Dubey and Geanakoplos  have developed a theory of competitive pooling, which incorporates adverse selection and signaling into general equilibrium. By recasting the Rothschild-Stiglitz model of insurance in this framework, they find that a separating equilibrium always exists and is unique. We prove that their uniqueness result is not a consequence of the framework, but rather of their definition of refined equilibria. When other types of perturbations are used, the model allows for many pooling allocations to be supported as such: in particular, this is the case for pooling allocations that Pareto dominate the separating equilibrium.
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