Segregation through Conflict
- 1 Department of Mathematics, Alabama A&M University, Normal, USA
- 2 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.
- Aoki, M. (2000). What are institutions and how should we approach them? http://www.dse.de/ef/instn/aoki.htm
- Aoki, M. (2001). Toward a comparative institutional analysis. Cambridge, MA: The MIT Press.
- 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
- Bruch, E., & Mare, R. D. (2005). Neighborhood choice and neighborhood change. Online Working Paper Series, Los Angeles: University of California.
- Gintis, H. (2000). Game theory evolving a problem-centered introduction to modeling strategic integration. Princeton, NJ: Princeton University Press.
- Hobbes, T. (1968) Leviathan, or the matter, forme, & power of a common wealth ecclesiasticall and civill. London: Penguin Books.
- Hume, D. (2000). A treatise on human nature. Oxford: Oxford University Press.
- Kandori, M. et al. (1993) Learning, mutation, and long run equilibria in games. Econometrica, 61, 29-56. http://dx.doi.org/10.2307/2951777
- Khan, M. S., & Takahashi, K. (2006). Mathematical model of conflict with non-annihilating multi-opponent. Journal of Interdisciplinary Mathematics, 9, 459-473.
- 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
- 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
- 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
- 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
- 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
- Morrow, J. D. (1994). Game theory for political scientists. Princeton, NJ: Princeton University Press.