Makespan Minimization via Posted Prices

We consider job scheduling settings, with multiple machines, where jobs arrive online and choose a machine selfishly so as to minimize their cost. Our objective is the classic makespan minimization objective, which corresponds to the completion time of the last job to complete. The incentives of the selfish jobs may lead to poor performance. To reconcile the differing objectives, we introduce posted machine prices. The selfish job seeks to minimize the sum of its completion time on the machine and the posted price for the machine. Prices may be static (i.e., set once and for all before any arrival) or dynamic (i.e., change over time), but they are determined only by the past, assuming nothing about upcoming events. Obviously, such schemes are inherently truthful. We consider the competitive ratio: the ratio between the makespan achievable by the pricing scheme and that of the optimal algorithm. We give tight bounds on the competitive ratio for both dynamic and static pricing schemes for identical, restricted, related, and unrelated machine settings. Our main result is a dynamic pricing scheme for related machines that gives a constant competitive ratio, essentially matching the competitive ratio of online algorithms for this setting. In contrast, dynamic pricing gives poor performance for unrelated machines. This lower bound also exhibits a gap between what can be achieved by pricing versus what can be achieved by online algorithms

Pricing for Online Resource Allocation: Intervals and Paths

We present pricing mechanisms for several online resource allocation problems which obtain tight or nearly tight approximations to social welfare. In our settings, buyers arrive online and purchase bundles of items; buyers' values for the bundles are drawn from known distributions. This problem is closely related to the so-called prophet-inequality of Krengel and Sucheston and its extensions in recent literature. Motivated by applications to cloud economics, we consider two kinds of buyer preferences. In the first, items correspond to different units of time at which a resource is available; the items are arranged in a total order and buyers desire intervals of items. The second corresponds to bandwidth allocation over a tree network; the items are edges in the network and buyers desire paths. Because buyers' preferences have complementarities in the settings we consider, recent constant-factor approximations via item prices do not apply, and indeed strong negative results are known. We develop static, anonymous bundle pricing mechanisms. For the interval preferences setting, we show that static, anonymous bundle pricings achieve a sublogarithmic competitive ratio, which is optimal (within constant factors) over the class of all online allocation algorithms, truthful or not. For the path preferences setting, we obtain a nearly-tight logarithmic competitive ratio. Both of these results exhibit an exponential improvement over item pricings for these settings. Our results extend to settings where the seller has multiple copies of each item, with the competitive ratio decreasing linearly with supply. Such a gradual tradeoff between supply and the competitive ratio for welfare was previously known only for the single item prophet inequality

Dynamic Pricing Algorithms, Consumer Harm, and Regulatory Response

Pricing algorithms are rapidly transforming markets, from ride-sharing, to air travel, to online retail. Regulators and scholars have watched this development with a wary eye. Their focus so far has been on the potential for pricing algorithms to facilitate explicit and tacit collusion. This Article argues that the policy challenges pricing algorithms pose are far broader than collusive conduct. It demonstrates that algorithmic pricing can lead to higher prices for consumers in competitive markets and even in the absence of collusion. This consumer harm can be initiated by a single firm employing a superior pricing algorithm. Higher prices arise from the automated nature of algorithms, impacting any market where firms price algorithmically. Pricing algorithms that are already in widespread use may allow sellers to extract a massive amount of wealth from consumers. Because this consumer harm arises even when firms do not collude, antitrust law cannot solve the problem. This Article looks to the history of pricing innovation in the early twentieth century to show how government can respond when new pricing technologies and strategies disrupt markets. It argues for pricing regulation as a feasible solution to the challenges non-collusive algorithmic pricing poses, and it proposes interventions targeted at when and how firms set prices

Welfare maximization with production costs: a primal dual approach

CP2: Session 1BWe study online combinatorial auctions with production costs proposed by Blum et al. using the online primal dual framework. In this model, buyers arrive online, and the seller can produce multiple copies of each item subject to a non-decreasing marginal cost per copy. The goal is to allocate items to maximize social welfare less total production cost. For arbitrary (strictly convex and differentiable) production cost functions, we characterize the optimal competitive ratio achievable by online mechanisms/algorithms. We show that online posted pricing mechanisms, which are incentive compatible, can achieve competitive ratios arbitrarily close to the optimal, and construct lower bound instances on which no online algorithms, not necessarily incentive compatible, can do better. Our positive results improve or match the results in several previous work, e.g., Bartal et al., Blum et al., and Buchbinder and Gonen. Our lower bounds apply to randomized algorithms and resolve an open problem by Buchbinder and Gonen.published_or_final_versio

Online Combinatorial Auctions for Resource Allocation with Supply Costs and Capacity Limits

We study a general online combinatorial auction problem in algorithmic mechanism design. A provider allocates multiple types of capacity-limited resources to customers that arrive in a sequential and arbitrary manner. Each customer has a private valuation function on bundles of resources that she can purchase (e.g., a combination of different resources such as CPU and RAM in cloud computing). The provider charges payment from customers who purchase a bundle of resources and incurs an increasing supply cost with respect to the totality of resources allocated. The goal is to maximize the social welfare, namely, the total valuation of customers for their purchased bundles, minus the total supply cost of the provider for all the resources that have been allocated. We adopt the competitive analysis framework and provide posted-price mechanisms with optimal competitive ratios. Our pricing mechanism is optimal in the sense that no other online algorithms can achieve a better competitive ratio. We validate the theoretic results via empirical studies of online resource allocation in cloud computing. Our numerical results demonstrate that the proposed pricing mechanism is competitive and robust against system uncertainties and outperforms existing benchmarks.Comment: arXiv admin note: text overlap with arXiv:2004.0964