An example of non-existence of Riley equilibrium in markets with adverse selection

Rothschild and Stiglitz [1976] proposed a model of a competitive market with adverse selection and showed that a (pure strategy) Nash equilibrium may not exist. Among the solutions proposed to deal with this problem, a particularly influential one is the notion of Riley (or reactive) equilibrium [Riley, 1979]. We give an example that shows that a Riley equilibrium may not exist if consumers are not ordered.