Reputation in multi-unit ascending auction with common values

This paper considers a multi-unit ascending auction with two players and common values. A large set of equilibria in this model is not robust to a small reputational perturbation. In particular, if there is a positive probability that there is a type who always demands many units, regardless of price, then the model has a unique equilibrium payoff profile. If this uncertainty is only on one side, then the player who is known to be normal lowers her demand in order to stop the auction immediately at the reserve price. Hence, her possibly committed opponent buys all the units she demands at the lowest possible price. If the reputation is on both sides, then a War of Attrition emerges.