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Ruling out (strictly) overlapping intervals should be possible using the fact that players must be indifferent among all actions in the support of the mixed strategy, or that these type of auctions is efficient. Uniqueness is tricky, simply because there are many possible interval structures like that one. But I guess you mean, equilibria are always of ...


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The signal structure must specify what the DM learns in all possible states of the world, so I think your question should read: "Suppose that the DM discovers whether the state of the world $v\in V$ is in $[a,b]\subset V$ or not. Can this be written as an information structure?" or should read: "Suppose that the DM discovers the state of the world $v\in ...


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I am not entirely sure about what you mean with "Before choosing the DM can discover $z$ by searching sequentially and paying cost $c_y$ when uncovering $z_y$ for each $y\in Y$." However, it sounds like you want your DM to choose both a stoping time, $t$, and an action, $y$. Since the DM is searching sequentially, the decision to continue searching or not ...


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