The Triadic Conflict:

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  • SUZUKI Tetsutada
    Graduate School of Decision Science and Technology<BR>Tokyo Institute of Technology

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Other Title
  • トライアド・コンフリクト
  • トライアド・コンフリクト--ジンメル三者関係論のフォーマライゼーション
  • トライアド コンフリクト ジンメル サンシャ カンケイロン ノ フォーマライゼーション
  • ―ジンメル三者関係論の非協力ゲームによるフォーマライゼーション―
  • Non-cooperative Game Model of George Simmel's Formal Sociology

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Abstract

     Through all ages and countries, much is talked about the influence of the third person. One of the famous example is the historical event in China called by Gyohu-no-ri(If the two persons should quarrel, the third would be the one to profit from it). The German sociologist George Simmel considered the unique characters of social relationships consisted of three persons through the typical three forms of interaction: the impartial person and mediator, fish in troubled waters and divide and govern. The previous mathematical approach on the triadic relationship is, though, restricted to the coalition formation on the assumption of enforced agreement between players. The purpose of this paper is, therefore, to formulate the Simmel's classical work about three types into non-cooperative game models. The result of the analysis teaches us that (1) the equilibrium of the triadic conflict depends on the third person's capacity to arbitrate, appropriate and prohibit a quarrel between the two, (2) the more the capacity of the third toward the two persons increases, the less the third could govern the two, and (3) the triadic conflict models have a close affinity with the 'Hobbesian problem of order'.

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