuming that each member contributes to the forgiveness assessment equivalently: \[Disc_{vc}=\frac{\omega_{vc}F_{vc}(X,y,Y)}{Nm_{vc}}\times P_{t}(y),\] (5) where \(F_{vc}(X,y,Y)\) is the forgiveness value aggregated from members of victim community \(X\) for the violation committed by the transgressor \(y\) who is a member of the community \(Y\). \(\omega_{vc}\) is a weight factor of a forgiveness value provided by the victim community \(X\). \(Nm_{vc}\) is the number of victim community members.
* **Reputational incentive**. The transgressor has an obvious incentive to be trustworthy in order to build up its reputation. A one-time discount price as a reparative monetary compensation can motivate cooperation resulting in increasing the transgressor's reputation. We evaluate reputational incentive from cooperation between the transgressor and the victim according to the expression: \[RI_{v}=\begin{cases}\frac{Disc_{v}}{P_{tmax}}\times(1-R_{old}^{t})&if\quad R _{old}^{t}\geq 0\\ \frac{Disc_{v}}{P_{tmax}}\times(1+R_{old}^{t})&if\quad R_{old}^{t}<0\end{cases}\] (6) where \(P_{tmax}\) is the maximum price of product/service offered by the transgressor and \(R_{old}^{t}\) is the transgressor's reputation after trust is violated or before considering forgiveness. The reputational incentive from cooperation between the transgressor and the victim community members can be aggregated as follows: \[RI_{vc}=\begin{cases}\frac{Disc_{vc}}{P_{tmax}}\times Nm_{vc}\times(1-R_{old}^ {t})&if\quad R_{old}^{t}\geq 0\\ \frac{Disc_{vc}}{P_{tmax}}\times Nm_{vc}\times(1+R_{old}^{t})&if\quad R_{old}^{ t}<0\end{cases}\] (7)  
Therefore, the total reputational incentives the transgressor could obtain from cooperation providing financial incentives to the victim and the victim community members is:  
\[RI_{total}=RI_{v}+RI_{vc} \tag{8}\]