Auctions with discrete increments: a structural econometric approach based on dominated strategies

We propose a structural econometric evaluation for auctions with discrete increments. Although very common in practice, this kind of mechanism raises many theoretical difficulties. First, there are no closed form equilibrium strategies. Thus the econometrician cannot rely on a single formula to build a model. Second, the discrete nature of the outcome complicates the inference. Our econometric model is built on the weak assumption that bidders do not play some given dominated strategies. This implies that our results remain valid for many different kinds of equilibrium concepts. The specification of our model allows the computation of a Maximum Likelihood Estimator. Usual asymptotic tests and confidence regions derived from the likelihood function are shown to be unreliable. A new exact inference method proposed by Dufour [1998] is implemented to circumvent this difficulty. The procedure is applied to an auction in which travel agents bid to discount airline tickets. From an economic viewpoint, we find that although the profit of the travel agents may be small, it is very unlikely that competition is tight. We also compare the rent kept by the winner of a discrete increment auction with that of a continuous auction. Our data show that the number of players is crucial. If the number of player is small, then the winning price is smaller when the tick is zero. In this case, the Vickrey auction is dominated (from the risk-neutral principal viewpoint) by the discrete increment mechanism. This may explain why we observe substantial ticks in many actual auction mechanisms.