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.
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