The design of internet advertisement systems is both an auction design problem and an information retrieval (IR) problem. As an auction, the designer needs to take the participants incentives into account. As an information retrieval problem, it needs to identify the ad that it is the most relevant to a user out of an enormous set of ad candidates. Those aspects are combined by first having an IR system narrow down the initial set of ad candidates to a manageable size followed by an auction that ranks and prices those candidates.

Internet display advertising industry follows two main business models. One model is based on direct deals between publishers and advertisers where they sign legal contracts containing terms of fulfillment for a future inventory. The second model is a spot market based on auctioning page views in real-time on advertising exchange (AdX) platforms such as DoubleClick's Ad Exchange, RightMedia, or AppNexus. These exchanges play the role of intermediaries who sell items (e.g. page-views) on behalf of a seller (e.g. a publisher) to buyers (e.g., advertisers) on the opposite side of the market. The computational and economics issues arising in this second model have been extensively investigated in recent times. In this work, we consider a third emerging model called reservation exchange market. A reservation exchange is a two-sided market between buyer orders for blocks of advertisers' impressions and seller orders for blocks of publishers' page views. The goal is to match seller orders to buyer orders while providing the right incentives to both sides. In this work we first describe the important features of mechanisms for efficient reservation exchange markets. We then address the algorithmic problems of designing revenue sharing schemes to provide a fair division between sellers of the revenue collected from buyers. A major conceptual contribution of this work is in showing that even though both clinching ascending auctions and VCG mechanisms achieve the same outcome from a buyer perspective, however, from the perspective of revenue sharing among sellers, clinching ascending auctions are much more informative than VCG auctions.

One of the major drawbacks of the celebrated VCG auction is its low (or zero) revenue even when the agents have high value for the goods and a competitive outcome would have generated a significant revenue. A competitive outcome is one for which it is impossible for the seller and a subset of buyers to 'block' the auction by defecting and negotiating an outcome with higher payoffs for themselves. This corresponds to the well-known concept of core in cooperative game theory.

A central issue in applying auction theory in practice is the problem of dealing with budget-constrained agents. A desirable goal in practice is to design incentive compatible, individually rational, and Pareto optimal auctions while respecting the budget constraints. Achieving this goal is particularly challenging in the presence of nontrivial combinatorial constraints over the set of feasible allocations. Toward this goal and motivated by AdWords auctions, we present an auction for polymatroidal environments satisfying these properties. Our auction employs a novel clinching technique with a clean geometric description and only needs an oracle access to the submodular function defining the polymatroid. As a result, this auction not only simplifies and generalizes all previous results, it applies to several new applications including AdWords Auctions, bandwidth markets, and video on demand. In particular, our characterization of the AdWords auction as polymatroidal constraints might be of independent interest. This allows us to design the first mechanism for Ad Auctions taking into account simultaneously budgets, multiple keywords and multiple slots. We show that it is impossible to extend this result to generic polyhedral constraints. This also implies an impossibility result for multiunit auctions with decreasing marginal utilities in the presence of budget constraints.

In this paper we consider a mechanism design problem in the context of large-scale crowdsourcing markets such as Amazon's Mechanical Turk mturk, ClickWorker clickworker, CrowdFlower crowdflower. In these markets, there is a requester who wants to hire workers to accomplish some tasks. Each worker is assumed to give some utility to the requester on getting hired. Moreover each worker has a minimum cost that he wants to get paid for getting hired. This minimum cost is assumed to be private information of the workers. The question then is -- if the requester has a limited budget, how to design a direct revelation mechanism that picks the right set of workers to hire in order to maximize the requester's utility? We note that although the previous work (Singer (2010) chen et al. (2011)) has studied this problem, a crucial difference in which we deviate from earlier work is the notion of large-scale markets that we introduce in our model. Without the large market assumption, it is known that no mechanism can achieve a competitive ratio better than 0.414 and 0.5 for deterministic and randomized mechanisms respectively (while the best known deterministic and randomized mechanisms achieve an approximation ratio of 0.292 and 0.33 respectively). In this paper, we design a budget-feasible mechanism for large markets that achieves a competitive ratio of 1 - 1/e ≃ 0.63. Our mechanism can be seen as a generalization of an alternate way to look at the proportional share mechanism, which is used in all the previous works so far on this problem. Interestingly, we can also show that our mechanism is optimal by showing that no truthful mechanism can achieve a factor better than 1 - 1/e, thus, fully resolving this setting. Finally we consider the more general case of submodular utility functions and give new and improved mechanisms for the case when the market is large.

Designing optimal pricing policies and mechanisms for allocating tasks to workers is central to online crowdsourcing markets. In this paper, we consider the following realistic setting of online crowdsourcing markets -- we are given a set of heterogeneous tasks requiring certain skills; each worker has certain expertise and interests which define the set of tasks she is interested in and willing to do. Given this bipartite graph between workers and tasks, we design our mechanism \truthuniform which does the allocation of tasks to workers, while ensuring budget feasibility, incentive-compatibility and achieves near-optimal utility. We further extend our results by exploiting a link with online Adwords allocation problem and present a randomized mechanism \truthfractional with improved approximation guarantees. Apart from strong theoretical guarantees, we carry out extensive experimentation using simulations as well as on a realistic case study of Wikipedia translation project with Mechanical Turk workers. Our results demonstrate the practical applicability of our mechanisms for realistic crowdsourcing markets on the web.

Wireless Sensor Networks are increasingly employed as unobtrusive and infrastructureless networks in both indoor and outdoor environments. In order to reach their full potential, a number of key issues, such as localization and topology control, need to be addressed. However, the performance of these protocols is significantly impacted by the assumptions made about the underlying physical layer. Realistic radio propagation models, used as the physical layer models, provide a more accurate evaluation of protocols when performing network simulations. This paper therefore analyzes the performance of a number of propagation models in a real indoor environment. Specifically, the Unit Disk, Lognormal Shadowing, Volcano Indoor Multi-Wall and WINNER II Stochastic channel models are investigated. Field measurements are performed in an office building to empirically determine the channel parameters and evaluate the models based on various error metrics. A network connectivity analysis is also performed using Monte Carlo simulations to demonstrate the impact the choice of the physical layer model has on the network backbone construction. This paper shows that the Volcano Indoor Multi-Wall and WINNER II Stochastic channel models provide better estimate of the actual path losses in an indoor environment. It also shows that the errors introduced can cause connectivity algorithms to significantly under-estimate (sometimes up to a 14 times under-estimation) the power requirements necessary to guarantee a connected network.

Constraints on agent's ability to pay play a major role in auction design for any setting where the magnitude of financial transactions is sufficiently large. Those constraints have been traditionally modeled in mechanism design as hard budget, i.e., mechanism is not allowed to charge agents more than a certain amount. Yet, real auction systems (such as Google AdWords) allow more sophisticated constraints on agents' ability to pay, such as average budgets. In this work, we investigate the design of Pareto optimal and incentive compatible auctions for agents with constrained quasi-linear utilities, which captures more realistic models of liquidity constraints that the agents may have. Our result applies to a very general class of allocation constraints known as polymatroidal environments, encompassing many settings of interest such as multi-unit auctions, matching markets, video-on demand and advertisement systems.

Online advertising is an essential part of the Internet and the main source of revenue for many web-centric firms such as search engines, social networks, and online publishers. A key component of online advertising is the auction mechanism which selects and prices the set of winning ads. This work is inspired by one of the biggest practical drawbacks of the widely popular Vickrey-Clarke-Groves (VCG) mechanism, which is the unique incentive-compatible mechanism that maximizes social welfare. It is known that VCG lacks a desired property of revenue monotonicity - a natural notion which states that the revenue of a mechanism shouldn't go down as the number of bidders increase or if the bidders increase their bids. Most firms which depend on online advertising revenue have a large sales team to attract more bidders on their inventory as the general belief is that more bidders will increase competition, and hence revenue. However, the lack of revenue monotonicity of VCG conflicts with this general belief and can be strategically confusing for the firm's business.

Motivated by the recent work of [V. V. Vazirani, J. ACM, 59 (2012), 7], we take a fresh look at understanding the quality and robustness of solutions to Nash and nonsymmetric bargaining games by subjecting them to several stress tests. Our tests are quite basic; e.g., we ask whether the solutions are computable in polynomial time, and whether they have certain properties such as efficiency, fairness, and desirable response when agents change their disagreement points or play with a subset of the agents. Our main conclusion is that imposing submodularity, a natural economies of scale condition, on Nash and nonsymmetric bargaining games endows them with several desirable properties.

We revisit the classic problem of fair division from a mechanism design perspective and provide an elegant truthful mechanism that yields surprisingly good approximation guarantees for the widely used solution of Proportional Fairness. This solution, which is closely related to Nash bargaining and the competitive equilibrium, is known to be not implementable in a truthful fashion, which has been its main drawback. To alleviate this issue, we propose a new mechanism, which we call the Partial Allocation mechanism, that discards a carefully chosen fraction of the allocated resources in order to incentivize the agents to be truthful in reporting their valuations. This mechanism introduces a way to implement interesting truthful outcomes in settings where monetary payments are not an option.

Auctions for perishable goods such as internet ad inventory need to make real-time allocation and pricing decisions as the supply of the good arrives in an online manner, without knowing the entire supply in advance. These allocation and pricing decisions get complicated when buyers have some global constraints. In this work, we consider a multi-unit model where buyers have global {\em budget} constraints, and the supply arrives in an online manner. Our main contribution is to show that for this setting there is an individually-rational, incentive-compatible and Pareto-optimal auction that allocates these units and calculates prices on the fly, without knowledge of the total supply. We do so by showing that the Adaptive Clinching Auction satisfies a {\em supply-monotonicity} property. We also analyze and discuss, using examples, how the insights gained by the allocation and payment rule can be applied to design better ad allocation heuristics in practice. Finally, while our main technical result concerns multi-unit supply, we propose a formal model of online supply that captures scenarios beyond multi-unit supply and has applications to sponsored search. We conjecture that our results for multi-unit auctions can be extended to these more general models.

Motivated by an application in kidney exchange, we study the following query-commit problem: we are given the set of vertices of a non-bipartite graph G. The set of edges in this graph are not known ahead of time. We can query any pair of vertices to determine if they are adjacent. If the queried edge exists, we are committed to match the two endpoints. Our objective is to maximize the size of the matching. This restriction in the amount of information available to the algorithm constraints us to implement myopic, greedy-like algorithms. A simple deterministic greedy algorithm achieves a factor 1/2 which is tight for deterministic algorithms. An important open question in this direction is to give a randomized greedy algorithm that has a significantly better approximation factor. This question was first asked almost 20 years ago by Dyer and Frieze [9] where they showed that a natural randomized strategy of picking edges uniformly at random doesn't help and has an approximation factor of 1/2 + o(1). They left it as an open question to devise a better randomized greedy algorithm. In subsequent work, Aronson, Dyer, Frieze, and Suen [2] gave a different randomized greedy algorithm and showed that it attains a factor 0.5 + o where o is 0.0000025. In this paper we propose and analyze a new randomized greedy algorithm for finding a large matching in a general graph and use it to solve the query commit problem mentioned above. We show that our algorithm attains a factor of at least 0.56, a significant improvement over 0.50000025. We also show that no randomized algorithm can have an approximation factor better than 0.7916 for the query commit problem. For another large and interesting class of randomized algorithms that we call vertex-iterative algorithms, we show that no vertex iterative algorithm can have an approximation factor better than 0.75.

A central issue in applying auction theory in practice is the problem of dealing with budget-constrained agents. A desirable goal in practice is to design incentive compatible, individually rational, and Pareto optimal auctions while respecting the budget constraints. Achieving this goal is particularly challenging in the presence of nontrivial combinatorial constraints over the set of feasible allocations. Toward this goal and motivated by AdWords auctions, we present an auction for polymatroidal environments satisfying the above properties. Our auction employs a novel clinching technique with a clean geometric description and only needs an oracle access to the submodular function defining the polymatroid. As a result, this auction not only simplifies and generalizes all previous results, it applies to several new applications including AdWords Auctions, bandwidth markets, and video on demand. In particular, our characterization of the AdWords auction as polymatroidal constraints might be of independent interest. This allows us to design the first mechanism for Ad Auctions taking into account simultaneously budgets, multiple keywords and multiple slots.

We study the following vertex-weighted online bipartite matching problem: G(U, V, E) is a bipartite graph. The vertices in U have weights and are known ahead of time, while the vertices in V arrive online in an arbitrary order and have to be matched upon arrival. The goal is to maximize the sum of weights of the matched vertices in U. When all the weights are equal, this reduces to the classic online bipartite matching problem for which Karp, Vazirani and Vazirani gave an optimal (1 − 1/e)-competitive algorithm in their seminal work [10]. Our main result is an optimal (1 − 1/e)-competitive randomized algorithm for general vertex weights. We use random perturbations of weights by appropriately chosen multiplicative factors. Our solution constitutes the first known generalization of the algorithm in [10] in this model and provides new insights into the role of randomization in online allocation problems. It also effectively solves the problem of online budgeted allocations [14] in the case when an agent makes the same bid for any desired item, even if the bid is comparable to his budget - complementing the results of [14, 3] which apply when the bids are much smaller than the budgets.

Motivated by economic thought, a recent research agenda has suggested the algorithmic study of combinatorial optimization problems under functions which satisfy the property of decreasing marginal cost. A natural first step to model such functions is to consider submodular functions. However, many fundamental problems have turned out to be extremely hard to approximate under general submodular functions, thus indicating the need for a systematic study of subclasses of submodular functions that are practically motivated and yield good approximation ratios. In this paper, we introduce and study an important subclass of submodular functions, which we call discounted price functions. These functions are succinctly representable and generalize linear(additive) price functions. We study the following fundamental combinatorial optimization problems: edge cover, spanning tree, perfect matching and $s-t$ path. We give both upper and lower bound for the approximability of these problems.

In this paper, we present the first approximation algorithms for the problem of designing revenue optimal Bayesian incentive compatible auctions when there are multiple (heterogeneous) items and when bidders have arbitrary demand and budget constraints (and additive valuations). Our mechanisms are surprisingly simple: We show that a sequential all-pay mechanism is a 4 approximation to the revenue of the optimal ex-interim truthful mechanism with a discrete type space for each bidder, where her valuations for different items can be correlated. We also show that a sequential posted price mechanism is a O(1) approximation to the revenue of the optimal ex-post truthful mechanism when the type space of each bidder is a product distribution that satisfies the standard hazard rate condition. We further show a logarithmic approximation when the hazard rate condition is removed, and complete the picture by showing that achieving a sub-logarithmic approximation, even for regular distributions and one bidder, requires pricing bundles of items. Our results are based on formulating novel LP relaxations for these problems, and developing generic rounding schemes from first principles.

In this paper we consider the following maximum budgeted allocation (MBA) problem: Given a set of m indivisible items and n agents, with each agent i willing to pay $b_{ij}$ on item j and with a maximum budget of $B_i$, the goal is to allocate items to agents to maximize revenue. The problem naturally arises as auctioneer revenue maximization in budget-constrained auctions and as the winner determination problem in combinatorial auctions when utilities of agents are budgeted-additive. Our main results are as follows: (i) We give a $3/4$-approximation algorithm for MBA improving upon the previous best of $\simeq0.632$ [N. Andelman and Y. Mansour, Proceedings of the 9th Scandinavian Workshop on Algorithm Theory (SWAT), 2004, pp. 26–38], [J. Vondrák, Proceedings of the 40th Annual ACM Symposium on the Theory of Computing (STOC), 2008, pp. 67–74] (also implied by the result of [U. Feige and J. Vondrák, Proceedings of the 47th IEEE Symposium on Foundations of Computer Science (FOCS), 2006, pp. 667–676]). Our techniques are based on a natural LP relaxation of MBA, and our factor is optimal in the sense that it matches the integrality gap of the LP. (ii) We prove it is NP-hard to approximate MBA to any factor better than $15/16$; previously only NP-hardness was known [T. Sandholm and S. Suri, Games Econom. Behav., 55 (2006), pp. 321–330], [B. Lehmann, D. Lehmann, and N. Nisan, Proceedings of the 3rd ACM Conference on Electronic Commerce (EC), 2001, pp. 18–28]. Our result also implies NP-hardness of approximating maximum submodular welfare with demand oracle to a factor better than $15/16$, improving upon the best known hardness of $275/276$ [U. Feige and J. Vondrák, Proceedings of the 47th IEEE Symposium on Foundations of Computer Science (FOCS), 2006, pp. 667–676]. (iii) Our hardness techniques can be modified to prove that it is NP-hard to approximate the generalized assignment problem (GAP) to any factor better than $10/11$. This improves upon the $422/423$ hardness of [C. Chekuri and S. Khanna, Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2000, pp. 213–222], [M. Chlebík and J. Chlebíková, Proceedings of the 8th Scandinavian Workshop on Algorithm Theory (SWAT), 2002, pp. 170–179]. We use iterative rounding on a natural LP relaxation of the MBA problem to obtain the $3/4$-approximation. We also give a $(3/4-\epsilon)$-factor algorithm based on the primal-dual schema which runs in $\tilde{O}(nm)$ time, for any constant $\epsilon>0$.

Applications in complex systems such as the Internet have spawned recent interest in studying situations involving multiple agents with their individual cost or utility functions. In this paper, we introduce an algorithmic framework for studying combinatorial problems in the presence of multiple agents with submodular cost functions. We study several fundamental covering problems (Vertex Cover, Shortest Path, Perfect Matching, and Spanning Tree) in this setting and establish tight upper and lower bounds for the approximability of these problems.

We compare the expected efficiency of revenue maximizing (or optimal) mechanisms with that of efficiency maximizing ones. We show that the efficiency of the revenue maximizing mechanism for selling a single item with (k + logeovere-1 k + 1) bidders is at least as much as the efficiency of the efficiency-maximizing mechanism with k bidders, when bidder valuations are drawn i.i.d. from a Monotone Hazard Rate distribution. Surprisingly, we also show that this bound is tight within a small additive constant of 4.7. In other words, Θ(log k) extra bidders suffice for the revenue-maximizing mechanism to match the efficiency of the efficiency-maximizing mechanism, while o(log k) do not. This is in contrast to the result of Bulow and Klemperer comparing the revenue of the two mechanisms, where only one extra bidder suffices. More precisely, they show that the revenue of the efficiency-maximizing mechanism with k + 1 bidders is no less than the revenue of the revenue-maximizing mechanism with k bidders.

In this paper we consider the following maximum budgeted allocation (MBA) problem: Given a set of m indivisible items and n agents; each agent i willing to pay bijon item j and with a maximum budget of Bi, the goal is to allocate items to agents to maximize revenue. The problem naturally arises as auctioneer revenue maximization in budget-constrained auctions and as winner determination problem in combinatorial auctions when utilities of agents are budgeted-additive.We give a 3/4-approximation algorithm for MBA improving upon the previous best of sime0.632[2, 10]. Our techniques are based on a natural LP relaxation of MBA and our factor is optimal in the sense that it matches the integrality gap of the LP.We prove it is NP-hard to approximate MBA to any factor better than 15/16, previously only NP-hardness was known [21, 17]. Our result also implies NP- hardness of approximating maximum submodular welfare with demand oracle to a factor better than 15/16, improving upon the best known hardness of 275/276[10].Our hardness techniques can be modified to prove that it is NP-hard to approximate the Generalized Assignment Problem (GAP) to any factor better than 10/11. This improves upon the 422/423 hardness of [7, 9].We use iterative rounding on a natural LP relaxation of MBA to obtain the 3/4-approximation. We also give a (3/4 - epsiv) -factor algorithm based on the primal-dual schema which runs in O(nm) time, for any constant epsiv > 0.

We focus on efficient protocols that enhance a network with topology awareness. We discuss centralized algorithms with provable performance, and introduce decentralized asynchronous heuristics that use only local information and local computations. These algorithms are based on distributed solutions of convex programs expressing optimization of various spectral properties of the matrix associated with the graph of the network topology. For example, these algorithms assign special weights to links crossing or directed towards small cuts by minimizing the second eigenvalue. Our main technical ingredient is to perform the decentralized asynchronous computations in a manner that preserves critical invariants of the exact second eigenvalue of the adjacency matrix associated with the network topology.