Informationally robust trade and limits to contagion

Two agents can each accept or reject a proposed deal, whose value for each agent depends on an unknown state, and may be positive or negative. The deal takes place only if both accept. Each agent can be imperfectly informed, in an arbitrary way, about both her own value and the other agent's. In such environments, contagious adverse selection may prevent the deal from being reached even when it is mutually beneficial ex post. We give an upper bound on the ex-ante expected welfare loss in equilibrium due to such contagion, valid for any information structure. The welfare loss is small if negative values are unlikely ex ante; and under an assumption of known aggregate gains from the deal, our bound is sharp. The bound has a succinct description, even though the equilibrium itself, in any given information structure, may be hard to describe explicitly.