This paper considers a model of multi-unit ascending auction with two players and known values. This standard model is not robust to a small reputational perturbation. If reputation is one-sided, then the player without reputation lowers her demand in order to clear the market and stop the auction immediately at the reserve price. Hence, the player with reputation buys all the units she demands at the lowest possible price. If the reputation is on both sides, then the War of Attrition emerges. In any case, there is a unique equilibrium payoff profile. One feature of the equilibrium of the two-sided model is that market clearing is delayed and the expected realized price is higher than the reserve price.
