Essays on learning and level-k reasoning with evidence from experimental games
In the first chapter of this dissertation, I develop a new model of learning and level-k reasoning in games. My model frames attraction learning in the language of beliefs and extends it to include two important features. The first of these features is an implicit pattern recognition mechanism that learns the importance of contextual information, while the second is a nonlinear probability weighting function with an endogenous fixed point location. The resulting beliefs determine level-1 behavior in a larger level-k rule learning model. In keeping with the literature, I assume that rule learning occurs according to a reinforcement learning mechanism, but I improve the approximation of latent rule reinforcements to simulate the effect of rule exercise. A cognitive foundation for the full model is also provided by implementing it within the ACT-R cognitive architecture.
The second chapter investigates the extent to which human agents use level-k reasoning in repeated mixed strategy games. Towards this end, the Chapter 1 model is estimated using data from a novel experiment. The experiment consisted of two between-subject treatments: in one treatment, the information provided was sufficient to use any level of reasoning, while in the other treatment subjects were only provided with enough information to be level-1. A random effects model is estimated using the data from both treatments to identify the model's belief learning parameters. In the unrestricted treatment, I find that subjects learned to engage almost exclusively in level-1 reasoning. Simulations suggest that this result may be explained by the difficulty of exploiting a player who is level-1.