|InterJournal Complex Systems, 1722
|Manuscript Number: |
Submission Date: 2006
|Mathematical model of conflict and cooperation with non-annihilating multi-opponent|
In biology and social science, conflict theory states that the society or organization functions in a way that each individual participant and its groups struggle to maximize their benefits, which inevitably contributes to social change such as changes in politics and revolutions. This struggle generates conflict interaction. Usually conflict interaction takes place in micro level i.e in individual interaction or in semi-macro level i.e. in group interaction. Then these interactions give impact on macro level. Here we would like to highlight the relation between macro level phenomena and semi macro level dynamics. We construct a framework of conflict and cooperation model by using group dynamics. First we introduce a conflict composition for multi-opponent and consider the associated dynamical system for a finite collection of positions. Opponents have no strategic priority with respect to each other. The conflict interaction among the opponents only produces a certain redistribution of common area of interests. The limiting distribution of the conflicting areas, as a result of `infinite conflict interaction for existence space, is investigated. We have developed this model based on some recent papers by V. Koshmanenko, which describes a conflict model for non-annihilating two opponents. By means of conflict among races how segregation emerges in the society is shown. We investigate our model by using empirical data. Next we extend our conflict model to conflict and cooperation model, where some opponents cooperate with each other in the conflict interaction. Here we investigate the evolution of the redistribution of the probabilities with respect to the conflict and cooperation composition, and to determine invariant states. Therefore, here we introduce a new mathematical procedure which is a realization of the above description. There are some previous works on conflict theory from game theoretical point of view. Our framework differ from traditional game theory. Our framework also differ from Schelling's segregation model in several respects. Particularly Schelling's results are derived from an extremely small population and his model is limited to only two race-ethnic groups. In our model limiting distribution depends on initial distribution and here we use stochastic dynamics which produce conflict among groups.
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