Pay-as-bid auctions are commonly used to sell treasury securities, purchase government debt, distribute electrical generation, and allocate emissions credits. In spite of the practical relevance of the format, the pay-as-bid auction is a fundamentally misunderstood object. As compared to other popular auction formats used in the sale of homogeneous goods, the pay-as-bid auction is often incorrectly assumed to have comparatively bad incentive properties and to induce suboptimal outcomes. In this dissertation I model the pay-as-bid auction as a set of strategic bidders competing for units of a perfectly-divisible commodity. This model allows surprisingly tractable representations of bidder behavior, which provide novel evidence uniformly in favor of the pay-as-bid auction format.

Chapters 2 and 3 consider the theoretical implications of this model for existing empirical work. I demonstrate that when bidders have private information, equilibrium behavior is well-defined and there is an equilibrium in pure strategies. I additionally show that, through a process I call strategic ironing, bidders face strong incentives to submit bids substantially below their true values. The nature of these incentives implies that previous intuition---the pay-as-bid auction is strategically similar to a single-unit first-price auction---is ill-founded. Although strategic ironing is shown to dramatically reduce equilibrium bids below an intuitive benchmark, the current misunderstanding of the properties of the auction format may perversely imply that the pay-as-bid format generates comparatively higher revenues than has been inferred.

Chapters 4 and 5 engage in a direct comparative investigation of the pay-as-bid format when bidders have no private information. I obtain results on the existence and uniqueness of equilibria in this setting, and show that optimally-parameterized auction formats are revenue equivalent. When the auctions are nonoptimally parameterized, I demonstrate that the pay-as-bid auction revenue-dominates alternate formats. I show computationally that this dominance continues to hold within a broader class of randomized mechanisms. The computational results suggest large-market revenue equivalence within this class.

The findings in this dissertation emphatically support the implementation of the pay-as-bid mechanism. It is well-behaved, potentially tractable, and smoothly revenue-dominant when compared to alternate auction formats.

This dissertation studies market design and auction theory. Chapter 1 studies the impact of school choice on segregation. It shows that the popular school choice mechanisms lead to substantially different school and residential segregation, an important and overlooked aspect of choosing among school choice mechanisms. We show that open enrollment policy in public school choice program can decrease diversity of individual schools and increase segregation depending on which student allocation mechanism is used. Without open enrollment, we study the model of location choice and show that segregation is mainly associated with income. In comparing mechanisms, we show that Boston mechanism fosters segregation more than the deferred acceptance. With open enrollment, the difference between BM and DA becomes more drastic. We show that BM can actually intensify segregation when open enrollment policy is adopted, while DA is more resilient to segregation. The deferred acceptance with multi tie breaking creates maximally diverse schools. Chapter 2 considers conventional auctions when the seller can design bid spaces. Any symmetric equilibrium in a second price auction with bid spaces can be replicated with an equilibrium in a first price auction with bid spaces, but the converse doesn't hold. First price auctions with designed bid spaces revenue dominates second price auction with designed bid spaces, and well-designed first price auction is an optimal selling mechanism. Chapter 3 studies one-to-one matching environment without transfer in the presence of incomplete information on one-side. The existing notions of stability under incomplete information are studied and two alternatives are proposed. Weak Bayesian stability requires that the beliefs of the agents are dervided from a common prior via Bayes' rule and are internally consistent with the presumption that the given matching is stable. Strong Bayesian stability refines weak Bayesian stability by requiring the beliefs of agents are also externally consistent in the sense that the beliefs are narrowed down only when there is a valid reason.

My dissertation is composed of three chapters. In the first, I study the incentive role of information – how the strategic release of information can induce an agent to exert more effort on a project. More specifically, I focus on how feedback can be provided to a worker who is uninformed about the progress they make on a long term project. I show that delaying feedback about their performance can induce the worker to continue working on the project longer than they would were they to learn about their performance without delay. Negative feedback, due to the absence of good news, received in the early stages of the project can cause them to quit prematurely. In the second chapter, I study a model of matching between individuals and institutions. Matching models allow researchers to identify optimal allocations of individuals to school seats, medical residency programs and other positions over which individuals have preferences and for which they may differ in suitability. While we know that in models in which individuals only care about the institution they match with, stable matchings always exist, I show that when individuals also care about the the number of matches made by the institution they join, stable matchings no longer exist in general. I show that stable matchings can only be found under a set of conditions I identify. Relaxing any of these conditions leads to examples of markets with no stable matchings. In the third chapter, I set out to understand why elected politicians choose to toe the party line instead of voting on issues according to their own preferences. I find that despite the short term benefits of voting for their preferred policies, there are long-term benefits from coordinating their voting behavior among like-minded legislators. These findings provide a rationale for why political parties form among politicians with similar policy positions.

The primary focus of this dissertation is to study the connections between the auction mechanism used to sell Treasuries securities and the secondary market activity, when auction participants can trade the auctioned securities among themselves. I use a game theoretically framework where participants understand the market rules and behave strategically so as to maximize their returns. The model is capable of explaining puzzling empirical patterns from the U.S. Treasury market and provides policy implications. In the third chapter of the dissertation I use tools developed by the auction theory to analyze corporate organizations capital structure decisions. For a firm's perspective, using debt to finance new investments could be cheaper than using equity. Nevertheless, a higher debt level increases the risks the investment will be liquidated before it yields the promised dividends. The chapter studies firms' optimal decisions when facing the trade-off between debt and equity and its implications on equilibrium prices and interest rates on the financial market.

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