A Game Theoretic Foundation for the Stiglitz-Weiss Model

Abstract

Contrary to what is usually assumed in the literature, the return function (i.e., the relation
between the interest rate on loans and the resulting rate of return) cannot be globally humpshaped
in the Stiglitz-Weiss (1981) adverse selection model with a continuum of borrower types.
It is possibly non-monotonic, but it attains its global maximum at the maximum interest rate
beyond which there is no demand for capital. Arnold and Riley (2007) argue that if the return
function has a unique local maximum and there is excess demand at the corresponding interest
rate, the two-interest rate equilibrium discussed by Stiglitz and Weiss (1981) in the context of
a return function with multiple humps is the natural equilibrium outcome of the model. The
present paper substantiates this claim by providing an explicit game theoretic foundation for
the Stiglitz-Weiss (1981) model. Modeling competition in the markets for deposits and credit
as a two-stage game, as in Stahl (1988) and Yanelle (1989), we show that the two-interest
rate allocation occurs in any subgame perfect pure-strategy equilibrium if the credit subgame
precedes the deposit subgame.