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Respond to the question: Beliefs about equilibrium paths with ove?

07/07/2017 03:52 AM by name withheld; Beliefs about equilibrium paths with overlapping strategies
Consider a classic signaling game (2 types, 2 actions) la Spence. Suppose furthermore that there are two equilibria: one pooling, one separating. In the pooling eq., say, both types of senders send "Low". In the separating, the
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07/07/2017 03:45 AM by name withheld; Beliefs about equilibrium paths with overlapping strategies
Consider a classic signaling game (2 types, 2 actions) la Spence. Suppose furthermore that there are two equilibria: one pooling, one separating. In the pooling eq., say, both types of senders send "Low". In the separating, the "Strong" type sends High, the Weak type sends Low.

The part that I struggle with is: how does the receiver know what equilibrium path they are in? For example, say the receiver observes "Low". If we are in "pooling world", then the receiver's posteriors are just going to be her priors. If, however, we are in "separating world", then she can update to p(Weak|Low)=1. But observing "Low" alone does not tell the receiver what strategy the sender is following, so how can she possibly update her beliefs? It seems to me that she would need to have beliefs not only about types, but also about strategies being followed.

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