Two-stage contests with preferences over style

Many grant applications have a preliminary stage where only a select group are invited to submit a full application. Similarly, procurement contracts by governments are often awarded through a two-stage procedure. We model and analyze such environments where the designer cares about the style of the application as well as its quality. The designer has the option of choosing an initial stage, where contestants can enter and learn about their desirability while the designer learns about their style. We determine closed form solutions for equilibrium outcomes and designer payoffs and use this to analyze whether or not a second stage is desirable, different rules for deciding who will advance, and whether or not to communicate the number of contestants that qualify for the second stage.