# An Extended Framework for Recovering From Trust Breakdowns in Online Community Settings
## 4 Experiments and Results
### Experiment 1: Robustness Evaluation  
The purpose of this experiment is to examine how robust the e-marketplace can operate as the number of untrustworthy service providers continuously increases over time and new service providers are not allowed to join the marketplace. The number of service providers is initially set to 50 and they are all trustworthy. However, at the end of each time period, some defective service providers will become untrustworthy and will be forced to leave the marketplace. As a result, the number of untrustworthy service providers continuously increases and ultimately leads to the e-marketplace failure due to the lack of trustworthy service providers. In the first sub-experiment, we compare the average reputation values of service providers in different e-marketplaces. The average reputation value is calculated only from the reputation of trustworthy service providers. Before the collapse of the e-marketplaces as shown in Figure 2a, the e-marketplace incorporating our framework has a more stable average reputation value and a longer period of interaction time than all other e-marketplaces. The average reputation values in ALLD and Griffiths nosolve to the lowest value much quicker, by about three times compared to ALLC and four times compared to our framework. In the second sub-experiment, we examine the numbers of market transactions generated at different time periods. The results are shown in Figure 2b. At the beginning, all e-marketplaces can successfully generate market transactions as all service providers are trustworthy. Over time, as the numbers of untrustworthy service providers increase, the transaction volumes in ALLD drop much more quickly while ALLC and the e-marketplace incorporating our framework decrease at a slower pace. A considerably different result can be observed in Griffiths where the maximum number of market transactions can be generated in each time step as long as there are trustworthy service \begin{table}
\begin{tabular}{l l} \hline \hline Number of service providers & 50 \\ Number of consumers & 100 \\ Number of products & 1000 \\ Service providers’ price of product & [100, 200] \\ Consumers’ price of product & [200, 250] \\ Reputation value of service providers & [\(-\)1, 1] \\ Initial reputation value of service providers & 0.5 \\ Service providers’ reputation fading factor (\(\Gamma_{sp}^{t=0}\)) & 0.2 \\ Service providers’ reputation fading factor (\(\Gamma_{sp}^{t=1}\)) & 0.8 \\ Consumers’ utility scaling factor (\(\lambda\)) & 5 \\ Consumers’ utility & [\(-\)1000, 1000] \\ Maximum defective service providers & 5 \\ Number of forgiveness interventions (\(\eta\)) & 2 \\ Forgivability threshold (\(F_{threshold}\)) & 0.5 \\ Cooperation threshold (\(C_{threshold}\)) & 0.5 \\ Forgiveness contribution weight factors (\(\omega_{v},\omega_{vc}\)) & 0.5,0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of experimental parameters. providers available to consumers. Otherwise, we can notice a sudden drop of transaction volumes as the e-marketplace only performs by defective service providers. In the third sub-experiment, we compare the numbers of untrustworthy service providers as time progresses. It can be seen in Figure 3a that the numbers of untrustworthy service providers increase constantly to the point that trustworthy service providers are no longer available to all consumers. However, the increasing rate of number of untrustworthy service providers in the e-marketplace incorporating our framework is much less than that in ALLD, Griffiths and ALLC. In other words, for the e-marketplace in which new service providers are not allowed to join, our framework can improve the e-marketplace to operate more efficiently than other approaches. In the fourth sub-experiment, we compare the utilities that all consumers obtain at different time points calculated by using Equation (13).