In-app advertising is a complex market worth billions of dollars per year, yet it has been studied significantly less than traditional web display ads. In this paper we study an important but often overlooked feature of ads in mobile apps (mostly absent in traditional web ads), that of ad refreshes : A user is shown a stream of banner ads during the app session, in which each ad is displayed in the ad slot for a certain amount of time (the refresh rate) before the ad-slot is refreshed to the next ad. Data analysis on our large-scale experiments that vary refresh rates reveals a surprising result, that cannot be explained by existing user click models: Varying ads» refresh almost preserves total number of clicks. We propose a new, natural, "two-phase" click model for this setting that explains this independence, as well as our measurements of the click-through rate as a function of the impression»s time-on-screen and of ad-repeat counts. The new click model leads to a clean formulation of the problem of auctioning the entire user-session: i.e., determining online, both the sequence of winning ads as well as the amount of time to display each one. We complement the theoretical auction design with results from a live-traffic experiment with its implementation. Our experiments and analysis provide the theoretical foundation for AdMob»s "Google-optimized refresh rate" feature, used by many mobile apps for better monetization of ads shown to millions of users.

In this paper we showcase the lack of robustness of one of the foremost results connecting game theory and learning theory. We show that the zero-sum, ie rank-zero, condition on a two-player game is critical to Freund and Schapire’s fundamental result (Freund & Schapire, 1996) that establishes convergence (of cumulative strategies to a Nash equilibrium) when each player uses the weighted majority algorithm. We show that weighted majority no longer accomplishes such distributed learning in the slightly wider class of games of rank at most one (nearly zero-sum). Our contribution stands in contrast with recent findings showing that the centralized tractability of computing a Nash equilibrium carries through from zero-sum games (as established by the minimax theorem) to nearly zero-sum games.

In this paper we study the approximate learnability of valuations commonly used throughout economics and game theory for the quantitative encoding of agent preferences. We provide upper and lower bounds regarding the learnability of important subclasses of valuation functions that express no-complementarities. Our main results concern their approximate learnability in the distributional learning (PAC-style) setting. We provide nearly tight lower and upper bounds of $\tilde{\Theta}(n^{1/2})$ on the approximation factor for learning XOS and subadditive valuations, both widely studied superclasses of submodular valuations. Interestingly, we show that the $\tilde{\Omega}(n^{1/2})$ lower bound can be circumvented for XOS functions of polynomial complexity; we provide an algorithm for learning the class of XOS valuations with a representation of polynomial size achieving an $O(n^{\eps})$ approximation factor in time $O(n^{1/\eps})$ for any $\eps > 0$. This highlights the importance of considering the complexity of the target function for polynomial time learning. We also provide new learning results for interesting subclasses of submodular functions. Our upper bounds for distributional learning leverage novel structural results for all these valuation classes. We show that many of these results provide new learnability results in the Goemans et al. model (SODA 2009) of approximate learning everywhere via value queries. We also introduce a new model that is more realistic in economic settings, in which the learner can set prices and observe purchase decisions at these prices rather than observing the valuation function directly. In this model, most of our upper bounds continue to hold despite the fact that the learner receives less information (both for learning in the distributional setting and with value queries), while our lower bounds naturally extend.

We introduce a bidding language for expressing negative value externalities in position auctions for online advertising. The unit-bidder constraints (UBC) language allows a bidder to condition a bid on its allocated slot and on the slots allocated to other bidders. We introduce a natural extension of the Generalized Second Price (GSP) auction, the expressive GSP (eGSP) auction, that induces truthful revelation of constraints for a rich subclass of unit-bidder types, namely downward-monotonic UBC. We establish the existence of envy-free Nash equilibrium in eGSP under a further restriction to a subclass of exclusion constraints, for which the standard GSP has no pure strategy Nash equilibrium. The equilibrium results are obtained by reduction to equilibrium analysis for reserve price GSP (Even-Dar et al. 2008). In considering the winner determination problem, which is NP-hard, we bound the approximation ratio for social welfare in eGSP and provide parameterized complexity results.

Uncertainty is present in different guises in many settings, in particular in environments with strategic interactions. However, most game-theoretic models assume that players can accurately observe interactions and their own costs. In this paper we quantify the effect on social costs of two different types of uncertainty: adversarial perturbations of small magnitude to costs (effect called the Price of Uncertainty (PoU) [3]) and the presence of several players with Byzantine, i.e. arbitrary, behavior (effect we call the Price of Byzantine behavior (PoB)). We provide lower and upper bounds on PoU and PoB in two well-studied classes of potential games: consensus games and set-covering games.

Modern engineering systems (such as the Internet) consist of multiple coupled subsystems. Such subsystems are designed with local (possibly conflicting) goals, with little or no knowledge of the implementation details of other subsystems. Despite the ubiquitous nature of such systems very little is formally known about their properties and global dynamics. We investigate such distributed systems by introducing a novel game-theoretic construct, that we call game-coupling. Game coupling intuitively allows us to stitch together the payoff structures of two or more games into a new game. In order to study efficiency issues, we extend the price of anarchy framework to this setting, where we now care about local and global performance. Such concerns give rise to a new notion of equilibrium, as well as a new learning paradigm. We prove matching welfare guarantees for both, both for individual subsystems as well as for the global system, using a generalization of the (λ,μ)-smoothness framework [17]. In the second part of the paper, we establish conditions leading to advantageous couplings that preserve or enhance desirable properties of the original games, such as convergence of best response dynamics and low price of anarchy.

We investigate the extent to which price updates can increase the revenue of a seller with little prior information on demand. We study prior-free revenue maximization for a seller with unlimited supply of n item types facing m myopic buyers present for k < log n days. For the static (k = 1) case, Balcan et al. [2] show that one random item price (the same on each item) yields revenue within a \Theta(log m + log n) factor of optimum and this factor is tight. We define the hereditary maximizers property of buyer valuations (satisfied by any multi-unit or gross substitutes valuation) that is sufficient for a significant improvement of the approximation factor in the dynamic (k > 1) setting. Our main result is a non-increasing, randomized, schedule of k equal item prices with expected revenue within a O((log m + log n) / k) factor of optimum for private valuations with hereditary maximizers. This factor is almost tight: we show that any pricing scheme over k days has a revenue approximation factor of at least (log m + log n) / (3k). We obtain analogous matching lower and upper bounds of \Theta((log n) / k) if all valuations have the same maximum. We expect our upper bound technique to be of broader interest; for example, it can significantly improve the result of Akhlaghpour et al. [1]. We also initiate the study of revenue maximization given allocative externalities (i.e. influences) between buyers with combinatorial valuations. We provide a rather general model of positive influence of others' ownership of items on a buyer's valuation. For affine, submodular externalities and valuations with hereditary maximizers we present an influence-and-exploit (Hartline et al. [13]) marketing strategy based on our algorithm for private valuations. This strategy preserves our approximation factor, despite an affine increase (due to externalities) in the optimum revenue.

Much of AI is concerned with the design of intelligent agents. A complementary challenge is to understand how to design “rules of encounter” (Rosenschein and Zlotkin 1994) by which to promote simple, robust and beneficial interactions between multiple intelligent agents. This is a natural development, as AI is increasingly used for automated decision making in real‐world settings. As we extend the ideas of mechanism design from economic theory, the mechanisms (or rules) become algorithmic and many new challenges surface. Starting with a short background on mechanism design theory, the aim of this paper is to provide a nontechnical exposition of recent results on dynamic incentive mechanisms, which provide rules for the coordination of agents in sequential decision problems. The framework of dynamic mechanism design embraces coordinated decision making both in the context of uncertainty about the world external to an agent and also in regard to the dynamics of agent preferences. In addition to tracing some recent developments, we point to ongoing research challenges.

We exploit methods of sample-based stochastic optimization for the purpose of strategyproof dynamic, multi-unit auctions. There are no analytic characterizations of optimal policies for this domain and thus a heuristic approach, such as that proposed here, seems necessary in practice. Following the suggestion of Parkes and Duong [17], we perform sensitivity analysis on the allocation decisions of an online algorithm for stochastic optimization, and correct the decisions to enable a strategyproof auction. In applying this approach to the allocation of non-expiring goods, the technical problem that we must address is related to achieving strategyproofness for reports of departure. This cannot be achieved through self-correction without canceling many allocation decisions, and must instead be achieved by first modifying the underlying algorithm. We introduce the NowWait method for this purpose, prove its successful interfacing with sensitivity analysis and demonstrate good empirical performance. Our method is quite general, requiring a technical property of uncertainty independence, and that values are not too positively correlated with agent patience. We also show how to incorporate "virtual valuations" in order to increase the seller's revenue.

Many advertisers (bidders) use Internet systems to buy display advertisements on publishers' webpages or on traditional media such as radio, TV and newsprint. They seek a simple, online mechanism to reserve ad slots in advance. On the other hand, media publishers (sellers) represent a vast and varying inventory, and they too seek automatic, online mechanisms for pricing and allocating such reservations. We propose and study a simple model for auctioning such ad slot reservations in advance. A seller will display a set of slots at some point T in the future. Until T, bidders arrive sequentially and place a bid on the slots they are interested in. The seller must decide immediately whether or not to grant a reservation. Our model allows the seller to cancel at any time any reservation made earlier, in which case the holder of the reservation incurs a utility loss amounting to a fraction of her value for the reservation and may also receive a cancellation fee from the seller. Our main result is an online mechanism for allocation and pricing in this model with many desirable game-theoretic properties. It is individually rational. Winners have an incentive to be honest and bidding one's true value dominates any lower bid. Further, it bounds the earnings of speculators who are in the game to obtain the cancellation fees. The mechanism in addition has optimization guarantees. Its revenue is within a constant fraction of the a posteriori revenue of the Vickrey-Clarke-Groves (VCG) mechanism which is known to be truthful (in the offline case). Our mechanism's efficiency is within a constant fraction of the a posteriori optimally efficient solution. If efficiency also takes into account the utility losses of bidders whose reservation was canceled, we show that our mechanism matches (for appropriate values of the parameters) an upper bound on the competitive ratio of any deterministic online algorithm. Our mechanism's technical core is a variant of the online weighted bipartite matching problem where unlike prior variants in which one randomizes edge arrivals or bounds edge weights, we may revoke previously committed edges. Our results make no assumptions about bidders' arrival order or value distribution. They still hold if we replace items with elements of a matroid and matchings with independent sets, or if all bidders have additive value for a set of items.

Through the history of Computer Science, new technologies have emerged and generated fundamental problems of interest to theoretical computer scientists. From the era of telecommunications to computing and now, the Internet and the web, there are many such examples. This article is derived from the emergence of web search and associated technologies, and focuses on the problems of research interest to theoretical computer scientists that arise, in particular at Google.

In a dynamic market, being able to update one’s value based on information available to other bidders currently in the market can be critical to having profitable transactions. This is nicely captured by the model of interdependent values (IDV): a bidder’s value can explicitly depend on the private information of other bidders. In this paper we present preliminary results about the revenue properties of dynamic auctions for IDV bidders. We adopt a computational approach to design single-item revenue-optimal dynamic auctions with known arrivals and departures but (private) signals that arrive online. In leveraging a characterization of truthful auctions, we present a mixed-integer programming formulation of the design problem. Although a discretization is imposed on bidder signals the solution is a mechanism applicable to continuous signals. The formulation size grows exponentially in the dependence of bidders’ values on other bidders’ signals. We highlight general properties of revenue-optimal dynamic auctions in a simple parametrized example and study the sensitivity of prices and revenue to model parameters.

Many advertisers buy advertisements (ads) on the Internet or on traditional media and seek simple, online mechanisms to reserve ad slots in advance. Media publishers represent a vast and varying inventory, and they too seek automatic, online mechanisms for pricing and allocating such reservations. In this paper, we present and study a simple model for auctioning such ad slots in advance. Bidders arrive sequentially and report which slots they are interested in. The seller must decide immediately whether or not to grant a reservation. Our model allows a seller to accept reservations, but possibly cancel the allocations later and pay the bidder a cancellation compensation (bump payment). Our main result is an online mechanism to derive prices and bump payments that is efficient to implement. This mechanism has many desirable properties. It is individually rational; winners have an incentive to be honest and bidding one's true value dominates any lower bid. Our mechanism's efficiency is within a constant fraction of the a posteriori optimally efficient solution. Its revenue is within a constant fraction of the a posteriori revenue of the Vickrey-Clarke-Groves mechanism. Our results make no assumptions about the order of arrival of bids or the value distribution of bidders and still hold if the items for sale are elements of a matroid, a more general setting than slot allocation.

Interdependent values (IDV) is a valuation model allowing bidders in an auction to express their value for the item(s) to sell as a function of the other bidders' information.We investigate the incentive compatibility (IC) of single-item auctions for IDV bidders in dynamic environments.We provide a necessary and sufficient characterization for IC in this setting.We show that if bidders can misreport departure times and private signals, no reasonable auction can be IC.We present a reasonable IC auction for the case where bidders cannot misreport departures.

Query learning models from computational learning theory (CLT) can be adopted to perform elicitation in combinatorial auctions. Indeed, a recent elicitation framework demonstrated that the equivalence queries of CLT can be usefully simulated with price-based demand queries. In this paper, we validate the flexibility of this framework by defining a learning algorithm for atomic bidding languages, a class that includes XOR and OR. We also handle incentives, characterizing the communication requirements of the Vickrey-Clarke-Groves outcome rule. This motivates an extension to the earlier learning framework that brings truthful responses to queries into an equilibrium.

In this paper we examine the role of very simple and noisy sensors for the tracking problem. We propose a binary sensor model, where each sensor's value is converted reliably to one bit of information only: whether the object is moving toward the sensor or away from the sensor. We show that a network of binary sensors has geometric properties that can be used to develop a solution for tracking with binary sensors and present resulting algorithms and simulation experiments. We develop a particle filtering style algorithm for target tracking using such minimalist sensors. We present an analysis of fundamental tracking limitation under this sensor model, and show how this limitation can be overcome through the use of a single bit of proximity information at each sensor node. Our extensive simulations show low error that decreases with sensor density.

An interesting problem in the experiments using visualisation detectors is that of the geometrical reconstruction of the trajectories. In this work a new method for the geometrical reconstruction of trajectories of the charged particles obtained in nucleus–nucleus collisions at 4.5 A GeV/c is proposed. The experiments have been performed at the Syncrophasotron from the JINR Dubna, in the frame of the SKM 200 Collaboration, and the geometrical reconstruction method is based on the facilities offered by the Sun3VME – MaxVideo20 work-station.

We extend the semi-online unit-demand reservations with costly cancel- lations model of Babaioff et al. (1) and Constantin et al. (3) to multi-unit demand bidders with decreasing marginal values. We show how a natural extension of the unit-demand pricing scheme loses important incentive properties. We recover the property that bidding true value(s) dominates any lower bid together with (slightly weaker) opti- mization properties by a simple modification in the pricing scheme.

An important direction in computational mechanism design is to characterize the space of choice functions that can be truthfully implemented. For this, one must carefully describe the class of preferences in a domain. For unrestricted preferences the domain is well-characterized, and small. More-over, recent work [Lavi et al. , 2003] has allowed for “order-based” preferences but found essentially the same (negative) characterization. However, most interesting domains have preferences that are still more structured than those allowed in the order-based model. We highlight this issue in our paper, through many examples, thus demonstrating the limited applicability of this result. We propose extensions to the model of order-based domains to capture new preference structure, and conjec-ture that more positive characterizations for truthfulness are possible. We also advocate, in proposing a research direction for sufficient conditions for truthfulness, that attention be restricted to natural (critical-value based) payment functions.