Segregation through Conflict

Affiliation(s)

Department of Mathematics, Alabama A&M University, Normal, USA.

School of Political Economy, Meiji University, Tokyo, Japan.

Department of Mathematics, Alabama A&M University, Normal, USA.

School of Political Economy, Meiji University, Tokyo, Japan.

ABSTRACT

This paper begins by introducing the game theory to explain how an institution emerges. It then goes on to employ a conflict model, using the probability distribution introduced by Koshmanenko, to show how institutions emerge through mathematical formation. This is followed by a consideration of the authors’ development of a segregation simulation based on this conflict theory. An institution is defined as the equilibrium achieved through the segregation of conflicting groups (for example groups differing accord- ing to “race”, or language, education or income level among other factors). A simulation is made ex- plaining how equilibrium is reached through changing probability. This simulation also shows the dy- namics of an emerging new order.

This paper begins by introducing the game theory to explain how an institution emerges. It then goes on to employ a conflict model, using the probability distribution introduced by Koshmanenko, to show how institutions emerge through mathematical formation. This is followed by a consideration of the authors’ development of a segregation simulation based on this conflict theory. An institution is defined as the equilibrium achieved through the segregation of conflicting groups (for example groups differing accord- ing to “race”, or language, education or income level among other factors). A simulation is made ex- plaining how equilibrium is reached through changing probability. This simulation also shows the dy- namics of an emerging new order.

Cite this paper

Khan, S. & Takahashi, K. (2013). Segregation through Conflict.*Advances in Applied Sociology, 3,* 315-319. doi: 10.4236/aasoci.2013.38040.

Khan, S. & Takahashi, K. (2013). Segregation through Conflict.

References

[1] Aoki, M. (2000). What are institutions and how should we approach them?

http://www.dse.de/ef/instn/aoki.htm

[2] Aoki, M. (2001). Toward a comparative institutional analysis. Cambridge, MA: The MIT Press.

[3] Bayer, P. et al. (2004). What drives racial segregation? New evidence using census microdata. Journal of Urban Economics, 56, 514-535.

http://dx.doi.org/10.1016/j.jue.2004.06.002

[4] Bruch, E., & Mare, R. D. (2005). Neighborhood choice and neighborhood change. Online Working Paper Series, Los Angeles: University of California.

[5] Gintis, H. (2000). Game theory evolving a problem-centered introduction to modeling strategic integration. Princeton, NJ: Princeton University Press.

[6] Hobbes, T. (1968) Leviathan, or the matter, forme, & power of a common wealth ecclesiasticall and civill. London: Penguin Books.

[7] Hume, D. (2000). A treatise on human nature. Oxford: Oxford University Press.

[8] Kandori, M. et al. (1993) Learning, mutation, and long run equilibria in games. Econometrica, 61, 29-56.

http://dx.doi.org/10.2307/2951777

[9] Khan, M. S., & Takahashi, K. (2006). Mathematical model of conflict with non-annihilating multi-opponent. Journal of Interdisciplinary Mathematics, 9, 459-473.

[10] Koshmanenko, V. (2003). Theorem on conflicts for a pair of stochastic vectors. Ukrainian Mathematical Journal, 55, 671-678.

http://dx.doi.org/10.1023/B:UKMA.0000010167.63115.37

[11] Koshmanenko, V. (2004) . Theorem of conflicts for a pair of probability measures. Mathematical Methods of Operations Research, 59, 303-313. http://dx.doi.org/10.1007/s001860300330

[12] Massey, D. S., & Denton, N. A. (1987). Trends in the residential segregation of blacks, Hispanics, and Asians: 1970-1980. American Sociological Review, 52, 802-825.

http://dx.doi.org/10.2307/2095836

[13] Matsui, A. (1996). On cultural evolution: Social norms, rational behavior, and evolutionary game theory. Journal of The Japanese and International Economies, 10, 262-294.

http://dx.doi.org/10.1006/jjie.1996.0015

[14] Miller, V. P., & Quigley, J. M. (1990). Segregation by racial and demographic group: Evidence from the San Francisco Bay Area. Urban Studies, 27, 3-21.

http://dx.doi.org/10.1080/00420989020080011

[15] Morrow, J. D. (1994). Game theory for political scientists. Princeton, NJ: Princeton University Press.

[16] Schelling, T. C. (1969). Models of segregation. American Economic Review, Papers and Proceedings, 59, 488-493.

[17] Smith, A. (1976). The theory of moral sentiments. Oxford: Oxford University Press.

[18] Young, P. H. (1993). The evolution of conventions. Econometrica, 61, 57-84.

http://dx.doi.org/10.2307/2951778

[19] Young, P. H. (1998). Individual strategy and social structure. Princeton, NJ: Princeton University Press.

[20] Weibull, J. W. (1995). Evolutionary game theory. Cambridge, MA: The MIT Press.

[1] Aoki, M. (2000). What are institutions and how should we approach them?

http://www.dse.de/ef/instn/aoki.htm

[2] Aoki, M. (2001). Toward a comparative institutional analysis. Cambridge, MA: The MIT Press.

[3] Bayer, P. et al. (2004). What drives racial segregation? New evidence using census microdata. Journal of Urban Economics, 56, 514-535.

http://dx.doi.org/10.1016/j.jue.2004.06.002

[4] Bruch, E., & Mare, R. D. (2005). Neighborhood choice and neighborhood change. Online Working Paper Series, Los Angeles: University of California.

[5] Gintis, H. (2000). Game theory evolving a problem-centered introduction to modeling strategic integration. Princeton, NJ: Princeton University Press.

[6] Hobbes, T. (1968) Leviathan, or the matter, forme, & power of a common wealth ecclesiasticall and civill. London: Penguin Books.

[7] Hume, D. (2000). A treatise on human nature. Oxford: Oxford University Press.

[8] Kandori, M. et al. (1993) Learning, mutation, and long run equilibria in games. Econometrica, 61, 29-56.

http://dx.doi.org/10.2307/2951777

[9] Khan, M. S., & Takahashi, K. (2006). Mathematical model of conflict with non-annihilating multi-opponent. Journal of Interdisciplinary Mathematics, 9, 459-473.

[10] Koshmanenko, V. (2003). Theorem on conflicts for a pair of stochastic vectors. Ukrainian Mathematical Journal, 55, 671-678.

http://dx.doi.org/10.1023/B:UKMA.0000010167.63115.37

[11] Koshmanenko, V. (2004) . Theorem of conflicts for a pair of probability measures. Mathematical Methods of Operations Research, 59, 303-313. http://dx.doi.org/10.1007/s001860300330

[12] Massey, D. S., & Denton, N. A. (1987). Trends in the residential segregation of blacks, Hispanics, and Asians: 1970-1980. American Sociological Review, 52, 802-825.

http://dx.doi.org/10.2307/2095836

[13] Matsui, A. (1996). On cultural evolution: Social norms, rational behavior, and evolutionary game theory. Journal of The Japanese and International Economies, 10, 262-294.

http://dx.doi.org/10.1006/jjie.1996.0015

[14] Miller, V. P., & Quigley, J. M. (1990). Segregation by racial and demographic group: Evidence from the San Francisco Bay Area. Urban Studies, 27, 3-21.

http://dx.doi.org/10.1080/00420989020080011

[15] Morrow, J. D. (1994). Game theory for political scientists. Princeton, NJ: Princeton University Press.

[16] Schelling, T. C. (1969). Models of segregation. American Economic Review, Papers and Proceedings, 59, 488-493.

[17] Smith, A. (1976). The theory of moral sentiments. Oxford: Oxford University Press.

[18] Young, P. H. (1993). The evolution of conventions. Econometrica, 61, 57-84.

http://dx.doi.org/10.2307/2951778

[19] Young, P. H. (1998). Individual strategy and social structure. Princeton, NJ: Princeton University Press.

[20] Weibull, J. W. (1995). Evolutionary game theory. Cambridge, MA: The MIT Press.