Jason D. Hartline

Algorithmic pricing via virtual valuations

Algorithmic pricing is the computational problem that sellers (e.g.,in supermarkets) face when trying to set prices for their items to maximize their profit in the presence of a known demand. Guruswami etal. (SODA, 2005) proposed this problem and gave logarithmic approximations (in the number of consumers) for the unit-demand and single-parameter cases where there is a specific set of consumers and their valuations for bundles are known precisely. Subsequently several versions of the problem have been shown to have poly-logarithmic in approximability. This problem has direct ties to the important open question of better understanding the Bayesian optimal mechanism in multi-parameter agent settings; however, for this purpose approximation factors logarithmic in the number of agents are inadequate. It is therefore of vital interest to consider special cases where constant approximations are possible. We consider the unit-demand variant of this pricing problem. Here a consumer has a valuation for each different item and their value for aset of items is simply the maximum value they have for any item in the set. Instead of considering a set of consumers with precisely known preferences, like the prior algorithmic pricing literature, we assume that the preferences of the consumers are drawn from a distribution. This is the standard assumption in economics; furthermore, the setting of a specific set of customers with specific preferences, which is employed in all of the prior work in algorithmic pricing, is a special case of this general Bayesian pricing problem, where there is a discrete Bayesian distribution for preferences specified by picking one consumer uniformly from the given set of consumers. Notice that the distribution over the valuations for the individual items that this generates is obviously correlated. Our work complements these existing works by considering the case where the consumers valuations for the different items are independent random variables. Our main result is a constant approximation algorithm for this problem that makes use of an interesting connection between this problem and the concept of virtual valuations from the single-parameter Bayesian optimal mechanism design literature.

Bayesian algorithmic mechanism design

The principal problem in algorithmic mechanism design is in merging the incentive constraints imposed by selfish behavior with the algorithmic constraints imposed by computational intractability. This field is motivated by the observation that the preeminent approach for designing incentive compatible mechanisms, namely that of Vickrey, Clarke, and Groves; and the central approach for circumventing computational obstacles, that of approximation algorithms, are fundamentally incompatible: natural applications of the VCG approach to an approximation algorithm fails to yield an incentive compatible mechanism. We consider relaxing the desideratum of (ex post) incentive compatibility (IC) to Bayesian incentive compatibility (BIC), where truthtelling is a Bayes-Nash equilibrium (the standard notion of incentive compatibility in economics). For welfare maximization in single-parameter agent settings, we give a general black-box reduction that turns any approximation algorithm into a Bayesian incentive compatible mechanism with essentially the same approximation factor.

An Experimental Study of Data Migration Algorithms

The data migration problem is the problem ofc omputing a plan for moving data objects stored on devices in a network from one configuration to another. Load balancing or changing usage patterns might necessitate such a rearrangement ofda ta. In this paper, we consider the case where the objects are fixed-size and the network is complete. We introduce two new data migration algorithms, one ofwh ich has provably good bounds. We empirically compare the performance of these new algorithms against similar algorithms from Hall et al. [7] which have better theoretical guarantees and find that in almost all cases, the new algorithms perform better. We also find that both the new algorithms and the ones from Hall et al. perform much better in practice than the theoretical bounds suggest.

Near-optimal pricing in near-linear time

We present efficient approximation algorithms for a number of problems that call for computing the prices that maximize the revenue of the seller on a set of items. Algorithms for such problems enable the design of auctions and related pricing mechanisms [3]. In light of the fact that the problems we address are APX-hard in general [5], we design near-linear and near-cubic time approximation schemes under the assumption that the number of distinct items for sale is constant.

Envy-free auctions for digital goods

We study auctions for a commodity in unlimited supply, e.g., a digital good. In particular we consider three desirable properties for auctions: item Competitive: the auction achieves a constant fraction of the optimal revenue even on worst case inputs. item Truthful: any bidders best strategy is to bid the maximum value they are willing to pay. item Envy-free: after the auction is run, no bidder would be happier with the outcome of another bidder (for digital good auctions, this means that there is a single sale price and goods are allocated to all bidders willing to pay this price).Our main result is to show that no constant-competitive auction that is truthful and always gives outcomes are envy-free. We consider two relaxations of these requirements, allowing the auction to be untruthful with vanishingly small probability, and allowing the auction to give non-envy-free outcomes with vanishingly small probability. Under both of these relaxations we get competitive auctions.

From optimal limited to unlimited supply auctions

We investigate the class of single-round, sealed-bid auctions for a set of identical items to bidders who each desire one unit. We adopt the worst-case competitive framework defined by [9, 5] that compares the profit of an auction to that of an optimal single-price sale of least two items. In this paper, we first derive an optimal auction for three items, answering an open question from [8]. Second, we show that the form of this auction is independent of the competitive framework used. Third, we propose a schema for converting a given limited-supply auction into an unlimited supply auction. Applying this technique to our optimal auction for three items, we achieve an auction with a competitive ratio of 3.25, which improves upon the previously best-known competitive ratio of 3.39 from [7]. Finally, we generalize a result from [8] and extend our understanding of the nature of the optimal competitive auction by showing that the optimal competitive auction occasionally offers prices that are higher than all bid values.

Selling ad campaigns: online algorithms with cancellations

We study online pricing problems in markets with cancellations, i.e., markets in which prior allocation decisions can be revoked, but at a cost. In our model, a seller receives requests online and chooses which requests to accept, subject to constraints on the subsets of requests which may be accepted simultaneously. A request, once accepted, can be canceled at a cost which is a fixed fraction of the request value. This scenario models a market for web advertising campaigns, in which the buyback cost represents the cost of canceling an existing contract. We analyze a simple constant-competitive algorithm for a single-item auction in this model, and we prove that its competitive ratio is optimal among deterministic algorithms, but that the competitive ratio can be improved using a randomized algorithm. We then model ad campaigns using knapsack domains, in which the requests differ in size as well as in value. We give a deterministic online algorithm that achieves a bi-criterion approximation in which both approximation factors approach 1 as the buyback factor and the size of the maximum request approach 0. We show that the bi-criterion approximation is unavoidable for deterministic algorithms, but that a randomized algorithm is capable of achieving a constant competitive ratio. Finally, we discuss an extension of our randomized algorithm to matroid domains (in which the sets of simultaneously satisfiable requests constitute the independent sets of a matroid) as well as present results for domains in which the buyback factor of different requests varies.

Competitive Auctions for Multiple Digital Goods

Competitive auctions encourage consumers to bid their utility values while achieving revenue close to that of fixed pricing with perfect market analysis. These auctions were introduced in [6] in the context of selling an unlimited number of copies of a single item (e.g., rights to watch a movie broadcast). In this paper we study the case of multiple items (e.g., concurrent broadcast of several movies). We show auctions that are competitive for this case. The underlying auction mechanisms are more sophisticated than in the single item case, and require solving an interesting optimization problem. Our results are based on a sampling problem that may have other applications.

Derandomization of auctions

We study the problem of designing seller-optimal auctions, i.e. auctions where the objective is to maximize revenue. Prior to this work, the only auctions known to be approximately optimal in the worst case employed randomization. Our main result is the existence of deterministic auctions that approximately match the performance guarantees of these randomized auctions. We give a fairly general derandomization technique for turning any randomized mechanism into an asymmetric deterministic one with approximately the same revenue. In doing so, we bypass the impossibility result for symmetric deterministic auctions and show that asymmetry is nearly as powerful as randomization for solving optimal mechanism design problems. Our general construction involves solving an exponential-sized flow problem and thus is not polynomial-time computable. To complete the picture, we give an explicit polynomial-time construction for derandomizing a specific auction with good worst-case revenue. Our results are based on toy problems that have a flavor similar to the hat problem from [3].

Limited and online supply and the bayesian foundations of prior-free mechanism design

We study auctions for selling a limited supply of a single commodity in the case where the supply is known in advance and the case it is unknown and must be instead allocated in an online fashion. The latter variant was proposed by Mahdian and Saberi [12] as a model of an important phenomena in auctions for selling Internet advertising: advertising impressions must be allocated as they arrive and the total quantity available is unknown in advance. We describe the Bayesian optimal mechanism for these variants and extend the random sampling auction of Goldberg et al. [8] to address the prior-free case.