Song Zuo

Tighter Relations between Sensitivity and Other Complexity Measures

The sensitivity conjecture of Nisan and Szegedy [12] asks whether the maximum sensitivity of a Boolean function is polynomially related to the other major complexity measures of Boolean functions. Despite major advances in analysis of Boolean functions in the past decade, the problem remains wide open with no positive result toward the conjecture since the work of Kenyon and Kutin from 2004 [11].

Dynamic Revenue Sharing

Many online platforms act as intermediaries between a seller and a set of buyers. Examples of such settings include online retailers (such as Ebay) selling items on behalf of sellers to buyers, or advertising exchanges (such as AdX) selling pageviews on behalf of publishers to advertisers. In such settings, revenue sharing is a central part of running such a marketplace for the intermediary, and fixed-percentage revenue sharing schemes are often used to split the revenue among the platform and the sellers. In particular, such revenue sharing schemes require the platform to (i) take at most a constant fraction \alpha of the revenue from auctions and (ii) pay the seller at least the seller declared opportunity cost c for each item sold. A straightforward way to satisfy the constraints is to set a reserve price at c / (1 - \alpha) for each item, but it is not the optimal solution on maximizing the profit of the intermediary. While previous studies (by Mirrokni and Gomes, and by Niazadeh et al) focused on revenue-sharing schemes in static double auctions, in this paper, we take advantage of the repeated nature of the auctions. In particular, we introduce dynamic revenue sharing schemes where we balance the two constraints over different auctions to achieve higher profit and seller revenue. This is directly motivated by the practice of advertising exchanges where the fixed-percentage revenue-share should be met across all auctions and not in each auction. In this paper, we characterize the optimal revenue sharing scheme that satisfies both constraints in expectation. Finally, we empirically evaluate our revenue sharing scheme on real data.

Dynamic Mechanism Design in the Field

Dynamic mechanisms are a powerful technique in designing revenue-maximizing repeated auctions. Despite their strength, these types of mechanisms have not been widely adopted in practice for several reasons, e.g., for their complexity, and for their sensitivity to the accuracy of predicting buyers» value distributions. In this paper, we aim to address these shortcomings and develop simple dynamic mechanisms that can be implemented efficiently, and provide theoretical guidelines for decreasing the sensitivity of dynamic mechanisms on prediction accuracy of buyers» value distributions. We prove that the dynamic mechanism we propose is provably dynamic incentive compatible, and introduce a notion of buyers» regret in dynamic mechanisms, and show that our mechanism achieves bounded regret while improving revenue and social welfare compared to a static reserve pricing policy. Finally, we confirm our theoretical analysis via an extensive empirical study of our dynamic auction on real data sets from online adverting. For example, we show our dynamic mechanisms can provide a +17% revenue lift with relative regret less than 0.2%.

Ex-post IR dynamic auctions with cost-per-action payments

Consider a repeated auction between one seller and many buyers, where each buyer only has an estimation of her value in each period until she actually receives the item in that period. The seller is allowed to conduct a dynamic auction to sell the items but must guarantee ex-post individual rationality. In other words, if the buyer realized that her value of the item she just received was zero, she did not need to pay anything. Unlike the clicks on the ads, these actions are private information only observable by the buyers (advertisers). Hence they may have incentives to misreport the user actions, because they can pay less under cost-per-action payment schemes with ex-post individual rationality guarantees. In this paper, we use a structure that we call credit accounts to enable a general reduction from any incentive compatible and ex-ante individual rational dynamic auction to an approximate incentive compatible and ex-post individually rational dynamic auction with credit accounts. Our reduction can obtain stronger individual rationality guarantees at of the cost of weaker incentive compatibility. Surprisingly, our reduction works without making any common knowledge assumptions. Finally, as a complement to our reduction, we prove that there is no non-trivial auction that is exactly incentive compatible and ex-post individually rational under this setting.

Non-clairvoyant Dynamic Mechanism Design

Despite their better revenue and welfare guarantees for repeated auctions, dynamic mechanisms have not been widely adopted in practice. This is partly due to the complexity of their implementation as well as their unrealistic use of forecasting for future periods. We address these shortcomings and present a new family of dynamic mechanisms that are simple and require no distribution knowledge of future periods. This paper introduces the concept of non-clairvoyance in dynamic mechanism design, which is a measure-theoretic restriction on the information that the seller can use. A dynamic mechanism is non-clairvoyant if the allocation and pricing rule at each period does not depend on the type distributions in future periods. We develop a framework (bank account mechanisms) for characterizing, designing, and proving lower bounds for dynamic mechanisms (clairvoyant or non-clairvoyant). This framework is used to characterize the revenue extraction power of non-clairvoyant mechanisms with respect to mechanisms that are allowed unrestricted use of distributional knowledge.

Dynamic Double Auctions: Towards First Best

We study the problem of designing dynamic double auctions for two-sided markets in which a platform intermediates the trade between one seller offering independent items to multiple buyers, repeatedly over a finite horizon, when agents have private values. Motivated by online platforms for advertising, ride-sharing, and freelancing markets, we seek to design mechanisms satisfying the following properties: no positive transfers, i.e., the platform never asks the seller to make payments nor are buyers ever paid and periodic individual rationality, i.e., every agent derives a non-negative utility from every trade opportunity. We provide mechanisms satisfying these requirements that are asymptotically efficient and budget-balanced with high probability as the number of trading opportunities grows. Moreover, we show that the average expected profit obtained by the platform under these mechanisms asymptotically approaches first best (the maximum possible welfare generated by the market). We also to extend our approach to general environments with complex, combinatorial preferences.

Randomized Assignments for Barter Exchanges: Fairness vs. Efficiency

We study fairness and efficiency properties of randomized algorithms for barter exchanges with direct applications to kidney exchange problems. It is well documented that randomization can serve as a tool to ensure fairness among participants. However, in many applications, practical constraints often restrict the maximum allowed cycle-length of the exchange and for randomized algorithms, this imposes constraints of the cycle-length of every realized exchange in their decomposition. We prove that standard fairness properties such as envy-freeness or symmetry are incompatible with even the weakest notion of economic efficiency in this setting. On the plus side, we adapt some well-known matching mechanisms to incorporate the restricted cycle constraint and evaluate their performance experimentally on instances of the kidney exchange problem, showing tradeoffs between fairness and efficiency.