Stability of Equilibria in Games with Procedurally Rational Players

One approach to the modeling of bounded rationality in strategic environments is based on the dynamics of evolution and learning in games. An entirely different approach has been developed recently by Osborne and Rubinstein (1998). This latter approach is static and equilibrium based, but relies on less stringent assumptions regarding the knowledge and understanding of players than does the standard theory of Nash equilibrium. This paper formalizes Osborne and Rubinstein's dynamic interpretation of their equilibrium concept and thereby facilitates a comparison of this approach with the explicitly dynamic approach of evolutionary game theory. It turns out that the two approaches give rise to radically different static and dynamic predictions. For instance, dynamically stable equilibria can involve the playing of strictly dominated actions, and equilibria in which strictly actions are played with probability 1 can be unstable. Sufficient conditions for the instability of equilibria are provided for symmetric and asymmetric games.Dynamic Stability, S(1) Equilibrium, Procedural Rationality, Evolutionary Games

Understanding reciprocity

This paper surveys the evolutionary game theoretic literature on reciprocity in human interactions, dealing both with long-term relationships and with sporadic interactions. Four basic themes, repetition, commitment, assortation, and parochialism, appear repeatedly throughout the literature. Repetition can give rise to the evolution of behavior that exhibits reciprocity-like features but a vast array of other behaviors are also stable. In sporadic interactions, reciprocity can be stable if the propensity to punish selfish actions can induce opportunists to cooperate, if reciprocators themselves behave opportunistically when they expect others to do so, or if matching is sufficiently assortative.Reciprocity, Evolution, Assortation, Commitment, Parochialism

Statistical Discrimination with Neighborhood Effects: Can Integration Eliminate Negative Stereotypes?

We introduce neighborhood effects in the costs of human capital acquisition into a model of statistical discrimination in labor markets. This creates a link between the level of segregation and the likelihood and extent of statistical discrimination. As long as negative stereotypes persist in the face of increasing integration, skill levels rise in the disadvantaged group and fall in the advantaged group. If integration proceeds beyond some threshold, however, there can be a qualitative change in the set of equilibria, with negative stereotypes becoming unsustainable and skill levels in both groups changing significantly. This change can work in either direction: skill levels may rise in both groups, or fall in both groups. Which of these outcomes arises depends on the population share of the disadvantaged group, and on the curvature of the relationship between neighborhood quality and the costs of human capital accumulation.Statistical discrimination, Neighborhood effects, Human capital spillovers

Inequality and segregation

Despite the decline in group inequality and the rapid expansion of the black middle class in the United States, major urban centers with significant black populations continue to exhibit extreme levels of racial separation. Using a theoretical framework in which individuals care both about the level of affluence and the racial composition of their communities, we show that no monotonic relationship exists between narrowing racial income disparities and segregation even when all households prefer somewhat integrated communities to segregated ones. Low racial inequality is consistent with extreme and even rising levels of segregation in cities where the minority population is large. Our results can help explain why racial segregration continues to characterize the urban landscape in the United States even though survey evidence suggests that all groups favor more integration than they did in the past.

Social Segregation and the Dynamics of Group Inequality

We explore the dynamics of group inequality when segregation of social networks places the initially less affluent group at a disadvantage in acquiring human capital. Extending Loury (1977), we demonstrate that (i) group differences in economic success can persist across generations in the absence of either discrimination or group differences in ability, provided that social segregation is sufficiently great, (ii) there is threshold level of integration above which group inequality cannot be sustained, (iii) this threshold varies systematically but non-monotonically with the population share of the disadvantaged group, (iv) crossing the threshold induces convergence to a common high level of human capital if the less affluent population share is suf- ficiently small (and the opposite, otherwise), and (v) a race-neutral policy that reduces the cost of acquiring human capital can expand the range over which reducing segregation can be Pareto-improving. JEL Categories: D31, Z13, J71segregation, networks, group inequality, human capital

Public Disagreement

Members of different social groups often hold widely divergent public beliefs regarding the nature of the world in which they live. We develop a model that can accommodate such public disagreement, and use it to explore questions concerning the aggregation of distributed information and the consequences of social integration. The model involves heterogeneous priors, private information, and repeated communication until beliefs become public information. We show that when priors are correlated, all private information is eventually aggregated and public beliefs are identical to those arising under observable priors. When priors are independently distributed, however, some private information is never revealed and the expected value of public disagreement is greater when priors are unobservable than when they are observable. If the number of individuals is large, communication breaks down entirely in the sense that disagreement in public beliefs is approximately equal to disagreement in prior beliefs. Interpreting integration in terms of the observability of priors, we show how increases in social integration can give rise to less divergent public beliefs on average. Communication in segregated societies can cause initial biases to be amplified and new biases to emerge where none previously existed. Even though all announcements are public and all signals equally precise, minority group members face a disadvantage in the interpretation of public information that results in medium run beliefs that are less closely aligned with the true state.

Inequality and Segregation

This paper explores the manner in which race and income interact to determine patterns of residential location in metropolitan areas. We use a framework in which individuals care about both the level of affluence and the racial composition of their communities, and in which there are differences in income both within and between groups. Three main findings emerge. First, conditional on income, black households experience lower neighborhood quality relative to whites at any stable equilibrium. Second, extreme levels of segregation can be stable when racial income disparities are either large or negligible, but unstable in some intermediate range. Third, there exist multiple stable equilibria with very different levels of segregation when racial income disparities are sufficiently small. These results hold even when preferences are pro-integrationist, in the sense that racially mixed neighborhoods within a certain range are strictly preferred by all households to homogenous neighborhoods of either type.Race, Inequality, Segregation

Preference Evolution and Reciprocity

This paper provides an evolutionary theory of reciprocity as an aspect of preference interdependence. It is shown that reciprocal preferences, which place negative weight on the payoffs of materialists and positive weight on the payoffs of sufficiently altruistic individuals can invade a population of materialists in a class of aggregative games under both individual selection and random matching. Such preferences are efficiency-reducing when they are rare and efficiency-enhancing when they are widespread, suggesting that they can persist even under group selection and assortative matching. In comparison with simpler specifications of preference interdependence (such as pure altruism or envy), the survival of such preferences is therefore less sensitive to details of the evolutionary selection process.Reciprocity, Evolution, Preference Interdependence

Inequality and segregation

This paper explores the manner in which race and income interact to determine patterns of residential location in metropolitan areas. We use a framework in which individuals care about both the level of affluence and the racial composition of their communities, and in which there are differences in income both within and between groups. Three main findings emerge. First, conditional on income, black households experience lower neighborhood quality relative to whites at any stable equilibrium. Second, extreme levels of segregation can be stable when racial income disparities are either large or negligible, but unstable in some intermediate range. Third, there exist multiple stable equilibria with very different levels of segregation when racial income disparities are sufficiently small. These results hold even when preferences are pro-integrationist, in the sense that racially mixed neighborhoods within a certain range are strictly preferred by all households to homogenous neighborhoods of either type.