The predominant setting in classic auction theory considers bidders as utility maximizers (UMs), who aim to maximize quasi-linear utility functions. Recent autobidding strategies in online advertising have sparked interest in auction design with value maximizers (VMs), who aim to maximize the total value obtained. In this work, we investigate revenue-maximizing auction design for selling a single item to a mix of UMs and VMs. Crucially, we assume the UM/VM type is private information of a bidder. This shift to a multi-parameter domain complicates the design of incentive compatible mechanisms. Under this setting, we first characterize the optimal auction structure for auctions with a single bidder. We observe that the optimal auction moves gradually from a first-price auction to a Myerson auction as the probability of the bidder being a UM increases from 0 to 1. We also extend our study to multi-bidder setting and present an algorithm for deriving the optimal lookahead auction with multiple mixed types of bidders.
This paper reexamines the classic problem of revenue maximization in single-item auctions with n buyers under the lens of the robust optimization framework. The celebrated Myerson’s mechanism is the format that maximizes the seller’s revenue under the prior distribution, which is mutually independent across all n buyers. As argued in a recent line of work (Caragiannis et al. 22), (Dughmi et al. 24), mutual independence is a strong assumption that is extremely hard to verify statistically, thus it is important to relax the assumption.
While optimal under mutual independent prior, we find that Myerson’s mechanism may lose almost all of its revenue when the independence assumption is relaxed to pairwise independence, i.e., Myerson’s mechanism is not pairwise-robust. The mechanism regains robustness when the prior is assumed to be 3-wise independent. In contrast, we show that second-price auctions with anonymous reserve, including optimal auctions under i.i.d. priors, lose at most a constant fraction of their revenues on any regular pairwise independent prior. Our findings draw a comprehensive picture of robustness to k-wise independence in single-item auction settings.
Multi-winner voting plays a crucial role in selecting representative committees based on voter preferences. Previous research has predominantly focused on single-stage voting rules, which are susceptible to manipulation during preference collection. In order to mitigate manipulation and increase the cost associated with it, we propose the introduction of multiple stages in the voting procedure, leading to the development of a unified framework of multi-stage multi-winner voting rules. To shed light on this framework of voting methods, we conduct an axiomatic study, establishing provable conditions for achieving desired axioms within our model. Our theoretical findings can serve as a guide for the selection of appropriate multi-stage multi-winner voting rules.
Understanding the data value for energy-storage control is critical. The performance of the control policy is highly related to the quality of demand information. An accurate prediction about future demand can better the performance of energy storage control. Thus, the storage control asks for sufficient data-sample collection for qualified prediction. However, the lack of a theory to quantify the data sufficiency for the energy-storage control problem. Meanwhile, demand data samples include privacy information while the storage managers have to procure the data from data owners. Thus, it is necessary to determine the relationship between the data size and the storage-control performance. In addition, a growing number of studies have proposed many storage-control policies. However, we are unknown how to theoretically verify their data-use efficiency. Here, we develop the sample complexity theory of storage-control problem, which enables us to theoretically measure the data-use efficiency of the control strategy and assess the data value. We proposed the sample-based dynamic programming (SDP) algorithm that is both cost-minimization and data-use efficient. Based on the SDP and the sample complexity theory, we manifest the trade-off between data size, computational load, and storage-control performances. Finally, we used real-world data to conduct numerical experiments to validate the effectiveness of the proposed method.
The transportation sector is one of the main consumers of global energy. So, its electrification is crucial for a sustainable future. However, the slow developments in the public infrastructure can be a major bottleneck for such electrification. An increasing number of electric vehicle (EV) charging stations are being built across the world to improve this infrastructure. Competition amongst the EV charging stations improves the market efficiency. In this paper, the effect of this competition on the setting of the service surcharge is investigated. The service surcharge design characterization at the Nash equilibrium for both the symmetric as well as the general market conditions is discussed. The value of the storage system to the transportation sector electrification is also analyzed. It is observed that the storage system helps in improving social welfare by reducing the service surcharge in the market, without hurting the revenue of the EV charging stations.
Dynamic pricing is both an opportunity and a challenge to the end-users. It is an opportunity as it better reflects the real-time market conditions and hence enables an active demand side. However, demand’s active participation does not necessarily lead to benefits. The challenge conventionally comes from the limited flexible resources and limited intelligent devices on the demand side. The decreasing cost of the storage system and the widely deployed smart meters inspire us to design a data-driven storage control framework for dynamic prices. Our work first establishes a stylized model by assuming the knowledge on the structure of dynamic price distributions, and designs the optimal storage control policy. Based on Gaussian Mixture Model, we propose a practical data-driven control framework, which helps relax the assumptions in the stylized model. Numerical studies illustrate the remarkable performance of the proposed data-driven framework.