Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms

How to optimize posted price mechanisms? The sequential posted-price (SPP) mechanism is one of the widely used selling mechanisms in practice. In this mechanism, the seller presents each buyer with a price sequentially and the buyer can either accept or reject the mechanism's offer. Despite the widespread use of the SPP mechanism, the problem of optimizing prices in this mechanism has not been fully addressed. In a paper entitled, “Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms,” H. Beyhaghi, N. Golrezaei, R. Paes Leme, M. Pal, and B. Sivan construct SPP mechanisms by considering the best of two simple pricing rules: one that imitates the optimal mechanism and the other that posts a uniform price (same price for every buyer). Their simple pricing rules can be easily generalized to the setting with multiple units and yield the first improvement over long-established approximation factors.

On the Futility of Dynamics in Robust Mechanism Design

We consider a principal who repeatedly interacts with a strategic agent holding private information. In each round, the agent observes an idiosyncratic shock drawn independently and identically from a distribution known to the agent but not to the principal. The utilities of the principal and the agent are determined by the values of the shock and outcomes that are chosen by the principal based on reports made by the agent. When the principal commits to a dynamic mechanism, the agent best-responds to maximize his aggregate utility over the whole time horizon. The principal’s goal is to design a dynamic mechanism to minimize his worst-case regret, that is, the largest difference possible between the aggregate utility he could obtain if he knew the agent’s distribution and the actual aggregate utility he obtains. We identify a broad class of games in which the principal’s optimal mechanism is static without any meaningful dynamics. The optimal dynamic mechanism, if it exists, simply repeats an optimal mechanism for a single-round problem in each round. The minimax regret is the number of rounds times the minimax regret in the single-round problem. The class of games includes repeated selling of identical copies of a single good or multiple goods, repeated principal-agent relationships with hidden information, and repeated allocation of a resource without money. Outside this class of games, we construct examples in which a dynamic mechanism provably outperforms any static mechanism.

How to Sell a Data Set? Pricing Policies for Data Monetization

The wide variety of pricing policies used in practice by data sellers suggests that there are significant challenges in pricing data sets. In this paper, we develop a utility framework that is appropriate for data buyers and the corresponding pricing of the data by the data seller. Buyers interested in purchasing a data set have private valuations in two aspects—their ideal record that they value the most, and the rate at which their valuation for the records in the data set decays as they differ from the buyers’ ideal record. The seller allows individual buyers to filter the data set and select the records that are of interest to them. The multidimensional private information of the buyers coupled with the endogenous selection of records makes the seller’s problem of optimally pricing the data set a challenging one. We formulate a tractable model and successfully exploit its special structure to obtain optimal and near-optimal data-selling mechanisms. Specifically, we provide insights into the conditions under which a commonly used mechanism—namely, a price-quantity schedule—is optimal for the data seller. When the conditions leading to the optimality of a price-quantity schedule do not hold, we show that the optimal price-quantity schedule offers an attractive worst-case guarantee relative to an optimal mechanism. Further, we numerically solve for the optimal mechanism and show that the actual performance of two simple and well-known price-quantity schedules—namely, two-part tariff and two-block tariff—is near optimal. We also quantify the value to the seller from allowing buyers to filter the data set.

Optimal auctions through deep learning

Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981. Even after 30--40 years of intense research, the problem remains unsolved for settings with two or more items. We overview recent research results that show how tools from deep learning are shaping up to become a powerful tool for the automated design of near-optimal auctions auctions. In this approach, an auction is modeled as a multilayer neural network, with optimal auction design framed as a constrained learning problem that can be addressed with standard machine learning pipelines. Through this approach, it is possible to recover to a high degree of accuracy essentially all known analytically derived solutions for multi-item settings and obtain novel mechanisms for settings in which the optimal mechanism is unknown.

EXPRESS: First-Price Auctions in Online Display Advertising

We link the rapid and dramatic move from second-price to first-price auction format in the display advertising market to the move from the waterfalling mechanism employed by publishers for soliciting bids in a pre-ordered cascade over exchanges, to an alternate header bidding strategy that broadcasts the request for bid to all exchanges simultaneously. First, we argue that the move by the publishers from waterfalling to header bidding was a revenue improving move for publishers in the old regime when exchanges employed second-price auctions. Given the publisher move to header bidding, we show that exchanges move from second-price to first-price auctions to increase their expected clearing prices. Interestingly, when all exchanges move to first-price auctions, each exchange faces stronger competition from other exchanges and some exchanges may end up with lower revenue than when all exchanges use second-price auctions; yet, all exchanges move to first-price auctions in the unique equilibrium of the game. We show that the new regime hinders the exchanges’ ability to differentiate in equilibrium. Furthermore, it allows the publishers to achieve the revenue of the optimal mechanism despite not having direct access to the advertisers.

The Optimal Mechanism Design of Retail Prices in the Electricity Market for Several Types of Consumers

In this paper, we discuss the demand side management (DSM) problem: how to incentivize a consumer to equalize the load during the day through price-dependent demand. Traditionally, the retail market offers several electricity payment schemes. A scheme is effective when the different tariffs satisfy different consumers. At the same time, the existing and generally accepted retail pricing schemes can lead to an "adverse selection" problem when all consumers choose the same price, thereby, reducing the possible general welfare. We propose an optimal design of pricing mechanisms, taking into account the interests of the electricity supplier and different types of consumers. The results of our work are that the optimal mechanism is implemented simultaneously for several periods, including the case when the ratio of types of consumers in periods changes. In addition, the mechanism proposed by us, in contrast to the studies of other researchers, provides an equilibrium close to the socially optimal maximum. We describe the implementation algorithm of the mechanism and provide examples of its action in the electric power system with different types and numbers of consumers.