Optimal Strategies in Sequential Bidding

TL;DR

This paper explores sequential versions of two classic auction mechanisms, proposing optimal strategies that can enhance social welfare beyond simultaneous settings and establishing Pareto optimality among these strategies.

Contribution

It introduces natural optimal strategies for sequential Vickrey and Bailey-Cavallo mechanisms, demonstrating their effectiveness in maximizing social welfare and their Pareto optimality.

Findings

Optimal strategies increase social welfare over simultaneous auctions.

Strategies differ in behavior between mechanisms.

Proposed strategies form a Pareto optimal Nash equilibrium.

Abstract

We are interested in mechanisms that maximize social welfare. In [1] this problem was studied for multi-unit 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 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. Finally, we show that, when interpreting both mechanisms as simultaneous ones, the vectors of the proposed strategies form a Pareto optimal Nash equilibrium in the class of optimal strategies.