Abstract
Bullying in school is a serious problem in Japan as well as in most other countries. Bystanders rarely report instances of bullying to teachers, parents and other authorities. In this paper, we model bystander behavior by utilizing the theory of non-cooperative games, which assumes that bullying acts are stopped by a classroom teacher only when more than a certain number of students report the instances. Every bystander stands to gain from the resolution of bullying activity. But when a bystander reports this activity, she will have to deal with psychological and/or physical costs if the total number of reports falls below the required minimum. Under this structure of payoffs in our “bullying game” it can be shown that if all bystanders maximize their expected payoffs, there are two stable symmetric Nash equilibria. At one equilibrium, all bystanders report the instances of bullying to their teacher, and at the other equilibrium, no one reports. We conducted a series of experiments in which subjects played our “bullying game” under various values of parameters. The results of our experiments support the expected payoff-maximizing behavior of bystanders. Based on this verification of expected-payoff maximizing behavior through experiments, we develop guidelines for policies which could serve to increase reporting activity of bystanders and dissolve bullying activity. These include reducing the threshold number for reporting from students, increasing the disutility of students' observing bullying behavior, mitigating the psychological and/or physical costs for the reporting of bullying, and scale down of class size. The effectiveness of each policy is then analyzed theoretically and compared with the other alternatives.
