The project consists of two parts. The first part involves collaboration with Franklin Allen of the Wharton School, University of Pennsylvania. The second part involve collaboration with Robert Rosenthal of Boston University. Part one of the project addresses three aspects of optimal central bank policies to achieve financial stability. One is the development of a model of optimal intervention by a central bank when liquidity shortages cause bank runs. The second is the study of contagion in financial systems, that is, investigating how small shocks can spread throughout the banking system or from one country to another. The third is the role of credit policy in inflating asset prices and precipitating a collapse in financial markets. The second part will analyze the properties of a behavioral model of learning, in which individuals adapt their behavior through experimentation (randomly trying new strategies) and imitation (adopting strategies they observe others use). The research involves a combination of mathematical and computational methods. It will also apply adaptive algorithms to the models of markets in order to investigate the conditions under which simple, adaptive behavior can lead to optimal outcomes in competitive markets.