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.

The paper presents an evolutionary model illustrating the dynamics that give rise to discriminatory social norms i.e. such rules of behaviour that fulfi l two conditions: (1) they treat differently actors having the same abilities and technical options, but differing in some arbitrary sense (2) they are supported by socially enforced sanctions. In the presented model both discrimination and social norms are necessary to solve a coordination problem that arises when the situation requires different actors to perform different tasks. The properties of behavioural rules relying on discrimination and leading to various degrees of inequality are analysed. It is demonstrated that in general norms ensuring equal payoffs are easier to stabilize, but unfair norms can also be stable.

The article examines the decision-making components of Jane Austen’s six major novels as reconstructed in Michael Chwe’s book and his argument that Austen was a precursor of game theory. In her novels, Austen describes an abundance of strategic situations in the mating process within the British higher classes. Social constraints made mating within this world a tough game due to harsh punishments for failure, especially for women, and severe limitation on signaling interest or sympathy. Austen cleverly investigates this environment and reconstructs many aspects of strategic behavior that have their counterparts in formal concepts of game and decision theory. While she hasn’t made contributions to theory per se, she deserves being named a precursor of applied strategic thinking and an expert on a particular strategically sophisticated social environment.

This paper revisits one of the most debated tales from the Old Testament, Jacob’s deception of his father Isaac, and models it in the framework of a Bayesian game. Solving for the equilibrium that occurs in the Torah reveals what conditions must hold for biblical characters to be willing to make the decisions that they make. The paper also examines how the protagonists’ decisions would have changed if they had held different values. The analysis sheds light on which interpretations of the biblical story hold the most weight when its characters maintain consistent beliefs and act upon them in a sequentially rational manner.

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.

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.

The aim of the article is to present the idea of common knowledge in the wide range: from intuitions to formal definitions. At the beginning the concept of common knowledge will be exemplified by several anecdotes. Then the hierarchical account (the most popular way of common knowledge formalization) will be presented. The additional advantage of hierarchical account is easiness of its description with use of the notions derived from logic and sciences. Next, Aumann's No Disagreement Theorem is presented. This theorem has greatly contributed to making economists and social researchers interested in common knowledge concept.At the end of the article several of many applications of common knowledge concept are indicated. Special weight is given to game theory as a primary domain for the concept. The role of common knowledge in the games solutions' seeking techniques is mentioned.

Auction theory belongs to one of the most important applications of game theory in economics. The possibility of presenting an auction as a game facilitates its strategic analysis and the comparison of different auction rules in relation to the player`s expected payoffs. The aim of this paper is to review basic knowledge concerning symmetric auctions for which we assume that all bidders possess the same amount of information concerning sold objects and all bidders` valuations are independent as well as identically distributed random variables. The first part of this paper is devoted to unit object auctions. We will present strategic analysis of the family of such auctions within the model proposed by Riley and Samuelson (1981). The second part of the thesis will be devoted to the description of different types of multiple object auctions: the simultaneous ascending auction and the Anglo-Dutch auction which have been created to sell telecommunication licenses, the combinatorial auction, during which buyers receive the possibility to place their offers on sets of items, and finally the double auction in which many buyers and sellers participate.