The Sign-up Game, Sophisticated Learning and Learning Variable Demand

This dissertation makes contributions in topics related to mechanism design and learn-ing in game theoretic environments through three essays. The rst essay deals withthe question of mechanism design in the principal-agent model. The main contribu-tion of this essay is in extending the work by Piketty (1993). It prescribes a mechanismin incomplete informational settings where the principal is able to implement rst-best contracts while extracting the entire surplus. Importantly, the mechanism issuch that the desired outcome can be uniquely obtained when agents play the actionthat survives iterative elimination of dominated strategies. Furthermore, given themechanism, the desired outcome is shown to be a truth-revealing Nash equilibriumwhich is also Pareto-ecient. It is shown that the proposed mechanism also has thefeature that none of the agents prefer any of the other possible Nash Equilibria tothe status quo. It thus gives insights into possible mechanisms in nite agent settingsthat could improve upon the traditional second-best results.In the second essay, a model of sophisticated learning is developed where itassumes that a fraction of the population is sophisticated while the rest are adaptive learners. Sophisticated learners in the model try to maximize their cumulative payoin the entire length of the repeated game and are aware of the way adaptive learnerslearn. Sophisticated learning contrasts other models of learning which typically tendto maximize the payo for the next period by extrapolating the history of play.The sophisticated learning model is estimated on data of experiments on repeatedcoordination games where it provides evidence of such learning behavior.The third essay deals with the optimal pricing policy for a rm in an oligopolythat is uncertain about the demand it faces. The demand facing the oligopoly, whichcan be learned through their pricing policy, changes over time in a Markovian fashion.It also deduces the conditions in which learning (experimentation) is not achievableand outlines the dierent learning policies that are possible in other settings. Themodel combines the monopoly learning literature with that of the literature on pric-ing behavior of rms over business cycles. The model has interesting insights onthe pricing behavior over business cycles. It predicts that prices jump as the beliefof a possible future boom rises over a certain threshold. The model also predictscompetition to be quite vigorous following a boom while rms are predicted not toexperiment with their (pricing) policies for many periods following a bust.