A discrete model of discriminatory price auctions - an alternative to Menezes-Monteiro

Menezes and Monteiro, Math. Soc. Sci. (1995), show that a multi-unit discriminatory price auction does not have a pure strategy equilibrium unless one imposes some rather special conditions on the demand functions. This non-existence result might indicate a problem either with the underlying auction procedure (as Menezes and Monteiro suggest) or with the modelling approach (as we suggest). We observe that the non-existence problem disappears if bids must come in multiples of smallest units --- a realistic feature. Moreover, we show that most of the analysis can be recast in a discrete action model.