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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Hybrid Mechanisms for the Sale of Divisible Goods
I provide a closedform expression for equilibrium bids in hybrid auctions, where the payment rule is a convex combination of discriminatory and uniform price payment rules. All equilibria are symmetric, and the closedform expression encapsulates all possible equilibria. The class of valid solutions to the expression suggests that the equilibrium multiplicity problem, observed in uniform price auctions, smoothly disappears as an auction becomes discriminatory, or as the market becomes large. When marginal values and bids are both linear, I show that discriminatory auctions strictly revenuedominate any other hybrid mechanism, including pure uniform price auctions. Even if bids are not linear, linear marginal values imply that the discriminatory auction raises strictly more revenue than any equilibrium of the uniform price auction. In large markets all hybrid auctions have incentives that are identical to the discriminatory auction, scaled by the extent of price discrimination, and all hybrid auctions are revenue equivalent.

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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
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 these information sharing agreements lead to higher prices and additionally reduce consumer surplus when either demand is sufficiently inelastic or goods are sufficiently substitutable. In general, information sharing agreements that increase the equilibrium informativeness of prices will increase expected prices, and will reduce consumer surplus. For 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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Equilibrium with Monotone Actions
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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Auctions and Other Games with MaxMin Players (slides only)

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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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Auctions of Homogeneous Goods: A Case for PayasBid
With Marek Pycia
Payasbid and uniform price are the two main formats for selling homogenous goods such as treasury securities and commodities. For payasbid we prove the uniqueness of purestrategy BayesianNash equilibria, establish a tight sufficient condition for the existence of this equilibrium, and an unexpectedly tractable separable representation of equilibrium bids. Building on these results we analyze the optimal design of payasbid and uniformprice auctions and prove that they are revenue and welfare equivalent in any Perfect Bayesian Equilibrium of the auction design game in which the seller can choose either format. We also show that if the seller is constrained to one of the two formats, then payasbid is weakly revenue dominant while the welfare comparison is ambiguous.

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Sharpness of Approximation Boundary in the Bipartite Pricing Problem
The bipartite demand problem is known to have an easy approximation which generates at least half the maximum profits for the selling side of the market. We demonstrate via an example that this approximation is tight, and that the results of the approximation algorithm cannot necessarily be improved upon any subsequent algorithm which takes the approximation as given.

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White Elephant is not StrategyProof
In an extended blog post, I show that the traditional American holiday game White Elephant — alternatively, Yankee Swap — is not strategyproof.
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.
programming
Coding helps me explore unusual, aesthetic questions. While it might be a stretch to classify the following as research proper, each represents something deeper than justawebsite. All can be played with to satisfy your own curiosity, although some need to be downloaded first.

Fractal generator
HTML5 implementation of the splash page fractals, built to test realtime image generation prior to site upgrade. 2D rendering in WebGL is still an emerging feature, with especial pitfalls if the underlying optimization problems are not known in advance; there's a <canvas> backup for browsers that don't make the grade.

Javascript Logo
A partial (yet fairly robust) implementation of the Microworlds dialect of Logo through Javascript and canvas. Documentation is asyet nonexistent, but there are several examples to demonstrate basic features; the header graphics on this website are generated through the interpreter, so viewing source is another excellent tool. Currently there is no turtle icon moving around, since Inkscape runs like molasses on my machine.

LaTeX to png
Generates png graphics from LaTeX math markup; although there are many similar services out there at present, back in 2008 this was pretty much the option. As of right now, I am hosting 60412 mathematical formulas available to the world, which proves that someone out there finds this useful.

ROFLBOT
A locallysuccessful rockpaperscissors runnerup, coming in second place in the firstandlast annual Homestead RockPaperScissors championship (where the only rule was to not implement Iocaine Powder). The primary challenge of this was not so much implementing a complex decision rule as it was implementing it in LOLCODE; I am proud of its performance given the constraints.

YALI
A Perl interpreter for LOLCODE; now ships with FreeBSD. While cat macros have come and gone — and good riddance — this experiment in language design and implementation has proved fairly instructive downstream.