The aim of the paper is to analyse group characteristic related to the problem of bullying, from a game-theoretical perspective. Bullying is a specific type of violence that happens in schools and it is a group phenomenon. The behaviour of bystanders can either encourage or discourage potential bullies. The paper presents a game-theoretical model of bystanders’ behaviour. It is assumed that bystanders feel morally obliged to defend the victim (internalised norm) but they also want to conform (conformity). In order to analyse the factors that can infl uence the scope of group reaction, a structurally embedded sequential coordination game was played for different initial conditions. Computer
simulations were conducted for networks of a specifi c type (Erdős–Rényi random graph). The main aim of analyses was to identify structural features of the group that can enable or block the intervention of bystanders. There is a non-linear relationship between network density and the scope of reaction. Both low and high density can make it harder for the bystanders to oppose the bully. Interactions between structural and non-structural features of the group have been observed. Depending on the strength of the internalized norm and conformity level, different structural characteristics may improve or lower the
chances of group intervention. As far as non-structural group characteristics are concerned, there is a positive relationship between the scope of group reaction and the strength of the internalized norm, whereas the level of conformity affects the chances of group intervention in a negative way.

Game theory and sociology have nearly sixty years of relations. Published 54 years ago in the U.S., and this year in Poland, Thomas C. Schelling Strategies of conflict was an important step in the perception of game theory by sociologists. Despite initial signs of enthusiasm, especially in the 60s, and the publication of a number of major sociological works referring to the theory of games, in the end position of game-theoretical approach in sociology turns out to be marginal, even within rational choice sociology. Using the background of the history of the relationship between sociology and game theory, this paper analyzes factors that make game theory a potentially attractive tool for a sociologist, and the reasons why sociologists rarely use it.