Eliciting willingness-to-pay to decompose beliefs and preferences that determine selection into competition in lab experiments

This paper develops a partial-identification methodology for analyzing self-selection into alternative compensation schemes in a laboratory environment. We formulate a model of self-selection in which individuals select the compensation scheme with the largest expected valuation, which depends on individual- and scheme-specific beliefs and non-monetary preferences. We characterize the resulting sharp identified sets for individual-specific willingness-to-pay, subjective beliefs, and preferences, and develop conditions on the experimental design under which these identified sets are informative. We apply our methods to examine gender differences in preference for winner-take-all compensation schemes. We find that what has commonly been attributed to a gender difference in preference for performing in a competition is instead explained by men being more confident than women in their probability of winning a future (though not necessarily a past) competition.