I formalise a rather stylised insurance market with adverse selection as a standard duopoly. I formally specify demand functions and profits and I prove that a Nash equilibrium in pure strategies exists if and only if the well-known Rothschild-Stiglitz allocation is efficient

This paper studies stylised markets with asymmetric information. When the market is modelled as a standard signalling game, inefficient outcomes arise due to the arbitrariness of off-the-equilibrium path beliefs. Such inefficient outcomes are shown not to arise in a novel game that combines...