Three Sequential Cases: from Symmetry to Asymmetry

Three critical cases, involving asymmetric and symmetric cases, in the sequential stages of the n-player repeated auctions are analyzed and compared. These cases might arise in a process of sequential, identical or equivalent auctions, where the auction result may reveal information about the strength or competitiveness of the participants. The behaviours of different players are characterized. Generally a player bids more aggressively when facing a strong player rather than a weak player. However a player favours competing with a weak one rather than a strong one. By applying the concept of Conditional Stochastic Dominance, revenues of players and the seller between the three stages are compared. It is proved that in this sequential process the information structure of the auctions changes and the seller’s revenue increases. Finally, this n-player asymmetric auction model can also be used to compare the revenues between high-bid and open auctions and especially the results first derived by Maskin and Riley (2000) in two-player case are proved to be valid in the n-player case.