‘The friend of my enemy is my enemy’: Modeling triadic internation relationships

The evolution of internation relationships is studied by means of a mathematical model based on a popular rule of triadic interaction: “the friend of my friend is my friend, the friend of my enemy is my enemy, the enemy of my enemy is my friend, the enemy of my friend is my enemy”. The rule is shown to lead to the formation and preservation of unipolar and bipolar configurations of nations, with the strengths of relationships, both friendly and conflictual, intensifying through time. These results confirm speculations originally made in static, graph theoretic studies of the balancing of relationships within individuals, small groups and systems of nations.

[1]  Philip A. Schrodt.  Richardson's N-Nation Model and the Balance of Power , 1978 .

[2]  Morton A. Kaplan,et al.  System and Process in International Politics. , 1958 .

[3]  Claude Flament,et al.  Applications of Graph Theory to Group Structure , 1963 .

[4]  Harvey Starr,et al.  Inquiry, logic, and international politics , 1989 .

[5]  Julian O. Morrissette,et al.  An Experimental Study of the Theory of Structural Balance , 1958 .

[6]  F. Harary,et al.  A note on Freud's 'instincts and their vicissitudes'. , 1959, The International journal of psycho-analysis.

[7]  R. Rosecrance,et al.  Alliance and Structural Balance in the International System , 1985 .

[8]  F. Harary.  On the measurement of structural balance , 2007 .

[9]  Richard K. Ashley,et al.  The political economy of war and peace : the Sino-Soviet-American triangle and the modern security problematique , 1982 .

[10]  N. Rashevsky,et al.  Arms and insecurity , 1960 .

[11]  Frank Harary,et al.  A structural analysis of the situation in the Middle East in 1956 , 1961 .

[12]  F. Heider.  Attitudes and cognitive organization. , 1946, The Journal of psychology.

[13]  B. Healy,et al.  The Balance of Power in International History , 1973 .

[14]  John R. Freeman,et al.  Three-Way Street: Strategic Reciprocity in World Politics , 1990, American Political Science Review.

[15]  Jeffrey A. Hart,et al.  Symmetry and Polarization in the European International System, 1870 - 1879 , 1974 .

[16]  Harvey Starr,et al.  Conceptualizing “War” , 1983 .

[17]  Theresa C. Smith,et al.  Arms Race Instability and War , 1980 .

[18]  M. Ward.  Differential Paths to Parity: A Study of the Contemporary Arms Race , 1984, American Political Science Review.

[19]  Kenneth N. Waltz,et al.  Theory of International Politics , 1979 .

[20]  S. Grossmann,et al.  Chaos in the international arms race , 1989, Nature.

[21]  F. Harary,et al.  STRUCTURAL BALANCE: A GENERALIZATION OF HEIDER'S THEORY1 , 1977 .

[22]  A. F. Pollard,et al.  The Balance of Power , 1923 .