Essays on Multi-Agent Learning in Economic Theory

Abstract

This dissertation presents three independent essays in microeconomic theory and behavioral economics, focusing on the implications of multi-agent learning. Chapter 1 studies endogenous learning dynamics for people expecting systematic reversals from random sequences — the gambler's fallacy.'' Biased agents face an optimal-stopping problem. They are uncertain about the underlying distribution and must learn its parameters from previous agents' histories. Agents stop when early draws are deemed good enough,'' so predecessors' histories contain negative streaks but not positive streaks. Since biased learners understate the likelihood of consecutive below-average draws, histories induce pessimistic beliefs about the distribution's mean. When early agents decrease their acceptance thresholds due to pessimism, later learners will become more surprised by the lack of positive reversals in their predecessors' histories, leading to even more pessimistic inferences and even lower acceptance thresholds -- a positive-feedback loop. In signaling games, which equilibria will arise depends on how the receiver interprets deviations from the path of play. Chapter 2 (coauthored with Drew Fudenberg) develops a micro-foundation for these off-path beliefs in a model where equilibrium arises through non-equilibrium learning. Young senders are uncertain about the prevailing distribution of play, so they rationally send out-of-equilibrium signals as experiments to learn about the behavior of the population of receivers. Using the Gittins index (Gittins, 1979), we characterize which sender types use each signal more often, leading to a constraint on the receiver's off-path beliefs based on ``type compatibility'' and hence a learning-based equilibrium selection. Chapter 3 (coauthored with Krishna Dasaratha) studies a sequential learning model featuring a network of naive agents with Gaussian information structures. Agents wrongly believe their predecessors act solely on private information, so they neglect redundancies among observed actions. We provide a simple linear formula expressing agents' actions in terms of network paths. The probability of mislearning increases when link densities are higher and when networks are more integrated. In partially segregated networks, divergent early signals can lead to persistent disagreement between groups. We conduct an experiment and find that the accuracy gain from social learning is twice as large on sparser networks.