تجزیه و تحلیل اقتصادی رفتار بی تفاوتی : نظریه و آزمایش

The apathy of bystanders often prevails when instances of bullying, hidden crime and extortion occur in communities such as schools, business work areas, underclass ghettos, prisons and the military. The present study models apathetic behavior as a non-cooperative game and attempts to verify this theory through experiments. Furthermore, our research suggests that the apathy of bystanders generally decrease as the number of citizens in a community decrease. In our experimental cases, if the number of members in a group decreases from 40 members to 20 members, the concerned and helpful behavior of bystanders increases by 21%.

Bullying can contribute to an environment of fear and intimidation in school and other places, and has become serious matters in the world (Olweus et al., 1999). For example, according to National Conference of State Legislatures in the U.S.A., 17 states enacted school safety laws concerning bullying and student harassment between 1994 and 2004. The OECD jointly with Norwegian Government and University held an International Policy Conference on School Bullying and Violence in 2004. According to a 1996-survey of 2900 middle and high school students by the Seoul Family Court in South Korea, about 90% of the students was physically threatened by other students (Ort, 1999). However, bystanders may not be willing to tattle the illegal activities to the school authorities. Bullying is also observed at workplace. The cost of violence and bullying at work is very large as well. For example, the UK nation-wide survey of workplace bullying reported that the bullied group was found to have higher absenteeism due to bullying and, the currently bullied group was found to have on average 7 days more off work in a year than those who were neither bullied nor had witnessed bullying taking place. Those who are bullied also decide to leave their organization as a result of their experience. This example of bullying in the UK could be appropriate for other countries as well (Martino, 2002 and Hoel et al., 2001). There are similar situations as bullying. In crime-ridden areas, people are extremely reluctant to testify against those whom they have observed robbing and killing because they expect that the criminals will not go to jail and will punish any witnesses that testify. Another situation may be political revolution. If you revolt and not enough others join you, you will be punished. If the number of people who revolt reaches a threshold, the revolt will succeed and revolutionaries will be rewarded rather than punished. The purpose of this paper is to address this question of why the apathy of bystanders predominates despites their compassionate feelings1. To this end, we formulate the phenomenon of bullying in a school as a non-cooperative n person game. This game is a kind of binary choice public goods game with threshold. We will also examine the relevance of our model by experiment. The rest of paper is organized as follows: Section 2 formulates the model. Section 3 derives three type Nash equilibria and examines the stability of the equilibrium by introducing a dynamic adjustment process. We consider policy implications in Section 4. Experiment study is reported in Section 5. Final section gives concluding remarks.

We model the apathy of bystanders as a non-cooperative game and show that there are exactly two symmetric pure strategy equilibria, all tattle and none tattle, and exactly one symmetric mixed strategy equilibrium. Under monotonic dynamic process, the pure strategy equilibria are both stable and the mixed strategy equilibrium is unstable. We also verify the theoretical adjustment process by experiments. The following policy implications are obtained. This analysis implies that in classroom and other communities such as work areas, prisons, the military and underclass ghettos, grouping the members into smaller groups may help to induce concerned and helpful behavior among members of these communities. That is, from Proposition 3-3, we see that the smaller the size of a community, the larger the probability of resolving the continuing illegal activities. And this result is not based on the general belief that a supervisor or a teacher can supervise the smaller group or classroom more easily than the larger group or classroom. Rather, the players choose to act as concerned and helpful with their decisions. Our research also implies that the following measures encourage bystanders to choose the concerned and helpful behavior. (i) The authorities, firms and schools are encouraged to advocate to members of communities that hidden crime, extortion and bullying are illegal activities and violations of human rights.13 This may increase the value of b (negative public goods) and according to Proposition 3-1, an increase in b encourages the concerned and helpful behavior of bystanders. (ii) Another measure is that the private cost c of tattling could be made as small as possible, even negative. (iii) According to our Proposition 3-2, if the threshold number t, the minimum necessary number of tattlers, decreases, the possibility of apathetic behavior also increases. (iv) It is implied that these measures will be more effective if they are introduced as early as possible. Because it is important that the initial probability of tattling by the bystanders, q0, exceed the critical probability q* which is the dividing probability between converting all tattle and none tattle.