Three essays on social institutions and individual behavior
This thesis studies the interactions between individual behavior and social institutions. The first chapter proposes a model of equilibrium switching in games with mul tiple strict Nash equilibria such as the evolution of social conventions. In our model, players are forward-looking but use level-k reasoning about their peers’ choices. We find that equilibrium switching is deterministic and gradual, with higher k players switching first. In some cases, the final equilibrium is reached only after several other equilibria are visited, where each step is Pareto improving. We completely characterize the switching paths for all games with finite strict Nash equilibria, and a large class of level-k populations. The model provides a unified explanation for puzzling equilibrium switching results reported in recent experimental studies, including the direction of transition, asynchronous participation, and alternations between strict Nash equilibria. The second chapter empirically tests a theory of equilibrium transition among strict Nash equilibria, the sampling best response dynamic that predicts equilibrium transitions under inexact (inaccurate but unbiased) information of opponents’ behaviors. We design a quasi-continuous-time experiment in which a group of subjects plays a coordination game recurrently under either more or less accurate information. We observe that more accurate information facilitates efficiency-improving transitions among strict Nash equilibria than less accurate information, which is in contrast with the evolutionary theory but supports the models of strategic teaching. More accurate information about opponents’ behaviors induces more subjects to engage in persistent strategic deviations from inefficient Nash equilibria that can induce more subjects to deviate in the future, resulting in efficiency-improving equilibrium transitions. When information is less accurate, subjects’ choices are less responsive to changes in the information received. The slow response to the information either blocks or delays efficiency-improving equilibrium transitions. The third chapter investigates the optimal fertility strategy and its impact on the fertility rate and parental investment under patriarchal institutions. We show that the optimal fertility strategy is a one-stage look-ahead strategy and represents a son-preferring stopping rule if there is a patriarchal institution in favor of sons over daughters. We further characterize the resulting demographic distribution of the possible sex combinations of children in a family. It suggests that, under the optimal fertility strategy, females are disproportionately born into larger families, and therefore receive lower average investment than males. In addition, both under and over-reproduction exist in a patriarchal society, but the average fertility rate can be lower than in a gender-neutral society.