Sequential bidding in the Bailey-Cavallo mechanism

We are interested in mechanisms that maximize social welfare. In [2] this problem was studied for multi-unit auctions and for public project problems, and in each case social welfare undominated mechanisms were identified. One way to improve upon these optimality results is by allowing the players to move sequentially. With this in mind, we study here a sequential version of the Bailey-Cavallo mechanism, a natural mechanism that was proved to be welfare undominated in the simultaneous setting by [2]. Because of the absence of dominant strategies in the sequential setting, we focus on a weaker concept of an optimal strategy. We proceed by introducing natural optimal strategies and show that among all optimal strategies, the one we introduce generates maximal social welfare. Finally, we show that the proposed strategies form a safety level equilibrium and within the class of optimal strategies they also form a Pareto optimal ex-post equilibrium.