A DYNAMIC MODEL OF RESIDENTIAL SEGREGATION

Abstract

Using dimes and pennies on a checkerboard, Schelling (1971, 1978) studied the link between residential preferences and segregational neighborhood patterns. While his approach clearly has methodological advantages in studying the dynamics of residential segregation, Schelling's checkerboard model has never been rigorously analyzed. We propose an extension of the Schelling model that incorporates economic variables. Using techniques recently developed in stochastic evolutionary game theory, we mathematically characterize the model's long-term dynamics.

Keywords:

• Potential game
• Stochastic stability
• Agent-based simulation
• Residential segregation

I would like to thank Peyton Young for his guidance. I am also grateful to Carl Christ, Bruce Hamilton, Joe Harrington and seminar participants at the Brookings Institution and the Santa Fe Institute for helpful comments.

Notes

¹This corresponds to the “wage curve” in the labor market, which describes the negative relationship between wages and local unemployment (see, for example, Blanchflower and Oswald, 1994)

²Writing H − B _i  − W _i as the total number of vacancies, we are assuming that location i is always considered occupied when its price is calculated. We need this assumption to avoid “dynamic inconsistency”. Without this assumption, location i commands different' prices before and after an agent moves in, which seems odd. This assumption is innocuous especially when H is large.

³ Karlin and Taylor (1975) is a standard reference.

⁴Interested readers may want to try out the simulations presented here and many other variations. The Java Applet is available from the author upon request.