Three essays on learning and information in games.
Robert S. Gazzale · Deep Blue (University of Michigan) · 2004
In these essays, I explore ways in which competitive outcomes are affected by learning and information use. In my first essay, I investigate how the desire to learn consumer demand affects a differentiated-product duopoly. I identify conditions under which firms desire to increase learning, and show that this may lead to firms competing less vigorously for the most attractive consumer niches. Analysis of equilibrium properties is valuable only insofar as agents play equilibrium strategies. In my second essay, I consider the role of supermodularity in the success of agents finding equilibrium strategies. We show that supermodularity is not a sine qua non: near-supermodular games converge just as well to equilibrium play, more super-modular games do not converge any better, and, in the long run, other features of the environment can be partial substitutes for supermodularity. My third essay considers reputation games in which information is contributed by others, rather than learned directly from the environment. I propose a simple mechanism for moral-hazard environments, and characterize conditions under which a seller's desire and ability to maintain a positive reputation overcomes the moral hazard problem even when we do not assume that buyers voluntarily provide information about sellers. By allowing buyers to develop a reputation for information sharing, they share their information as they rightly expect better treatment by sellers wishing to maintain their reputation for good service.