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This paper deals with the issue of screening. It focuses on a decision maker who, based on noisy unbiased assessments, screens elements from a general set. Our analysis shows that stricter screening not only reduces the number of accepted elements, but possibly reduces their average expected value. We provide a characterization for optimal threshold strategies for screening and also derive implications to cases where such screening strategies are suboptimal. We further provide various applications of our results to credit ratings, auctions, general trade, the Peter Principle, and affirmative action. (JEL C38, D44, F10, G24, J15)

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We define and characterize the notion of strong robustness to incomplete information, whereby a Nash equilibrium in a game u is strongly robust if, given that each player knows that his payoffs are those in u with high probability, all Bayesian-Nash equilibria in the corresponding incomplete-information game are close -in terms of action distribution -to that equilibrium of u. We prove, under some continuity requirements on payoffs, that a Nash equilibrium is strongly robust if and only if it is the unique correlated equilibrium. We then review and extend the conditions that guarantee the existence of a unique correlated equilibrium in games with a continuum of actions. The existence of a strongly robust Nash equilibrium is thereby established for several domains of games, including those that arise in economic environments as diverse as Tullock contests, Cournot and Bertrand competitions, network games, patent races, voting problems, and location games.

We design incentives schemes for portfolio managers that screen low-skill managers: only the best portfolio managers, in terms of expected payoffs, agree to participate in the single-period investment. The results hold in general financial markets, where uninformed investors face managers of different capabilities, and can only observe their one-shot realized returns. Our model is robust and accounts for general screening problems.