Abstract
We introduce social interactions into the Schelling model of residential choice; these interactions take the form of a Prisoner's Dilemma game. We first study a Schelling model and a spatial Prisoner's Dilemma model separately to provide benchmarks for studying a combined model, with preferences over like-typed neighbors and payoffs in the spatial Prisoner's Dilemma game. We find that the presence of these additional social interactions may increase or decrease segregation compared to the standard Schelling model. If the social interactions result in cooperation then segregation is reduced, otherwise it can be increased.
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Notes
Another interpretation of Frost's line is that residents prefer privacy or clear boundary demarcations over social interaction with their neighbors. However, the issue of taste for privacy is not included in the model.
Clearly education levels of both people and the neighborhoods they live in can help determine their trust levels, their attitudes toward other races, and their willingness to engage in neighboring. Here we do not explore the role of income or other class-related variables.
However, interestingly, this finding did not hold for whites in the sample; heterogeneity appeared to increase feelings of distrust for whites. These findings are clearly complicated by the fact that interactions occur within the context of minority–majority relationships.
Frank [1999] also points out that social interaction can lead to consumption “arms races” among neighbors, which can negatively impact feelings of well-being.
The introduction to Schweitzer et al. [2002] provides a nice overview of the literature on cooperation in the PD.
In addition, wrapping or not wrapping edges has been shown not to be crucial to the emergence of segregation in the Schelling model [Pancs and Vriend 2007].
Since agents are randomly placed on the board, when we say that agents are selected “in turn,” we mean that we begin with “agent 1” who could be located anywhere, then we go to “agent 2,” who could be anywhere, then on to “agent 3,” etc. Then we repeat this process starting with “agent 1.”
A run going for 100,000 iterations means that agents have up to 790 opportunities to move. A run going for this many observations is quite rare. Furthermore, if no agents move in a round that does not mean they would not move in future rounds, but we end the game at that point because it is sufficiently close to being an equilibrium.
Schelling [1971] refers to this measure as the “Share.”
Our measure of segregation produces qualitatively similar results as other measures commonly used in empirical studies such as the Dissimilarity Index [Duncan and Duncan 1955]. Also note that most of these commonly used measures are not amenable to our population. For instance, the Dissimilarity index is sensitive to neighborhood size. If one is working with a city population in the thousands or hundred-thousands with hundreds or thousands of neighborhoods (as is common in many large cities) the sensitivity is reduced. However, the Dissimilarity index would be sensitive to the choice of neighborhood size for the population size used here.
Note that agent movement can create different outcomes if agents can compare PD payoffs across locations. We do not address this type of movement here since it is not directly relevant for the comparison with the combined game section below. Furthermore, we also find that if agents move to new locations at random, there is no qualitative difference with the results presented here.
Our rule differs slightly from that of Nowak et al. [1994]. Their rule has an agent's probability coming from the sum of the payoffs of agent i's neighbors over all of the games played by the neighbors. In contrast, we only use the neighbor's payoffs resulting from the game played with agent i. The primary reason is that we assume that agent i can directly view his neighbor's payoff from playing the PD game with agent i but cannot view the payoff that a given neighbor receives from playing with his additional neighbors. Thus, we are restricting agent i's probability updating rule to include only items that i can directly observe from his own experience. As we demonstrate, our version of the rule only has two equilibria: all-cooperate or all-defect. Their rule has an additional mixed equilibria where defectors and cooperators co-exist.
We have checked other initial conditions such as p i =1/2 for all i, and other similar initial distributions, and have found the results to be qualitatively similar.
Note that the system running for 100,000 iterations is statistically rare, occurring roughly 5 percent or less across C payoffs.
There is no relationship between percent Similarity and number of periods till equilibrium in the all-defect case. Results available upon request.
For brevity, we do not present the results of convergence rates vs C; they are available upon request.
Note that we limit φ to a value less than but close to D/B=1.00333; this is the largest value for φ for which both the all-cooperate and all-defect equilibria exist.
Interestingly, the relationship between φ and defection appears to be relatively weak. For φ>1, defection rates are slightly above those for φ⩽1, for all values of C. We do not present these results here.
References
Aktipis, C. Athena . 2004. Know When to Walk Away: Contingent Movement and the Evolution of Cooperation. Journal of Theoretical Biology, 231: 249–260.
Axelrod, Robert . 1984. The Evolution of Cooperation. New York: Basic Books.
Clark, William.A.V., and Valerie Ledwith . 2005. Mobility, Housing Stress and Neighborhood Contexts: Evidence from Los Angeles, California Center for Population Research Working Paper, CCPR–005-005.
Cutler, David M., and Edward L. Glaeser . 1997. Are Ghettos Good or Bad? Quarterly Journal of Economics, 112 (3): 827–872.
Dokumaci, Emin, and William H. Sandholm . 2006. Schelling Redux: An Evolutionary Dynamic Model of Segregation, University of Wisconsin Working Paper.
Duncan, Otis, and Beverly Duncan . 1955. A Methodological Analysis of Segregation Indexes. American Sociological Review, 20: 210–217.
Farrell, Susan J., Tim Aubry, and Daniel Coulombe . 2004. Neighborhoods and Neighbors: Do They Contribute to Personal Well-being? Journal of Community Psychology, 32 (1): 9–25.
Fehr, Ernst, and Simon Gächter . 2000. Fairness and Retaliation: The Economics of Reciprocity. Journal of Economics Perspectives, 14 (3): 159–181.
Frank, Robert H . 1999. Luxury Fever: Why Money Fails to Satisfy in an Era of Excess. New York: Free Press.
Fudenberg, Drew, and Jean Tirole . 1991. Game Theory. Cambridge: The MIT Press.
Glaeser, Edward L., David I. Laibson, Jose A Scheinkman, and Christine L. Soutter . 2000. Measuring Trust. Quarterly Journal of Economics, 115 (3): 811–846.
Hales, David . 2001. Tag-based Cooperation in Artificial Societies, Ph.D. Thesis, University of Essex.
Janssen, Marco A . 2008. Evolution of Cooperation in a One-shot Prisoner's Dilemma Based on Recognition of Trustworthy and Untrustworthy Agents. Journal of Economic Behavior and Organization, 65 (3–4): 458–471.
Lee, Barret. A., R.S. Oropesa, and James W. Kanan . 1994. Neighborhood Context and Residential Mobility. Demography, 31 (2): 249–270.
Marschall, Melissa J., and Dietlind Stolle . 2004. Race and the City: Neighborhood Context and the Development of Generalized Trust. Political Behavior, 26 (2): 125–153.
Nowak, Martin A., and Karl Sigmund . 1998. Evolution of Indirect Reciprocity by Image Scoring. Nature, 393: 573–577.
Nowak, Martin A., and Robert M. May . 1992. Evolutionary Games and Spatial Chaos. Nature, 359: 826–829.
Nowak, Martin A., and Robert M. May . 1994. Spatial Games and the Maintenance of Cooperation. Proceedings of the National Academy of Science, 91: 4877–4881.
Pancs, Romans, and Nicolaas J. Vriend . 2007. Schelling's Spatial Proximity Model of Segregation Revisited. Journal of Public Economics, 91: 1–24.
Riolo, Rick L . 1997. The Effects of Tag Mediated Selection of Partners in Evolving Populations Playing the Iterated Prisoner's Dilemma, Santa Fe Institute Working Paper # 97-02-016.
Riolo, Rick L., Michael Cohen, and Robert Axelrod . 2001. Evolution of Cooperation without Reciprocity. Nature, 414: 441–443.
Schelling, Thomas C . 1969. Models of Segregation. American Economic Review, Papers and Proceedings, 59: 488–493.
Schelling . 1971. Dynamic Models of Segregation. Journal of Mathematical Sociology, 1 (2): 143–186.
Schweitzer, Frank, Laxmidhar Behera, and Heinz Mühlenbein . 2002. Evolution of Cooperation in a Spatial Prisoners Dilemma. Advances in Complex Systems, 5: 269–299.
Sethi, Rajiv, and Rohini Somanathan . 2004. Inequality and Segregation. Journal of Political Economy, 112 (6): 1296–1321.
Zhang, Junfu . 2004. A Dynamic Model of Residential Segregation. Journal of Mathematical Sociology, 28 (3): 147–170.
Acknowledgements
We thank Myong-Hun Chang for his helpful and insightful comments on an earlier draft. This paper was presented at one of the sessions sponsored by the NYC Computational Economics and Complexity Workshop at the 2007 Eastern Economic Association Meetings. We thank the session participants for their comments. Finally we thank three anonymous referees for their comments, which have helped to improve the paper. Any errors belong to the authors.
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M Barr, J., Tassier, T. Segregation and Strategic Neighborhood Interaction. Eastern Econ J 34, 480–503 (2008). https://doi.org/10.1057/eej.2008.26
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DOI: https://doi.org/10.1057/eej.2008.26