Efficient and truthful mechanisms to price resources on remote servers machines has been the subject of much work in recent years due to the importance of the cloud market. This paper considers revenue maximization in the online stochastic setting with non-preemptive jobs and a unit capacity server. One agent job arrives at every time step, with parameters drawn from an underlying unknown distribution. We design a posted-price mechanism which can be efficiently computed, and is revenue-optimal in expectation and in retrospect, up to additive error. The prices are posted prior to learning the agent's type, and the computed pricing scheme is deterministic, depending only on the length of the allotted time interval and on the earliest time the server is available. If the distribution of agent's type is only learned from observing the jobs that are executed, we prove that a polynomial number of samples is sufficient to obtain a near-optimal truthful pricing strategy.
Posted price mechanisms (PPM) have been introduced by @cite_9 and have gained attention due to their simplicity, robustness to collusion, and their ease of implementation in practice. One of the first theoretical results concerning PPM's is an asymptotic comparison to classical single-parameter mechanisms @cite_10 . They were later studied by @cite_18 for the objective of revenue maximization, and further strengthened by @cite_0 and @cite_19 . @cite_17 shows that sequential PPM's can @math -approximate social welfare for XOS valuation functions, if the price for an item is equal to the expected contribution of the item to the social welfare.
@cite_18 @cite_9 @cite_0 @cite_19 @cite_10 @cite_17
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We consider the problem of pricing n items to maximize revenue when faced with a series of unknown buyers with complex preferences, and show that a simple pricing scheme achieves surprisingly strong guarantees. We show that in the unlimited supply setting, a random single price achieves expected revenue within a logarithmic factor of the total social welfare for customers with general valuation functions, which may not even necessarily be monotone. This generalizes work of Guruswami et. al [18], who show a logarithmic factor for only the special cases of single-minded and unit-demand customers. In the limited supply setting, we show that for subadditive valuations, a random single price achieves revenue within a factor of 2O(√(log n loglog n) of the total social welfare, i.e., the optimal revenue the seller could hope to extract even if the seller could price each bundle differently for every buyer. This is the best approximation known for any item pricing scheme for subadditive (or even submodular) valuations, even using multiple prices. We complement this result with a lower bound showing a sequence of subadditive (in fact, XOS) buyers for which any single price has approximation ratio 2Ω(log1 4 n), thus showing that single price schemes cannot achieve a polylogarithmic ratio. This lower bound demonstrates a clear distinction between revenue maximization and social welfare maximization in this setting, for which [12,10] show that a fixed price achieves a logarithmic approximation in the case of XOS [12], and more generally subadditive [10], customers. We also consider the multi-unit case examined by [1111] in the context of social welfare, and show that so long as no buyer requires more than a 1 -- e fraction of the items, a random single price now does in fact achieve revenue within an O(log n) factor of the maximum social welfare. Abstract Consider the revenue-maximizing problem in which a single seller wants to sell k different items to a single buyer, who has independently distributed values for the items with additive valuation. The case was completely resolved by Myerson’s classical work in 1981, whereas for larger k the problem has been the subject of much research efforts ever since. Recently, Hart and Nisan analyzed two simple mechanisms: selling the items separately, or selling them as a single bundle. They showed that selling separately guarantees at least a fraction of the optimal revenue; and for identically distributed items, bundling yields at least a fraction of the optimal revenue. In this paper, we prove that selling separately guarantees at least fraction of the optimal revenue, whereas for identically distributed items, bundling yields at least a constant fraction of the optimal revenue. These bounds are tight (up to a constant factor), settling the open questions raised by Hart and Nisan. The results are valid for arbitrary probability distributions without restrictions. Our results also have implications on other interesting issues, such as monotonicity and randomization of selling mechanisms. The VCG mechanism is the gold standard for combinatorial auctions (CAs), and it maximizes social welfare. In contrast, the revenue-maximizing (aka optimal) CA is unknown, and designing one is NP-hard. Therefore, research on optimal CAs has progressed into special settings. Notably, Levin [1997] derived the optimal CA for complements when each agent's private type is one-dimensional. (This does not fall inside the well-studied "single-parameter environment".) We introduce a new research avenue for increasing revenue where we poke holes in the allocation space--based on the bids--and then use a welfare-maximizing allocation rule within the remaining allocation set. In this paper, the first step down this avenue, we introduce a new form of "reserve pricing" into CAs. We show that Levin's optimal revenue can be 2-approximated by using "monopoly reserve prices" to curtail the allocation set, followed by welfare-maximizing allocation and Levin's payment rule. A key lemma of potential independent interest is that the expected revenue from any truthful allocation-monotonic mechanism equals the expected virtual valuation; this generalizes Myerson's lemma [1981] from the single-parameter environment. Our mechanism is close to the gold standard and thus easier to adopt than Levin's. It also requires less information about the prior over the bidders' types, and is always more efficient. Finally, we show that the optimal revenue can be 6- approximated even if the "reserve pricing" is required to be symmetric across bidders. For revenue and welfare maximization in single-dimensional Bayesian settings, (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 (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 for several environments. In particular, we show that it gives an @math -approximation for matroid environments, gives asymptotically a @math -approximation for the important sub-case of @math -unit auctions, and gives a @math -approximation for environments with @math -independent set system constraints.