Simple vs. Optimal Mechanism Design

Mechanism design has found various applications in today\u27s economy, such as ad auctions and online markets. The goal of mechanism design is to design a mechanism or system such that a group of strategic agents are incentivized to choose actions that also help achieve the designer’s objective. However, in many of the mechanism design problems, the theoretically optimal mechanisms are complex and randomized, while mechanisms used in practice are usually simple and deterministic. The focus of this thesis is to resolve the discrepancy between theory and practice by studying the following questions: Are the mechanisms used in practice close to optimal? Can we design simple mechanisms to approximate the optimal one? In this thesis we focus on two important mechanism design settings: multi-item auctions and two-sided markets. We show that in both of the settings, there are indeed simple and approximately-optimal mechanisms. Following Myerson\u27s seminal result, which provides a simple and revenue-optimal auction when a seller is selling a singleitem to multiple buyers, there has been extensive research effort on maximizing revenue in multi-item auctions. However, the revenue-optimal mechanism is proved to be complex and randomized. We provide a unified framework to approximate the optimal revenue in a fairly general setting of multi-item auctions with multiple buyers. Our result substantially improves the results in the literature and applies to broader cases. Another line of works in this thesis focuses on two-sided markets, where sellers also participate in the mechanism and have their own costs. The impossibility result by Myerson and Satterthwaite shows that even in the simplist bilateral trade setting (1 buyer, 1 seller, 1 item), the full welfare is not achievable by a truthful mechanism that does not run a deficit. In this thesis we focus on a more challenging objective gains from trade --- the increment of the welfare, and provide simple mechanisms that approximate the optimal gains from trade, in bilateral trade and many other two-sided market settings

Physical Activity and Early Menopause in the Nurses’ Health Study II

Early menopause, the cessation of menstrual function before age 45, occurs in 10% of women, and is associated with higher premature mortality and increased risk of cardiovascular disease. Lifestyle factors like physical activity may influence menopause timing, but results from prior research are inconsistent. We evaluated the association between physical activity and the occurrence of early natural menopause in the Nurses’ Health Study II. Premenopausal women were followed prospectively from 1989 to 2011. Menopause status was self-reported biennially. Time per week participating in specific activities was reported every four years and used to calculate metabolic task hours (MET). Moderate and vigorous activity in adolescence and young adulthood was reported in 1997. We used Cox proportional hazards model to evaluate the association between physical activity and incidence of natural menopause before age 45 controlling for potential confounding factors. We observed no significant association between adulthood physical activity and early menopause. For example, compared to women with/wk, the hazard ratio for women in the highest category (≥42 MET h/wk) of cumulatively-averaged total physical activity was 0.90 (95% confidence interval: 0.76-1.07; P-trend: 0.63). Similarly, activity in adolescence and young adulthood were unrelated to risk. Body mass index did not modify the relation of physical activity and early menopause. Our findings suggest that physical activity is not associated with incident early menopause

Is Selling Complete Information (Approximately) Optimal?

We study the problem of selling information to a data-buyer who faces a decision problem under uncertainty. We consider the classic Bayesian decision-theoretic model pioneered by Blackwell [Bla51, Bla53]. Initially, the data buyer has only partial information about the payoff-relevant state of the world. A data seller offers additional information about the state of the world. The information is revealed through signaling schemes, also referred to as experiments. In the single-agent setting, any mechanism can be represented as a menu of experiments. A recent paper by Bergemann et al. [BBS18] present a complete characterization of the revenue-optimal mechanism in a binary state and binary action environment. By contrast, no characterization is known for the case with more actions. In this paper, we consider more general environments and study arguably the simplest mechanism, which only sells the fully informative experiment. In the environment with binary state and m ≥ 3 actions, we provide an O(m)-approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor. An important corollary of our lower bound is that the size of the optimal menu must grow at least linearly in the number of available actions, so no universal upper bound exists for the size of the optimal menu in the general single-dimensional setting. We also provide a sufficient condition under which selling only the fully informative experiment achieves the optimal revenue. For multi-dimensional environments, we prove that even in arguably the simplest matching utility environment with 3 states and 3 actions, the ratio between the optimal revenue and the revenue by selling only the fully informative experiment can grow immediately to a polynomial of the number of agent types. Nonetheless, if the distribution is uniform, we show that selling only the fully informative experiment is indeed the optimal mechanism

The Power of Two-sided Recruitment in Two-sided Markets

We consider the problem of maximizing the gains from trade (GFT) in two-sided markets. The seminal impossibility result by Myerson shows that even for bilateral trade, there is no individually rational (IR), Bayesian incentive compatible (BIC) and budget balanced (BB) mechanism that can achieve the full GFT. Moreover, the optimal BIC, IR and BB mechanism that maximizes the GFT is known to be complex and heavily depends on the prior. In this paper, we pursue a Bulow-Klemperer-style question, i.e. does augmentation allow for prior-independent mechanisms to beat the optimal mechanism? Our main result shows that in the double auction setting with $m$ i.i.d. buyers and $n$ i.i.d. sellers, by augmenting $O(1)$ buyers and sellers to the market, the GFT of a simple, dominant strategy incentive compatible (DSIC), and prior-independent mechanism in the augmented market is least the optimal in the original market, when the buyers' distribution first-order stochastically dominates the sellers' distribution. Furthermore, we consider general distributions without the stochastic dominance assumption. Existing hardness result by Babaioff et al. shows that no fixed finite number of agents is sufficient for all distributions. In the paper we provide a parameterized result, showing that $O(log(m/rn)/r)$ agents suffice, where $r$ is the probability that the buyer's value for the item exceeds the seller's value