Optimal strategies in sequential bidding

We are interested in mechanisms that maximize the final social welfare. In [1] this problem was studied for multiunit auctions with unit demand bidders and for the public project problem, and in each case social welfare undominated mechanisms in the class of feasible and incentive compatible mechanisms were identified.
One way to improve upon these optimality results is by relaxing the assumption of simultaneity and allowing the players to move sequentially. With this in mind, we study here sequential versions of two feasible Groves mechanisms used for single item auctions: the Vickrey auction and the Bailey-Cavallo mechanism.
Because of the absence of dominant strategies in this sequential setting, we focus on a weaker concept of an optimal strategy. For each mechanism, we introduce natural optimal strategies and observe that in each mechanism these strategies exhibit different behaviour. However, we then show that among all optimal strategies, the one we introduce for each mechanism maximizes the social welfare when each player follows it. The resulting social welfare can be larger than the one obtained in the simultaneous setting.