Essays on Population Learning Dynamics and Boundedly Rational Behavior

This dissertation contains four essays about evolutionary learning dynamics and the quantal response model of bounded rationality in game theory. The first essay examines the use of single-agent and representative-agent models to describe the aggregate behavior of heterogeneous quantal responders. Heterogeneous quantal response functions arise from a distribution of distributions of payoff noise. A representative agent would have the average quantal response function. Weakening a standard assumption about admissible distributions of payoff noise, we show existence of a representative agent. However, this representative agent does not have a representative noise distribution, nor any iid distribution in large enough games. We consider a specific case of heterogeneous logit responders and find that a mis-specified homogeneous logit parameter has downward bias. The remaining essays investigate the aggregate behavior of populations of learning agents. A deterministic learning model applied to a game with multiple equilibria produces distinct basins of attraction for those equilibria. We construct a class of three-by-three symmetric games for which the overlap in the basins of attraction under best response and replicator dynamics is arbitrarily small. We then derive necessary and sufficient conditions on payoffs for these two learning rules to create basins of attraction with vanishing overlap. We compare cultural learning, i.e., replicator dynamics, and individualistic learning, i.e., best response dynamics, in a class of generalized stag hunt games. We show that the basins of attraction for the efficient equilibria are much larger with cultural learning. Furthermore, as the stakes grow arbitrarily large, cultural learning always locates an efficient equilibrium while individualistic learning never does. We compare outcomes in homogeneous populations learning in accordance with best response dynamics and with replicator dynamics to outcomes in populations that mix these two learning rules. New outcomes emerge. In certain games, a linear combination of the two rules almost always attains an equilibrium that homogeneous learners almost never locate. Moreover, even when almost all weight is placed on one learning rule, the outcome can differ from homogeneous use of that rule. Thus, allowing an arbitrarily small chance of using an alternative learning style can shift a population to select a different equilibrium.PhDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/63738/1/rgolman_1.pd