Dynamic Games and Mechanisms with Serially Dependent Private Information

Download or read book Dynamic Games and Mechanisms with Serially Dependent Private Information written by Juuso Tuomas Toikka and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three essays. In "A Folk Theorem with Markovian Private Information" (with Juan F. Escobar) we consider repeated Bayesian two-player games in which the players' types evolve according to an irreducible Markov chain, type transitions are independent across players, and players have private values. The main result shows that, with communication, any Pareto efficient payoff vector above a minmax value can be approximated arbitrarily closely in a perfect Bayesian equilibrium as the discount factor goes to one. In the second essay, "Dynamic Mechanism Design: Incentive Compatibility, Profit Maximization, and Information Disclosure" (with Alessandro Pavan and Ilya R. Segal), we examine the design of dynamic screening mechanisms for environments in which the agents' types follow a stochastic process, decisions may be made over time, and the decisions may affect the type process. We derive a formula for an agent's equilibrium payoff in an incentive-compatible mechanism, which generalizes Mirrlees's envelope formula of static mechanism design. When specialized to quasi-linear environments, the formula yields a dynamic revenue-equivalence result and an expression for dynamic virtual surplus, which is instrumental for the design of profit-maximizing mechanisms. We also provide sufficient conditions for incentive compatibility. We apply the results to derive optimal dynamic contracts for a number of novel settings. The final essay, "Ironing without Control, " extends a method for solving a class of optimization problems, encountered frequently in mechanism design, where a functional is maximized over the set of nondecreasing functions. For example, the approach can be used to solve principal-agent models with adverse selection.