Rajiv Sethi

Inequality and segregation

Despite declining 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 racial separation. Using a theoretical framework in which individuals care about both the affluence and the racial composition of neighborhoods, we show that lower inequality is consistent with extreme and even rising levels of segregation in cities in which the minority population is large. Our results can help explain why segregation continues to characterize the urban landscape even though survey evidence suggests that individuals favor more integration than they did in the past.

The Strategic Advantage of Negatively Interdependent Preferences

We study certain classes of supermodular and submodular games which are symmetric with respect to material payoffs but in which not all players seek to maximize their material payoofs. Specially, a subset of players have negatively interdependent preferences and care not only about their own material payoffs but also about their payoffs relative to others. We identify sufficient conditions under which members of the latter group have a strategic advantage in the following sense: at all intragroup symmetric equilibria of the game, they earn strictly higher material payoffs than do players who seek to maximize their material payoffs.

Evolution of interdependent preferences in aggregative games

We study the evolution of preference interdependence in aggregative games which are symmetric with respect to material payoffs but asymmetric with respect to player objective functions. Specifically, some players have interdependent preferences (in the sense that they care not only about their own material payoffs but also about their payoffs relative to others) while the remainder are (material) payoff maximizers in the standard sense.

Evolutionary stability and social norms

Abstract Self-interested behavior need not earn higher material payoffs than norm-guided behavior in strategic environments in which a recognized adherence to social norms can help solve the commitment problem. This insight can provide the basis for an evolutionary theory of social norms. If the composition of behaviors evolves under pressure of differential payoffs, a population consisting exclusively of optimizers may be unstable, and there may exist a multiplicity of attractors representing a variety of stable norms. Societies facing similar material conditions may therefore come to adopt distinct norms as a result of chance events or differences in initial conditions.

Endogenous regime switching in speculative markets

Abstract This paper examines a nonlinear disequilibrium model of price formation in speculative markets with two groups of speculators, fundamentalists and chartists. The behavior of the fundamentalists is stabilizing, whereas that of the chartists is destabilizing; a sufficiently high share of wealth in the hands of the latter group can cause attracting periodic orbits to arise. If information about fundamentals is costly to obtain, then chartists obtain higher pay-offs in a stable regime, while fundamentalists perform better in an unstable regime. This gives rise to endogenous regime switching: the market alternates between periods of stability and instability, with the transition from one regime to another determined endogenously through the evolution of wealth shares.

Behavioural Heterogeneity under Evolutionary Pressure: Macroeconomic Implications of Costly Optimisation

A model is developed in which a continuum of agents makes interdependent output decisions in a stochastic environment characterized by strategic complementarity. Two groups are distinguished: naive agents follow a costless adaptive expectations rule, while sophisticated agents incur an optimization cost to achieve self-fulfilling expectations. The paper studies the dynamics generated as the population composition evolves under pressure of differential payoffs. Sophisticated agents are favored if optimization is cheap or the stochastic environment highly variable but naive agents generally persist. A higher long-run share of sophisticated agents is associated with greater output variability and low output persistence. Copyright 1995 by Royal Economic Society.

Metacognitive Control and Optimal Learning.

The notion of optimality is often invoked informally in the literature on metacognitive control. We provide a precise formulation of the optimization problem and show that optimal time allocation strategies depend critically on certain characteristics of the learning environment, such as the extent of time pressure, and the nature of the uptake function. When the learning curve is concave, optimality requires that items at lower levels of initial competence be allocated greater time. On the other hand, with logistic learning curves, optimal allocations vary with time availability in complex and surprising ways. Hence there are conditions under which optimal strategies will be relatively easy to uncover, and others in which suboptimal time allocation might be expected. The model can therefore be used to address the question of whether and when learners should be able to exercise good metacognitive control in practice.

A Simple Model of Collective Action

Successful collective action is usually accompanied by explicit systems for punishing noncooperators. A simple model of collective action is presented in which such punishment opportunities are available, and some individuals have a taste for exercising them. The model suggests that many of the correlates of successful collective action in the commons management literature are endogenous, and it clarifies the channels through which others operate. It points to the importance of communication costs and asymmetries in power rather than wealth in explaining when collective action fails. Heterogeneity in the ability to inflict punishment or be hurt by it may result in collective action becoming infeasible, especially when there are increasing returns in the production of the public good, but there is a range of parameters in which heterogeneity is favorable to cooperation.

Inequality and Network Structure

This paper explores the manner in which the structure of a social network constrains the level of inequality that can be sustained among its members. We assume that any distribution of value across the network must be stable with respect to coalitional deviations, and that players can form a deviating coalition only if they constitute a clique in the network. We show that if the network is bipartite, there is a unique stable payoff distribution that is maximally unequal in that it does not Lorenz dominate any other stable distribution. We obtain a complete ordering of the class of bipartite networks and show that those with larger maximum independent sets can sustain greater levels of inequality. The intuition behind this result is that networks with larger maximum independent sets are more sparse and hence offer fewer opportunities for coalitional deviations. We also demonstrate that standard centrality measures do not consistently predict inequality. We extend our framework by allowing a group of players to deviate if they are all within distance k of each other, and show that the ranking of networks by the extent of extremal inequality is not invariant in k.

Evolutionary Stability in a Reputational Model of Bargaining

A large and growing literature on reputation in games builds on the insight that the possibility of one or more players being other than fully rational can have significant effects on equilibrium behavior. This literature leaves unexplained the presence of behavioral players in the first place, and the particular forms of irrationality assumed. In this paper we endogenize departures from rationality on the basis of an evolutionary stability criterion, under the assumption that rational players incur a cost which reflects the greater sophistication of their behavior. This cost may be arbitrarily small. Within the context of a reputational model of bargaining, we show that evolutionary stability necessitates the presence of behavioral players, and places significant restrictions on the set of behavioral types that can coexist. It is consistent, however, with a broad variety of outcomes ranging from immediate agreement to complete surplus dissipation. The long run population share of behavioral types is greatest at states in which surplus dissipation is either negligible or almost complete.