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Efficient Competition in Insurance Markets

I construct an efficient mechanism for competitive markets with adverse selection. In the mechanism, each company offers two menus of contracts: a public menu and a private menu. The union of all the public menus needs to be offered by every active company in the market. On the contrary, a private menu concerns only the company who offers it. I show that this simple mechanism reduces the set of profitable deviations to the extent that a pure-strategy equilibrium exists in every market with adverse selection. Furthermore, I characterise general, well-studied environments, in which the set of equilibrium allocations coincides with the set of efficient allocations.