Advanced Microeconomics II
This course traces the extent to which modern economic theory, particularly as it pertains to pure competition in market and non-market games under the rationality postulate, is grounded in the language of probability and measure theory. Special attention is paid to the formal expression of ideas such as economic and numerical negligibility on the one hand, and diffuseness and conditional independence of information on the other. Toward this end, the course develops rigorous formulations of basic ideas of conceptual (rather than computational) probability, including spaces of events, random variables and their means, marginal and joint densities, stochastic independence, and derivatives of probabilities. We apply those formulations first to the basic theorems of welfare economics, including the core theorems; and second to large anonymous and non-anonymous games, as well as to finite-agent games with private information. If time permits, the course concludes with some basic vocabulary of evolutionary game theory. The course is self-contained from the technical point of view but presupposes a level of mathematical maturity that ought typically to be achieved by taking a course such as GECO 6189. Prospective students who are not sure they have the necessary interest and background should contact the instructor.