The monopolist’s theory of optimal single-item auctions for agents with independent private values can be summarized by two statements. The first is from Myerson [8]: the optimal auction is Vickrey with a reserve price. The second is from Bulow and Klemperer [1]: it is better to recruit one more bidder and run the Vickrey auction than to run the optimal auction. These results hold for single-item auctions under the assumption that the agents ’ valuations are independently and identically drawn from a distribution that satisfies a natural (and prevalent) regularity condition. These fundamental guarantees for the Vickrey auction fail to hold in general single-parameter agent mechanism design problems. We give precise (and weak) conditions under which approximate analogs of these two results hold, thereby demonstrating that simple mechanisms remain almost optimal in quite general single-parameter agent settings.

We design and analyze approximately revenue-maximizing auctions in general single-parameter settings. Bidders have publicly observable attributes, and we assume that the valuations of indistinguishable bidders are independent draws from a common distribution. Crucially, we assume all valuation distributions are a priori unknown to the seller. Despite this handicap, we show how to obtain approximately optimal expected revenue — nearly as large as what could be obtained if the distributions were known in advance — under quite general conditions. Our most general result concerns arbitrary downwardclosed single-parameter environments and valuation distributions that satisfy a standard hazard rate condition. We also assume that no bidder has a unique attribute value,

The existing literature on optimal auctions focuses on optimizing the expected revenue of the seller, and is appropriate for risk-neutral sellers. In this paper, we identify good mechanisms for risk-averse sellers. As is standard in the economics literature, we model the risk-aversion of a seller by endowing the seller with a monotone, concave utility function. We then seek robust mechanisms that are approximately optimal for all sellers, no matter what their levels of risk-aversion are. We have two main results for multi-unit auctions with unit-demand bidders whose valuations are drawn i.i.d. from a regular distribution. First, we identify a posted-price mechanism called the Hedge mechanism, which gives a universal constant factor approximation; we also show for the unlimited supply case that this mechanism is in a sense the best possible. Second, we show that the VCG mechanism gives a universal constant factor approximation when the number of bidders is even a small multiple of the number of items. Along the way we point out that Myerson’s characterization [11] fails to extend to utility-maximization for risk-averse sellers, and establish interesting properties of regular distributions and monotone hazard rate distributions.

For revenue and welfare maximization in singledimensional Bayesian settings, Chawla et al. (STOC10) recently showed that sequential posted-price mechanisms (SPMs), though simple in form, can perform surprisingly well compared to the optimal mechanisms. In this paper, we give a theoretical explanation of this fact, based on a connection to the notion of correlation gap. Loosely speaking, for auction environments with matroid constraints, we can relate the performance of a mechanism to the expectation of a monotone submodular function over a random set. This random set corresponds to the winner set for the optimal mechanism, which is highly correlated, and corresponds to certain demand set for SPMs, which is independent. The notion of correlation gap of Agrawal et al. (SODA10) quantifies how much we “lose ” in the expectation of the function by ignoring correlation in the random set, and hence bounds our loss in using certain SPM instead of the optimal mechanism. Furthermore, the correlation gap of a monotone and submodular function is known to be small, and it follows that certain SPM can approximate the optimal mechanism by a good constant factor. Exploiting this connection, we give tight analysis of a greedy-based SPM of Chawla et al. for several environments. In particular, we show that it gives an e/(e − 1)-approximation for matroid environments, gives asymptotically a 1/(1 − 1 / √ 2πk)-approximation for the important sub-case of k-unit auctions, and gives a (p + 1)-approximation for environments with p-independent set system constraints. 1

We consider profit maximizing (incentive compatible) mechanism design in general environments that include, e.g., position auctions (for selling advertisements on Internet search engines) and single-minded combinatorial auctions. We analyze optimal envy-free pricings in these settings, and give economic justification for using the optimal revenue of envyfree pricings as a benchmark for prior-free mechanism design and analysis. Moreover, we show that envy-free pricing has a simple nice structure and a strong connection to incentive compatible mechanism design, and we exploit this connection to design prior-free mechanisms with strong approximation guarantees.

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1.1. Motivation. Many modern computer science applications involve autonomous, self-interested agents. It is therefore important for us to consider agents ' strategic behavior in modelling the problems, where non-cooperative game theory can be very helpful. Unfortunately, as one can expect, strategic behavior of the agents often

Most results in revenue-maximizing auction design hinge on “getting the price right ” — offering goods to bidders at a price low enough to encourage a sale, but high enough to garner non-trivial revenue. Getting the price right can be hard work, especially when the seller has little or no a priori information about bidders’ valuations. A simple alternative approach is to “let the market do the work”, and have prices emerge from competition for scarce goods. The simplest-imaginable implementation of this idea is the following: first, if necessary, impose an artificial limit on the number of goods that can be sold; second, run the welfare-maximizing VCG mechanism subject to this limit. We prove that such “supply-limiting mechanisms ” achieve near-optimal expected revenue in a range of single- and multi-parameter Bayesian settings. Indeed, despite their simplicity, we prove that they essentially match the state-of-the-art in prior-independent mechanism design.

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