Definition of Signalling and Screening Games?

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I am currently studying some applied screening and signalling games in an advanced microeconomics course. Even though I understand the intuition and the idea of those games, I have not been able to find a formal and systematic way of defining screening and signalling games. Could anyone provide formal definitions for these two concepts? Also, some references would be appreciated.

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When there is asymmetric information, one party is informed and the other is not.

It is screening when the non-informed party takes action to discover some of the hidden information. F.i., an health insurer offers a menu of contracts to customers who have private information about their health status.

It is signaling when the informed party takes action to reveal some of the hidden information. F.i., students take up challenging courses to provide evidence about their (privately known) quality to potential employers.