Unravelling vs Unravelling: A Memo on Competitive Equilibriums and Trade in Insurance Markets

Both Akerlof (1970) and Rothschild and Stiglitz (1976) show that insurance markets may “unravel”. This memo clarifies the distinction between these two notions of unravelling in the context of a binary loss model of insurance. I show that the two concepts are mutually exclusive occurrences. Moreover, I provide a regularity condition under which the two concepts are exhaustive of the set of possible occurrences in the model. Akerlof unravelling characterises when there are no gains to trade; Rothschild and Stiglitz unravelling shows that the standard notion of competition (pure strategy Nash equilibrium) is inadequate to describe the workings of insurance markets when there are gains to trade.