economics
My economic research focuses on microeconomic theory, and in particular on the study of auctions. I am currently pursuing a thread of topics which relate to the provisioning of multiple homogeneous goods in the same auction, a method which is commonly used to allocate government securities, power generation, and other commodities routed through a central agency. I aim to lend theoretical support to arguments in favor of mechanism selection by the auctioneer, with an eye toward practical implementability.

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A Case for PayasBid Auctions
With Marek Pycia
Revise and resubmit, Journal of Political Economy
Payasbid (or discriminatory) auctions are frequently used to sell homogenous goods such as treasury securities and commodities. We prove the uniqueness of their purestrategy Bayesian Nash equilibrium and establish a tractable representation of equilibrium bids. Building on these results we analyze the optimal design of payasbid auctions, as well as uniformprice auctions (the main alternative auction format). We show that supply transparency and full disclosure are optimal in payasbid, though not necessarily in uniformprice; payasbid is revenue dominant and might be welfare dominant; and we provide an explanation for the revenue equivalence observed in empirical work.

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Bidding in MultiUnit Auctions under Limited Information
With Bernhard Kasberger
Revise and resubmit, Journal of Economic Theory
Multiunit auctions frequently take place in environments with limited information, such as in new markets and under volatile macroeconomic conditions We characterize optimal priorfree bids in such auctions; these bids minimize the maximal loss in expected utility resulting from uncertainty surrounding opponent behavior. We show that optimal bids are readily computable in this environment
despite bidders having multidimensional private information. In the payasbid auction the priorfree bid is unique; in the uniformprice auction the priorfree bid is unique if the bidder is allowed to determine the quantities for which they bid, as in many practical applications. We compare priorfree bids and auction outcomes across auction formats, as well as to equilibrium outcomes in highinformation environments.

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Intertemporal Allocation with Unknown Discounting
With Justin Burkett
Revise and resubmit, Journal of Economic Theory
We consider the problem faced by a durable good monopolist who can allocate a single good at any time, but is uncertain of a buyer's values and temporal preferences for receiving the good. We derive conditions under which it is optimal for the monopolist to ignore the uncertainty about the buyer's discount factor and allocate immediately via a single firstperiod price. Under one condition, the seller optimally offers a single firstperiod price if she would weakly raise this price upon learning that the buyer cannot be too impatient (Corollary 2). A related condition states that the single firstperiod price is optimal if buyer types with higher discount factors have stochastically higher values (Corollary 3). These conditions also apply when sellers face ambiguity regarding the buyer's discount factor. Our results provide a novel justification for ignoring heterogeneous discount factors when the seller is incompletely informed about buyer's temporal preferences.

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Supplementary Note for Pycia and Woodward (2023)

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SelfAuditable Auctions
We consider the amount of information necessary to verify that an auction has been run according to the specified rules. A mechanism is audited by a postauction disclosure policy if each outcome maximizes the auctioneer's utility, conditional on consistency with the information released. One mechanism is more auditable than another if any disclosure policy that audits the latter also audits the former. When the seller cannot commit to any bounds on supply, only menus are auditable without additional information. In contrast with other notions of auctioneer believability, claimedsupply discriminatory auctions are no more auditable than uniform price auctions. When the auctioneer claims to select an ex post profitmaximizing allocation, the discriminatory auction is auditable without additional disclosure, but the uniform price auction is not. Nonetheless, the ability to commit to a supply schedule via disclosure strictly improves auctioneer's expected revenue, even in the discriminatory auction.

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Sharing Cost Information in Dynamic Oligopoly
With Greg Kubitz
Revise and resubmit, American Economic Journal: Microeconomics
We study the effect of sharing cost information in dynamic oligopoly. Firms can agree to verifiably share information about common costs, as with the aggregation of input costs by an industry trade association. Cost information that is not directly shared is revealed through observed prices. We show that such information sharing agreements lead to higher prices and reduce consumer surplus when either demand is inelastic or goods are highly substitutable. Information sharing agreements that increase the equilibrium informativeness of prices increase expected prices and reduce consumer surplus. In markets with a large number of firms, information sharing has a minimal impact on expected prices and can increase both consumer and producer surplus when goods are not too substitutable.

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Reserve Prices Eliminate Low Revenue Equilibria in Uniform Price Auctions
With Justin Burkett
Games and Economic Behavior (2020)
Uniform price auctions frequently admit equilibria which raise zero seller revenue. We show that when demand is sufficiently strong — when market supply is more than covered by any bidder's opponents — the introduction of a reserve price improves revenue not only by directly increasing the market clearing price, but also by eliminating low revenue equilibria in which the market clearing price is almost always equal to the reserve. The condition on demand is sharp, and when it is not satisfied there exist equilibria in which the market clearing price almost always equals the reserve. Our results therefore fully characterize the existence of low revenue equilibria in terms of bidder demand at a given reserve price. This sharp characterization extends directly to the case of stochastic supply, and low revenue equilibria also fail to exist when supply is stochastic and elastic.

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Uniform Price Auctions with a Last Accepted Bid Pricing Rule
With Justin Burkett
Journal of Economic Theory (2020)
We model multiunit auctions in which bidders' valuations are multidimensional private information. Under a natural constraint on aggregate demand we show that the last accepted bid uniformpricing rule admits a unique equilibrium with a simple characterization: bids are identical to those submitted in a singleunit first price auction. The form of equilibrium bids suggests that last accepted bid uniformpricing is a generalization of singleunit firstpricing: in both auctions winners pay the highest market clearing price. In contrast with the separating equilibrium of the last accepted bid auction, we show that equilibrium bids in pay as bid and first rejected bid uniform price auctions must pool information. Thus other common multiunit auction formats cannot generalize singleunit firstpricing, in which equilibria do not pool information. Finally, the unique equilibrium we obtain shows that price selection may be an additional tool for avoiding the zerorevenue equilibria which exist in the first rejected bid uniform price auction.

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Equilibrium with Monotone Actions
Reject and resubmit, Econometrica
I show that purestrategy equilibria exist in a class of discontinuous games with private information. In my primary model actions are monotone functions on a compact and convex domain and range, and I provide conditions under which equilibria in discretizations of the primary model converge to an equilibrium in the primary model. The proof approach implies that if observable outcomes and utility are similarly continuous, they will be approximately equal in the primary model and its discretizations. I apply these results to divisiblegood auctions with private information, and simultaneously prove the existence of pure strategy equilibria in discriminatory, uniform price, and hybrid formats. Outcome approximation implies that observed allocations and revenue in multiunit auctions may be close to the theoretical predictions of divisiblegood models.

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MixedPrice Auctions for Divisible Goods
In a mixedprice auction, bidders' payments are convex combinations of price discrimination and the marketclearing price. In a symmetric divisiblegood model, I prove that all purestrategy equilibria in mixedprice auctions are symmetric, and give a closedform expression for equilibrium bids. I show that the set of feasible equilibrium bids shrinks as the auction becomes discriminatory, as aggregate supply becomes deterministic, and as the market becomes large. When bidders have linear marginal values the unique equilibrium of the discriminatory auction raises more revenue than any equilibrium of the uniformprice auction, but an additional bidder may be more valuable than proper selection of auction format. On the whole, sellers implementing uniformprice auctions may reap substantial gains by introducing mild price discrimination.

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Auctions and Other Games with MaxMin Players (slides only)
You might see me present any of the above projects (or others) if you check my calendar.
I am in the process of building and maintaining a list of references contained in my papers. Having been stymied by Google Scholar more than a few times, even with VPN, I think it's only fair to make accessible the papers that I have found in the public domain.
old stuff