Abstract
BackgroundCooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with different preferences or beliefs. Yet, people from different social or cultural backgrounds often meet and interact. This can yield conflict, since behavior that is considered cooperative by one population might be perceived as non-cooperative from the viewpoint of another.Methodology and Principal FindingsTo understand the dynamics and outcome of the competitive interactions within and between groups, we study game-dynamical replicator equations for multiple populations with incompatible interests and different power (be this due to different population sizes, material resources, social capital, or other factors). These equations allow us to address various important questions: For example, can cooperation in the prisoner's dilemma be promoted, when two interacting groups have different preferences? Under what conditions can costly punishment, or other mechanisms, foster the evolution of norms? When does cooperation fail, leading to antagonistic behavior, conflict, or even revolutions? And what incentives are needed to reach peaceful agreements between groups with conflicting interests?Conclusions and SignificanceOur detailed quantitative analysis reveals a large variety of interesting results, which are relevant for society, law and economics, and have implications for the evolution of language and culture as well.
Highlights
In order to gain a better understanding of factors preventing or promoting cooperation among humans or other species, biologists, economists, social scientists, mathematicians and physicists have intensively studied game theoretical problems such as the prisoner’s dilemma and the snowdrift game [1,2,3,4,5]
To investigate the relevance of this for the resulting outcome and dynamics of social interactions, we will consider that people of different gender, status, age, or cultural background may have heterogeneous preferences
We will not go into these technicalities, but rather discuss representative examples of the different kinds of system dynamics and their relevance for social systems
Summary
In order to gain a better understanding of factors preventing or promoting cooperation among humans or other species, biologists, economists, social scientists, mathematicians and physicists have intensively studied game theoretical problems such as the prisoner’s dilemma and the snowdrift game ( known as chicken or hawkdove game) [1,2,3,4,5]. In all these games, a certain fraction of people or even everyone is expected to behave uncooperatively (see Fig. 1). This can yield conflict, since behavior that is considered cooperative by one population might be perceived as non-cooperative from the viewpoint of another
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