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International Conference on Complex Systems (ICCS2006)

Mathematical model of conflict and cooperation with non-annihilating multi-opponent

Md. Mahbubush Salam Khan
Department of Information Management Science, The Universit

Kazuyuki Ikko Takahashi
Department of Political Science, Meiji University, Tokyo, Japan

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     Last modified: August 14, 2006

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

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

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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