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In a seminal paper, Karp, Vazirani, and Vazirani show that a simple ranking algorithm achieves a competitive ratio of 1-1/e for the online bipartite matching problem in the standard adversarial model, where the ratio of 1-1/e is also shown to be optimal. Their result also implies that in the random arrivals model defined by Goel and Mehta, where the online… (More)

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 <i>unknown</i> to the seller. Despite… (More)

In this paper, we first introduce a lower bound technique for the state complexity of transformations of automata. Namely we suggest first considering the class of full automata in lower bound analysis, and later reducing the size of the large alphabet via alphabet substitutions. Then we apply such technique to the complementation of nondeterministic… (More)

- Tim Roughgarden, Qiqi Yan
- 2011

We design an expected polynomial-time, truthful-in-expectation, (1 − 1/e)-approximation mechanism for welfare maximization in a fundamental class of combinatorial auctions. Our results apply to bidders with valuations that are matroid rank sums (MRS), which encompass most concrete examples of submodular functions studied in this context, including coverage… (More)

For revenue and welfare maximization in single-dimensional 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… (More)

The existing literature on optimal auctions focuses on optimizing the <i>expected revenue</i> of the seller, and is appropriate for risk-neutral sellers. In this paper, we identify good mechanisms for <i>risk-averse</i> sellers. As is standard in the economics literature, we model the risk-aversion of a seller by endowing the seller with a monotone concave… (More)

In the context of online ad serving, display ads may appear on different types of web-<i>pages</i>, where each page includes several ad slots and therefore multiple ads can be shown on each page. The set of ads that can be assigned to ad slots of the same page needs to satisfy various pre-specified constraints including exclusion constraints, diversity… (More)

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… (More)

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… (More)

We design an expected polynomial time, truthful in expectation, (1-1/e)-approximation mechanism for welfare maximization in a fundamental class of combinatorial auctions. Our results apply to bidders with valuations that are <i>matroid rank sums (MRS)</i>, which encompass most concrete examples of submodular functions studied in this context, including… (More)