VCG-Based Mechanism in Multi-Rounds Auction

Auction mechanisms are designed to address two fundamental issues: determining the winner of a specific item and establishing the payment required from the winner. In multi-round auctions where bidders directly report their valuations, as the scenario we study in this paper, the mechanism must define both the allocation and payment rules to achieve a specific objective, such as maximizing social welfare or revenue. In this study, we focus on identifying a welfare-optimal allocation strategy that ensures items are assigned to the bidders with the highest valuations among all participants. Regarding the payment rule, while the second-price mechanism is optimal in single-round auctions, the dynamic nature of multi-round auctions introduces a new challenge: ensuring incentive compatibility for every bidder, even when they have complete knowledge of other bidders' strategies. In an ideal mechanism, the winner should pay only the second-highest price among the other bidders in a given round, without being influenced by previous or future rounds. However, a strategic bidder may exploit their knowledge of others’ strategies, potentially causing honest bidders to experience regret. This regret is defined as the difference in utility when the strategic bidder bids honestly versus when they bid manipulatively, often at the expense of overall social welfare. This paper proposes a novel payment rule designed to maximize social welfare with less fluctuation while adhering to the constraints of auction design theory, defined in previous related work. The proposed mechanism ensures that, even if a strategic bidder has complete information about other participants, including their valuations and bidding strategies, they are still incentivized to bid truthfully based on their valuation. The results demonstrate that the mechanism mollifies strategic bidding from all participants, even in the presence of full strategic foresight, thereby optimizing social welfare and balancing utility across bidders.