Cross and Double Cross: Comparative Statics in First Price and All Pay Auctions

This paper analyses comparative statics for first price auctions and all pay auctions with independent private values. In all pay auctions, bidders with low values will respond to a stochastically higher (in the sense of likelihood ratio dominance) distribution of types by playing less aggressively while high value bidders bid more. In the first price auction, a similar change results in all types playing more aggressively. Furthermore, we show that a decrease in dispersion of values, in the sense of a refinement of second order stochastic dominance, although also associated with an increase in competitiveness, may in addition result in less aggressive play by bidders with high values in both auction forms. We also find similar considerations in an oligopoly game with incomplete information: stochastically lower costs can lead to higher prices.