The aim of this paper is to analyse the relation between the structure of a school-group and the problem of bullying. Bullying is a specific type of school violence, that occurs when a perpetrator or a group of perpetrators repeatedly attack a relatively helpless victim. This type of violence involves not only bullies and their victims, but also bystanders - other students who witness the process of bullying. Bullies’ behavior is planned and aimed at building social status in the group, and the suffering of the victims is not their main goal. Bystanders play a major role in the process, as their approval or disapproval can either encourage or discourage the bully. Behaviour of bystanders is analysed, with the use of a modifi ed structurally embedded coordination game, in order to show how the structure of the group can infl uence the process of bullying.

The article presents an important application of spatial generalization of Shapley value for simple games. Proposition presented by Shapley and Owen enables very interesting empirical interpretations. It has also strong contribution in the research of spatial voting models’ properties when there is no stable solution. This theorem enables us to fi nd the least unstable solution and therefore this is the valuable answer to the problem presented in the McKelvey’s theorem. The article presents the main postulates of the spatial voting theory, a geometric insight on which the general proof of Shapley-Owen theorem is based and empirical illustration of the presented concepts.

The gap between game-theoretic predictions and actual choices people make in, for instance, gaming experiments has been over-interpreted as evidence against rationality of players. I consider a version of the ultimatum game and examine its equilibria under different assumptions about players’ preferences. Using standard notions of rationality I show that the discrepancy between the “normative” and the “descriptive” cannot be established by a simple comparison of what is predicted by the equilibrium choices and the actual choices

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.

This study presents the results of an experiment on determinants of the strategy used by the participants and their profi tability. The study was based on N-person games in normal form 3x3. All games have clearly defined theoretical solution (the unique Nash equilibrium, which can be reached using the iterated elimination of strictly dominated strategy).The most important conclusion that can be drawn from this analysis is the failure of the theoretical model predictions based on Nash equilibrium. The use of non-equilibrium strategy for people with relatively little theoretical knowledge was due to the inability to find such a strategy. However, participants with a relatively high theoretical knowledge use non-equilibrium strategies deliberately expecting higher profi t. That is why theoretical knowledge is useful, but its use should be adapted to the situation in the real world. This enables players to achieve extra profits.

Indirect reciprocity explains exchange within large groups where a favour is returned by someone other than the beneficiary. Evolutionary games used to analyze this phenomenon are of two types: some authors show that simple strategies based on information about the past deeds of a partner are sufficient for indirect reciprocity to emerge; others indicate that complex strategies based on motivations have better dynamic properties. These complex strategies require knowledge of a considerable number of past interactions of partners and their former partners and use complicated reasoning. I present another approach to improve the performance of simple strategies using the ecological rationality concept. According to this approach, information can be useful in solving a problem even if it is not logically related to it. A probabilistic connection between information and an environmental criterion is sufficient. I present two simple strategies based on such connections. They use reference and experience. Neither needs information extending beyond the most recent interactions of chosen individuals. Using computer simulation I show that they can support indirect reciprocity. The strategies are particularly useful when conditions are unfavourable e.g. when the cost of helping is high and/or when information is difficult to obtain.

The aim of this paper is to analyse the behaviour of school violence bystanders from a game theoretical perspective. First, I describe the problem of bullying concentrating on the role of bystanders. Then I focus my attention on the witnesses of violence who either ignore a victim or try to defend him/her. A bystanders' decision consists of different elements and includes different stages, such as interpretation of the event and consideration of possible costs of intervention. In the article two models concerning two different stages of the decision making process are used to analyse the behaviour of bystanders: model of informational influence and a critical mass model. Informational influence model relates to interpretation of an act of violence as demanding or not demanding intervention. The observers decide whether intervening is an appropriate reaction, taking into account the behaviour of their classmates. This model shows the phenomenon of pluralistic ignorance and some factors that can influence its appearance. In the critical mass model, the bystanders assess the chances of success of their reaction in context of perception of the bully's power. This model is based on a public goods game model and it shows factors influencing the possibility of bystanders intervention.

The dynamic development of experimental economics, in particular of experimental work in game theory, has contributed to the questioning of the basic assumptions of classical game theory: the rationality and self-interest assumption. In response, those assumptions are being modified and more realistic models of human behavior in situations which can be described as games are being developed. The article provides a short overview of the models that abandon the self-interest assumption. An account is given mostly of the distributional models (i.a. inequity aversion models, model of quasi-maximin preferences). The results of the experiments designed to test the rival distributional models of social preferences are also presented in the article, as well as of the experiments that assess to the role played by intention-based reciprocity in motivating human behavior.