Recent evidence shows that within an industry, smaller firms grow faster and are
more likely to fail than large firms. This paper provides a theory of selection with
incomplete information that is consistent with these and other findings. Firms learn
about their efficiency as they operate in the industry. The efficient grow and survive;
the inefficient decline and fail. A perfect foresight equilibrium is proved by means
of showing that it is a unique maximum to discounted net surplus. The maximization
problem is not standard, and some mathematical results might be of independent interest.