Research

Precedent-Affirming Equilibrium (job market paper)

I introduce the concept of precedent-affirming equilibrium, a solution concept for games played in a population setting where players are strategically sophisticated and well-informed about typical play in the population, but have heterogeneous priors about unusual play. I provide a characterization result and derive from it an algorithm for finding the precedent-affirming equilibria of specific games. A novel rationale for forward induction reasoning emerges which does not require assumptions about how agents react to ex ante impossible events. I study an application to games of cooperation and coordination, in which I show that cooperation cannot be sustained through coordinated punishments, but fear of miscoordination can sustain cooperation if players depend sufficiently on the precedent to coordinate their expectations. The application also shows there are endogenous differences between precedents in the degree to which mistaken beliefs and strategies can coexist indefinitely with objectively correct ones. Precedent-affirming equilibrium thus shows promise for the further study of applications including cooperation, coordination, and the informal rules governing organizations or societies.

The Confidence Game: Equilibrium Bargaining Under Strategic Uncertainty

I study a simple bargaining game, in which populations of firms and workers bargain over whether they will split output according to a high or low wage, and study it from the perspective of precedent-affirming equilibrium, a notion of equilibrium for agents who are strategically sophisticated but do not know each other's strategies ex ante. I characterize a solution set in which most matches result in immediate agreement on either the high wage or the low wage. In the high-wage case, all agents are able to infer each other's equilibrium strategies from the available information. In the low-wage case, their equilibrium behavior instead reflects their subjective confidence in the demands they can successfully make, which is prior-dependent due to limited information. This highlights how both strong strategic inferences and subjective confidence (or lack thereof) in the absence of such inferences can support precedent-affirming equilibrium bargaining outcomes, and demonstrates the value of precedent-affirming equilibrium for understanding how the degree of strategic knowledge agents in a market will come to have can depend on the details of the setting and of the equilibrium outcome.