Optimal Competitive Auctions

We study the design of truthful auctions for selling identical items in unlimited supply (e.g., digital goods) to n unit demand buyers. This classic problem stands out from profit-maximizing auction design literature as it requires no probabilistic assumptions on buyers' valuations and employs the framework of competitive analysis. Our objective is to optimize the worst-case performance of an auction, measured by the ratio between a given benchmark and revenue generated by the auction. We establish a sufficient and necessary condition that characterizes competitive ratios for all monotone benchmarks. The characterization identifies the worst-case distribution of instances and reveals intrinsic relations between competitive ratios and benchmarks in the competitive analysis. With the characterization at hand, we show optimal competitive auctions for two natural benchmarks. The most well-studied benchmark $\mathcal{F}^{(2)}(\cdot)$ measures the envy-free optimal revenue where at least two buyers win. Goldberg et al. [13] showed a sequence of lower bounds on the competitive ratio for each number of buyers n. They conjectured that all these bounds are tight. We show that optimal competitive auctions match these bounds. Thus, we confirm the conjecture and settle a central open problem in the design of digital goods auctions. As one more application we examine another economically meaningful benchmark, which measures the optimal revenue across all limited-supply Vickrey auctions. We identify the optimal competitive ratios to be $(\frac{n}{n-1})^{n-1}-1$ for each number of buyers n, that is $e-1$ as $n$ approaches infinity

Constant-Competitive Prior-Free Auction with Ordered Bidders

A central problem in Microeconomics is to design auctions with good revenue properties. In this setting, the bidders' valuations for the items are private knowledge, but they are drawn from publicly known prior distributions. The goal is to find a truthful auction (no bidder can gain in utility by misreporting her valuation) that maximizes the expected revenue. Naturally, the optimal-auction is sensitive to the prior distributions. An intriguing question is to design a truthful auction that is oblivious to these priors, and yet manages to get a constant factor of the optimal revenue. Such auctions are called prior-free. Goldberg et al. presented a constant-approximate prior-free auction when there are identical copies of an item available in unlimited supply, bidders are unit-demand, and their valuations are drawn from i.i.d. distributions. The recent work of Leonardi et al. [STOC 2012] generalized this problem to non i.i.d. bidders, assuming that the auctioneer knows the ordering of their reserve prices. Leonardi et al. proposed a prior-free auction that achieves a $O(\log^* n)$ approximation. We improve upon this result, by giving the first prior-free auction with constant approximation guarantee.Comment: The same result has been obtained independently by E. Koutsoupias, S. Leonardi and T. Roughgarde

An investigation of the trading agent competition : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Computer Science at Massey University, Albany, New Zealand

The Internet has swept over the whole world. It is influencing almost every aspect of society. The blooming of electronic commerce on the back of the Internet further increases globalisation and free trade. However, the Internet will never reach its full potential as a new electronic media or marketplace unless agents are developed. The trading Agent Competition (TAC), which simulates online auctions, was designed to create a standard problem in the complex domain of electronic marketplaces and to inspire researchers from all over the world to develop distinctive software agents to a common exercise. In this thesis, a detailed study of intelligent software agents and a comprehensive investigation of the Trading Agent Competition will be presented. The design of the Risker Wise agent and a fuzzy logic system predicting the bid increase of the hotel auction in the TAC game will be discussed in detail

Revenue Equivalence Revisited

The conventional wisdom in the auction design literature is that first price sealed bid auctions tend to make more money while ascending auctions tend to be more efficient. We re-examine these issues in an environment in which bidders are allowed to endogenously choose in which auction format to participate. Our findings are that more bidders choose to enter the ascending auction than the first price sealed bid auction and this extra entry is enough to make up the revenue difference between the formats. Consequently, we find that both formats raise approximately the same amount of revenue. They also generate efficiency levels and bidder earnings that are roughly equivalent across mechanisms though the earnings in the ascending might be slightly higher. In expected utility terms though, we find that the expected utility of entering a first price sealed bid auction is greater than entering an ascending for any risk averse bidder suggesting that we are seeing “overentry” into the ascending auctions