A continuum of citizens with heterogeneous opportunity costs participate in a public protest, with well-defined demands. The government can concede at any time. As long as it does not, it shoulders a cost that is increasing in time and in participation rates. Apart from their collective demands, citizens enjoy a “merit reward” if the government concedes while they are actively participating. A protest equilibrium of the ensuing dynamic game must display: (a) a build-up stage during which citizens continuously join the protest, but the government ignores them, followed by (b) a peak at which the government concedes with some positive probability, failing which there is (c) a protracted decay stage, in which the government concedes with some density, and citizens continuously drop out. Citizens with higher opportunity costs enter later and exit earlier. While there are multiple equilibria, every equilibrium with protest has the above properties, and the set of all equilibria is fully described by a single pseudo-parameter, the protest peak time, which can vary within bounds that I characterize. Preliminary evidence from the Black Lives Matter movement supports the features that I extract from this model.
Segregation in different domains remains a pervasive social fact in contemporary societies. The lack of socioeconomic and racial diversity of interactions in schools and neighborhoods, and the exposure to like-minded ideological content can hinder a society's ability to embrace the value of diversity. This paper proposes a theory of segregation measurement based on the intensity and social diversity of pairwise interactions. In our framework societies are described by a space of locations and social groups, and a distribution of agents across locations and groups. Locations can be schools in a district, residences in a city or platforms such media outlets, where individuals interact. Social groups can defined by race, socioeconomic status, political ideology, or any other social identity. We axiomatize measures that can be expressed as a weighted sum across pairs of an interaction intensity that depends on locations and value of pairwise interactions that depends on social identities. We prove that the index is proportional to a correlation between spatial and social distances. The framework is illustrated with two applications. The first one measures socioeconomic segregation in Chilean schools, showing variation across cities and grades. The second one measures ideological segregation in the consumption of media outlets, for different media platforms -newspapers, radio, TV- for 27 European countries, finding systematic differences in segregation across countries and platforms.
Crises, Catharses, and Boiling Frogs: Path Dependence in Collective Action (with Mehdi Shadmehr and Gaetán Tchakounte Nandong)
We show a strong form of path-dependence in collective action. For a given distribution of anti-regime grievances and sentiments in the society, the size of the protest is larger when this distribution of grievances is the result of a sudden large change rather than a series of smaller unexpected changes. Society as a whole behaves like the legendary boiling frog, even though each individual does not. Large grievance shocks (crises) coordinate behavior far more effectively into revolts than a sequence of small shocks that generate the same final distribution of grievances. Our analysis applies advances in incomplete information coordination games (Morris and Yildiz 2019), deviating from the literature by relying only on the notion of rationalizability (as opposed to Nash equilibrium) and assuming heavy-tailed distributions of grievance shocks. We explore the unexpected link between this theory and Davies's (1962) classic J-curve theory of revolution.
Essential Equilibria in Large Generalized Games (2014) Economic Theory, 57, pp 479-513. (with Juan Pablo Torres-Martínez)
We characterize the essential stability of games with a continuum of players, where strategy profiles may affect objective functions and admissible strategies. Taking into account the perturbations defined by a continuous mapping from a complete metric space of parameters to the space of continuous games, we prove that essential stability is a generic property and every game has a stable subset of equilibria. These results are extended to discontinuous large generalized games assuming that only payoff functions are subject to perturbations. We apply our results in an electoral game with a continuum of Cournot-Nash equilibria, where the unique essential equilibrium is that only politically engaged players participate in the electoral process. In addition, employing our results for discontinuous games, we determine the stability properties of competitive prices in large economies.