Abstract We study identification and inference in first-price auctions with risk-averse bidders and selective entry, building on a flexible framework we call the Affiliated Signal with Risk Aversion (AS-RA) model. Assuming exogenous variation in either the number of potential bidders (N) or a continuous instrument (z) shifting opportunity costs of entry, we provide a sharp characterization of the nonparametric restrictions implied by equilibrium bidding. This characterization implies that risk neutrality is nonparametrically testable. In addition, with sufficient variation in both N and z, the AS-RA model primitives are nonparametrically identified (up to a bounded constant) on their equilibrium domains. Finally, we explore new methods for inference in set-identified auction models based on Chen et al. (2018, Econometrica, vol. 86, 1965–2018), as well as novel and fast computational strategies using Mathematical Programming with Equilibrium Constraints. Simulation studies reveal the good finite-sample performance of our inference methods, which can readily be adapted to other set-identified flexible equilibrium models with parameter-dependent support.

We consider a multi-battle team contest in which players from two rival teams form pairwise matches to fight in distinct component battles, which are carried out sequentially or (partially) simultaneously. A team wins if and only if its players win a majority of battles. Each player benefits from his team's win, while he can also receive a private reward for winning his own battle. We find that the outcomes of past battles do not distort the outcomes of future battles. Neither the total expected effort nor the overall outcome of the contest depends on the contest's temporal structure or its feedback policy. (JEL C72, D72, D74, D82)