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...zed for general valuation functions (Section 3.2). Finally, we give a decomposition algorithm (Section 3.3) which yields an α-approximation to the optimal social welfare of BFS. 3.1 LP Relaxation of BFS with Deadline Valuation Functions Linear Relaxation Consider the following relaxed linear program. Every variable yj (t) for t ∈ Tj in (LP-D) denotes the number of servers assigned to j at time t. We use yj to denote the mapping induced by the variables {yj (t)}t∈Tj and xj as the completed fraction of job j. (LP-D) max n∑ j=1 vjxj s.t. ∑ t∈Tj yj (t) = Dj · xj ∀j ∈ J (1)∑ j∈Jt yj (t) ≤ C ∀t ∈ T (2) 0 ≤ yj (t) ≤ kjxj ∀j ∈ J , t ∈ Tj (3) 0 ≤ xj ≤ 1 ∀j ∈ J (4) Constraints (1) and (2) are job demand and capacity constraints. Typically, the parallelized execution constraints would take the form 0 ≤ yj (t) ≤ k. However, the integrality gap in this case can be as high as Ω (n). Intuitively, (3) “prevents” us from getting bad mappings which do not correspond to feasible allocations. That is, if we would have extended a mapping yj (disregarding capacity constraints) by dividing every entry in yj by xj , we would have exceeded Reallocate(y) 1. While y contains non-MND mappings 1.1. Let j be a job...

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...page with a larger number of viewers potentially also has a larger number of contributors. Our setting is therefore most closely related to the models that do not assume there is a fixed finite number of arms, as in [6], [20], and [21]. All of these papers take a purely algorithmic approach to the learning problem, and so do not address a situation where the number and success probabilities of the arms are endogenously determined in response to the incentives created by the learning algorithm. There is a small but growing literature that addresses incentives in the multi-armed bandit setting. [2], [3], [9], [10], and [13] study multi-armed bandit problems in the context of online advertising with strategic advertisers, and investigate the design of truthful mechanisms when the system must learn the (unknown) click-through rates of ads. The strategic choice of the agents in these papers are the agents’ bids, rather than the click-through rates of the arms that are learned by the mechanism. [5] considers questions related to endogenous pricing decisions of firms when these decisions may influence whether consumers explore other firms and the consumers face a multi-armed bandit problem. ...

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...demand is realized, with no regret as to the outcome, whatever the future realization of demand. Our approach adopts a recent innovation in computational mechanism design due to Babaioff et al. (BKS) =-=[2]-=-, which provides incentive compatibility in domains where payments cannot be computed through “counterfactual” information. Counterfactual information is data about what an allocation would have been ...

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...and the error decreases with q 1 2T . 5.2 IC in expectation, ex post IR mechanisms, WBB in expectation In order to reduce further the compute time it is possible to resort to the approach proposed in =-=[4]-=- computing simultaneously the allocation and the payments with the single call to the allocation function f . Thus, the computational complexity of the mechanism is O(n2 ·k2 · 1 ǫ ). In addition to in...

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...ation rule having sublinear regret with time when the click through rates (CTR) of the advertisements (ads) are affected by ad-dependent externality or position-dependent externality. The above impossibility results motivate our second contribution: when the CTRs are affected by only position-dependent externality and follow click-precedence property, we design a novel ex-post truthful mechanism for multi-slot SSAs with sublinear regret. The ex-post monotone allocation rule in the proposed mechanism non-trivially generalizes the NewCB allocation rule presented by Babaioff, Sharma, and Slivkins[2]. We derive regret bounds for this allocation rule. When a strong property such as ex-post truthfulness is required, our allocation rule performs as well as the A-VCG mechanism presented by Gatti, Lazaric, and Trovo[4] and in the special case of identical slots, our allocation rule in fact outperforms the A-VCG mechanism and has a regret of O (√ T ) with time. Categories and Subject Descriptors 500 [Information systems]: Sponsored search advertising General Terms Economics, Algorithms Keywords Mechanism Design; Sponsored Search; Multi-Armed Bandit 1. INTRODUCTION Sponsored search auction (SSA...

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...various mechanisms including ascending price auctions. In the mechanism design literature, there exist several works that utilize expected values. Our mechanism is inspired by the well-known expected-externality mechanism [9], which achieves Bayesian Nash incentive compatibility, Pareto efficiency, and budget balancedness. Also, instead of using a truthful deterministic mechanism, a mechanism can be randomized so that it becomes truthful in expectation, while the computational or communication complexity of the randomized mechanism can be lower compared to the original deterministic mechanism [4]. 3. MODEL We use the following model of combinatorial auctions. A set of indivisible goods M = {1, . . . ,m} is allocated to a set of participants N = {1, . . . , n}. Participant i privately observes her type θi, which is chosen independently from Θi. For simplicity, we assume Θi is a finite, discrete set. For B ⊆ M , v(θi, B) represents the gross utility of a participant, whose type is θi and she obtains B. We assume v is normalized by v(θi, ∅) = 0, and satisfies free-disposal, i.e., for any B ⊆ B′, v(θi, B) ≤ v(θi, B′) holds. We assume quasi-linear utility, i.e., if a participant, whose typ...