The rise of big data technologies, allowing firms to collect detailed consumer data to estimate their willingness to pay, has reignited the longstanding debate on the welfare implications of price discrimination. A significant difficulty in regulating data collection practices is that it is close to impossible to perfectly monitor and control how firms use consumer data, which makes highly targeted regulation impractical. Often the relevant question is if data collection should be permitted, without knowing how much information the firm already has nor how much additional information it might be able to collect.

Screening settings, in which a profit-maximizing principal faces a privately-informed agent, have been studied extensively in the economics literature. A leading example is second-degree price discrimination with alternatives that correspond to different quantities or qualities of a product. In this case, it is natural to order the alternatives from worst (lowest quantity/quality) to best (highest quantity/quality) and to assume that the agent's private information concerns his marginal willingness to pay (for quantity/quality). This results in "increasing differences," which states that for any pair of alternatives, higher types are willing to pay more than lower types in order to obtain the better alternative instead of the worse one.

A group of agents can collectively purchase a public good that yields heterogeneous benefits to its members. Combining a reduced-form implementation result with a duality argument, we characterize the seller's profit-maximizing mechanism. Trade outcomes depend solely on a weighted average of the agents' virtual values, with endogenous voting weights. Heterogeneity in voting weights reflects heterogeneity in agents' value distributions, where agents with lower value distributions are given more weight in trade decisions. Simple pricing rules are generally not (even approximately) optimal.

We study a pricing problem that is motivated by the following examples. A cloud computing platform such as Amazon EC2 sells virtual machines to clients, each of who needs a different number of virtual machine hours. Similarly, cloud storage providers such as Dropbox have customers that require different amounts of storage. Software companies such as Microsoft sell software subscriptions that can have different levels of service. The levels could be the number of different documents you are allowed to create, or the number of hours you are allowed to use the software. Companies like Google and Microsoft sell API calls to artificial intelligence software such as face recognition, to other software developers. Video and mobile games are increasingly designed in such a way that one can pay for better access to certain features. Spotify and iTunes sell music subscription, and different people listen to different number of songs in a month. Cellphone service providers like AT&T and Verizon offer cellular phone call minutes and data. People have widely varying amounts of data consumption.

How should one sell an item to a buyer whose value for the item will only be realized next week? E.g. consider selling a flight to some executive who may or may not have a meeting with a client next week. Suppose that both the seller and the buyer only know a distribution, F, from which the buyer's value, v, for the item will be drawn. One way the seller could go about this sale is to make a take-it-or-leave-it offer today. The offer reads "pay the expected value today to get the item next week". A risk-neutral buyer would find this offer attractive, hence the seller would extract the full surplus.

Optimal mechanisms for agents with multi-dimensional preferences are generally complex. This complexity makes them challenging to solve for and impractical to run. In a typical mechanism design approach, a model is posited and then the optimal mechanism is designed for the model. Successful mechanism design gives mechanisms that one could at least imagine running. By this measure, multi-dimensional mechanism design has had only limited success. In this paper we take the opposite approach, which we term reverse mechanism design. We start by hypothesizing the optimality of a particular form of mechanism that is simple and reasonable to run, then we solve for sufficient conditions for the mechanism to be optimal (among all mechanisms). This paper has two main contributions. The first is in codifying the method of virtual values from single-dimensional auction theory and extending it to agents with multidimensional preferences. The second is in applying this method to two paradigmatic classes of multi-dimensional preferences. The first class is unit-demand preferences (e.g., a homebuyer who wishes to buy at most one house); for this class we give sufficient conditions under which posting a uniform price for each item is optimal. This result generalizes one of Alaei et al. [2013] for a consumer with values uniform on interval [0; 1], and contrasts with an example of Thanassoulis [2004] for a consumer with values uniform on interval [5; 6] where uniform pricing is not optimal. The second class is additive preferences, for this class we give sufficient conditions under which posting a price for the grand bundle is optimal. This result generalizes a recent result of Hart and Nisan [2012] and relates to work of Armstrong [1999]. Similarly to an approach of Alaei et al. [2013], these results for single-agent pricing problems can be generalized naturally to multi-agent auction problems.

Crémer and McLean [1985] showed that, when buyers' valuations are drawn from a correlated distribution, an auction with full knowledge on the distribution can extract the full social surplus. We study whether this phenomenon persists when the auctioneer has only incomplete knowledge of the distribution, represented by a finite family of candidate distributions, and has sample access to the real distribution. We show that the naive approach which uses samples to distinguish candidate distributions may fail, whereas an extended version of the Crémer-McLean auction simultaneously extracts full social surplus under each candidate distribution. With an algebraic argument, we give a tight bound on the number of samples needed by this auction, which is the difference between the number of candidate distributions and the dimension of the linear space they span.

The intuition that profit is optimized by maximizing marginal revenue is a guiding principle in microeconomics. In the classical auction theory for agents with quasi-linear utility and single-dimensional preferences, BR89 show that the optimal auction of M81 is in fact optimizing marginal revenue. In particular Myerson's virtual values are exactly the derivative of an appropriate revenue curve. This paper considers mechanism design in environments where the agents have multi-dimensional and non-linear preferences. Understanding good auctions for these environments is considered to be the main challenge in Bayesian optimal mechanism design. In these environments maximizing marginal revenue may not be optimal, and furthermore, there is sometimes no direct way to implement the marginal revenue maximization mechanism. Our contributions are three fold: we characterize the settings for which marginal revenue maximization is optimal (by identifying an important condition that we call revenue linearity), we give simple procedures for implementing marginal revenue maximization in general, and we show that marginal revenue maximization is approximately optimal. Our approximation factor smoothly degrades in a term that quantifies how far the environment is from an ideal one (i.e., where marginal revenue maximization is optimal). Because the marginal revenue mechanism is optimal for well-studied single-dimensional agents, our generalization immediately extends many approximation results for single-dimensional agents to more general preferences. Finally, one of the biggest open questions in Bayesian algorithmic mechanism design is in developing methodologies that are not brute-force in size of the agent type space (usually exponential in the dimension for multi-dimensional agents). Our methods identify a sub problem that, e.g., for unit-demand agents with values drawn from product distributions, enables approximation mechanisms that are polynomial in the dimension.

We study an abstract optimal auction problem for selecting a subset of self-interested agents to whom to provide a service. A feasibility constraint governs which subsets can be simultaneously served; however, the mechanism may additionally choose to bundle unconstrained attributes such as payments or add-ons with the service. An agent's preference over service and attributes is given by her private type and may be multi-dimensional and non-linear. A single-agent problem is to optimizes a menu to offer an agent subject to constraints on the probabilities with which each of the agent's types is served. We give computationally tractable reductions from multi-agent auction problems to these single-agent problems. Our discussion focuses on maximizing revenue, but our results can be applied to other objectives (e.g., welfare).

We consider the problem of designing auctions in social networks for goods that exhibit single-parameter submodular network externalities in which a bidder's value for an outcome is a fixed private type times a known submodular function of the allocation of his friends. Externalities pose many issues that are hard to address with traditional techniques; our work shows how to resolve these issues in a specific setting of particular interest. We operate in a Bayesian environment and so assume private values are drawn according to known distributions. We prove that the optimal auction is APX-hard. Thus we instead design auctions whose revenue approximates that of the optimal auction. Our main result considers step-function externalities in which a bidder's value for an outcome is either zero, or equal to his private type if at least one friend has the good. For these settings, we provide a e/e+1-approximation. We also give a $0.25$-approximation auction for general single-parameter submodular network externalities, and discuss optimizing over a class of simple pricing strategies.

Today's software systems are more frequently composed from preexisting commercial or non-commercial components and connectors. These components provide complex and independent functionality and are engaged in complex interactions. Component-Based Software Engineering (CBSE) is concerned with composing, selecting and designing such components. As the popularity of this approach and hence number of commercially available software components grows, selecting a set of components to satisfy a set of requirements while minimizing cost is becoming more difficult. This problem necessitates the design of efficient algorithms to automate component selection for software developing organizations. We address this challenge through analysis of Component Selection, the NP-complete process of selecting a minimal cost set of components to satisfy a set of objectives. Due to the high order of computational complexity of this problem, we examine approximating solutions that make the component selection process practicable. We adapt a greedy approach and a genetic algorithm to approximate this problem. We examined the performance of studied algorithms on a set of selected ActiveX components. Comparing the results of these two algorithms with the choices made by a group of human experts shows that we obtain better results using these approximation algorithms.