We extend the gross substitutes and complements framework (Sun and Yang, 2006). Competitive equilibrium with indivisible goods exists under significantly weaker, intuitive and interpretable conditions. A generalized dynamic double-track procedure (Sun and Yang, 2008, 2009) finds the competitive...

We provide a simple example demonstrating that the unconditional revelation information in a war of attrition with private budget constraints can decrease expected revenue. Our example suggests that information non-revelation can counteract the adverse revenue impact of budget constraints and...

We provide extensions of the Bulow and Klemperer (1996) result when the seller has value for the object above the minimum value of the buyers. The result may fail. We show that the seller does better with more participation and some exclusion than the optimal exclusion of buyers of low value...

We prove that the maximal bid in asymmetric first-price and all-pay auctions is the same for all bidders. Our proof is elementary, and does not require that bidders are risk neutral, or that the distribution functions of their valuations are independent or smooth.