Efficient Auctions with Identity-Dependent Negative Externalities

Chaoli Zhang, Xiang Wang, Fan Wu, Xiaohui Bei

Abstract: We investigate a class of single-item multi-supply auctions (including digital goods auctions with unlimited supply) with bidders who have identity-based negative externalities. In such an auction, each bidder has a set of competitors. Her private valuation from winning an item decreases with the number of her winning competitors. Negative externalities are prevalent in many applications, in which the auctioned goods play a role in future interactions among the auction's participants, such as patent licensing and sponsored search auctions. However, the development of auctions with such externalities is stymied by the computational difficulty of the underlying welfare maximization allocation problem; even without consideration of truthfulness, the problem of social welfare maximization with general competition relations is NP-hard and even hard to approximate within a constant factor (unless P=NP). In this work, we design polynomial time and strategy-proof mechanisms under different restrictions on the underlying competition graph structure. Our results can be summarized as follows. (1) When each bidder has only one competitor, we propose a truthful and welfare maximizing mechanism. (2) We design a truthful and (1 + ε )-approximation mechanism when the underlying competition graph is planar. (3) We give two truthful mechanisms when bidders have ar- bitrary competition relations, with welfare approximation ratio (n/ log n) and [(d + 1)/3], respectively, where d is the maximum degree of the "undirected" competition graph.