Through the use of game theory, this paper has analysed the bystander effect and has given insights on the choice situations among the players. It has provided a mathematical understanding to complement the psychological side on why people are less inclined to help others when more people are present. Nonetheless, this research is not without limitations. By using the standardized n for the number of players, individual differences, such as different tendencies towards altruistic behaviour, are disregarded. These differences can either be because of inherited characteristics or because of cultural differences, e.g. growing up in an individualistic or collectivistic society. For example, rewards and punishments will have a bigger effect on reducing the bystander effect in collectivistic societies compared to individualistic societies (Leung & Bond, 1984). Further research on the bystander effect should therefore focus on differences in altruism, by either creating a game in which chance determines whether a bystander is altruistic or not altruistic and solve this VD with the Bayesian NE solution concept, or by letting the researchers choose the number of altruistic players.
Additionally, since this paper is neither an economic nor a criminological paper, it is limited in assigning feasible values to the rewards and punishment introduced in the game, making it difficult to apply the formula to real-life situations. For example, what constitutes a punishment and what value do we give that respective punishment? Furthermore, the probability for rewards and punishments were based on b < c and r < c respectively. However, this meant that it was impossible to look at the effects of b and r being higher than the cost of helping. As the mixed strategy NE is not suited for this problem, further research should use other solution concepts. Another controversial but noteworthy point is that the bystander effect, and explicitly the case of Catherine Genovese, are according to some portrayed much more dramatic than it actually was. Catherine’s brother claimed that some witnesses did try to help her and that there were not 37 eyewitnesses but only six, of which only two people saw the attack (Jancelewicz, 2016). This perspective indicates that more research on the concept of the bystander effect itself is needed. Modelling game theory cannot always predict real-life situations, since it includes many simplifications.