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

Temperature effect on non-Darcian flow in low-permeability porous media

In low-permeability porous media, the velocity of a fluid flow exhibits a nonlinear dependence on the imposed pressure gradient. This non-Darcian flow behavior has important implications to geological disposal of nuclear waste, hydrocarbon extraction from shale, and flow and transport in clay-rich aquifers. Temperature has been postulated to affect the threshold pressure gradient of a non-Darcian flow; however, the supporting data is very limited. In this study we for the first time report a systematic measurement of the threshold pressure gradient under various permeabilities and temperatures. The results show that a higher temperature leads to a lower threshold pressure gradient under the same permeability and a faster reduction of the threshold pressure gradient with increasing permeability. The experimental data are fitted to a two-parameter model to determine the parameters, h0 and a, which characterize the interfacial fluid-solid interactions and the transition between the Darcy and non-Darcian regimes

Non-uniform Bid-scaling and Equilibria for Different Auctions: An Empirical Study

In recent years, the growing adoption of autobidding has motivated the study of auction design with value-maximizing auto-bidders. It is known that under mild assumptions, uniform bid-scaling is an optimal bidding strategy in truthful auctions, e.g., Vickrey-Clarke-Groves auction (VCG), and the price of anarchy for VCG is $2$. However, for other auction formats like First-Price Auction (FPA) and Generalized Second-Price auction (GSP), uniform bid-scaling may not be an optimal bidding strategy, and bidders have incentives to deviate to adopt strategies with non-uniform bid-scaling. Moreover, FPA can achieve optimal welfare if restricted to uniform bid-scaling, while its price of anarchy becomes $2$ when non-uniform bid-scaling strategies are allowed. All these price of anarchy results have been focused on welfare approximation in the worst-case scenarios. To complement theoretical understandings, we empirically study how different auction formats (FPA, GSP, VCG) with different levels of non-uniform bid-scaling perform in an autobidding world with a synthetic dataset for auctions. Our empirical findings include: * For both uniform bid-scaling and non-uniform bid-scaling, FPA is better than GSP and GSP is better than VCG in terms of both welfare and profit; * A higher level of non-uniform bid-scaling leads to lower welfare performance in both FPA and GSP, while different levels of non-uniform bid-scaling have no effect in VCG. Our methodology of synthetic data generation may be of independent interest