## Bullies Gonna Bully

We often here the phrase “there are no innocent bystanders,” and although this may be true, we can see that it is rational to not interfere with bullying by using what we learned in class about game theory. Bullying is a phenomenon that occurs beyond elementary and grade school; in fact twenty-one percent of all workers have been targeted by bullies in the office. Considering that eighty-one percent of bullies are in supervisory roles, it is hard for victims to stand up for themselves when they it is very likely that they could lose their jobs, so the only real hope for these people is that someone intervenes.
But this doesn’t happen.
Most of the time when bullying is witnessed, people usually side with the bully. Also bullies will show completely different sides of their personality when conversing with their superiors and thus will have gained a respectable reputation in the workplace. But outside of these circumstantial events, we know that no one wants to tattle on the bullies because it doesn’t benefit the snitcher – or at least not as much as it would an “innocent bystander.”
The argument follows the same logic that we went over in class about witnessing crime. If n people observe bullying, the value that people obtain if it is reported is V>0 since removing bullies should allow for a happier work environment. If the bully is not reported, then we get a value of 0 because nothing is changed and the cost for the person reporting the bullying is C>0 because nobody likes a snitch. For the sake of this argument we say that V>C though the cost could be higher especially if the bully being reported is in a supervisory role.
In a mixed strategy Nash Equilibrium we set the payoff to reporting equal to the payoff for not reporting. We have V-C = 0*Pr(No one else reports) + V*Pr(someone else reports). This is equivalent to the expression V-C = V*(1-Pr(no one else reports)). Through algebra we see that Pr(no one else reports) = C/V. This makes sense: if the cost is higher than the Value obtained, then no one should report because negative value is less than 0 which is what the snitch could have gotten if no one reported. As the cost gets smaller, the probability that someone reports should get higher since you get closer and closer to reaching the full value V.
Now we can model the probability that you should report by (1-P)^(n-1) = C/V. P is the probability that you report so 1-P is the probability that you do not report. Take this to the (n-1) power because there are n-1 people besides you. Set this equivalent to the total probability that no one else reports. From this we get that P = 1-(C/V)^(1/(n – 1)) and we can see that P goes to 0 as the number of people n increases.
Remember that this is only for the case that the cost is less than the value obtained from turning in a bully, but in most cases the cost is probably higher than the value in which case no one should report. Therefore logic seems to suggest that we let bullies bully unhindered; only thirteen percent of bullies are ever punished or terminated. So can we solve this problem? In the current system, someone would have to bite the bullet for the greater good of the office. But otherwise, bullies gonna bully.

We often here the phrase “there are no innocent bystanders,” and although this may be true, we can see that it is rational to not interfere with bullying by using what we learned in class about game theory. Bullying is a phenomenon that occurs beyond elementary and grade school; in fact twenty-one percent of all workers have been targeted by bullies in the office. Considering that eighty-one percent of bullies are in supervisory roles, it is hard for victims to stand up for themselves when they it is very likely that they could lose their jobs, so the only real hope for these people is that someone intervenes.

But this doesn’t happen.

Most of the time when bullying is witnessed, people usually side with the bully. Also bullies will show completely different sides of their personality when conversing with their superiors and thus will have gained a respectable reputation in the workplace. But outside of these circumstantial events, we know that no one wants to tattle on the bullies because it doesn’t benefit the snitcher – or at least not as much as it would an “innocent bystander.”

The argument follows the same logic that we went over in class about witnessing crime. If n people observe bullying, the value that people obtain if it is reported is V>0 since removing bullies should allow for a happier work environment. If the bully is not reported, then we get a value of 0 because nothing is changed and the cost for the person reporting the bullying is C>0 because nobody likes a snitch. For the sake of this argument we say that V>C though the cost could be higher especially if the bully being reported is in a supervisory role.

In a mixed strategy Nash Equilibrium we set the payoff to reporting equal to the payoff for not reporting. We have V-C = 0*Pr(No one else reports) + V*Pr(someone else reports). This is equivalent to the expression V-C = V*(1-Pr(no one else reports)). Through algebra we see that Pr(no one else reports) = C/V. This makes sense: if the cost is higher than the Value obtained, then no one should report because negative value is less than 0 which is what the snitch could have gotten if no one reported. As the cost gets smaller, the probability that someone reports should get higher since you get closer and closer to reaching the full value V.

Now we can model the probability that you should report by (1-P)^(n-1) = C/V. P is the probability that you report so 1-P is the probability that you do not report. Take this to the (n-1) power because there are n-1 people besides you. Set this equivalent to the total probability that no one else reports. From this we get that P = 1-(C/V)^(1/(n – 1)) and we can see that P goes to 0 as the number of people n increases.

Remember that this is only for the case that the cost is less than the value obtained from turning in a bully, but in most cases the cost is probably higher than the value in which case no one should report. Therefore logic seems to suggest that we let bullies bully unhindered; only thirteen percent of bullies are ever punished or terminated. So can we solve this problem? In the current system, someone would have to bite the bullet for the greater good of the office. But otherwise, bullies gonna bully.