10. "Menu mechanisms." Submitted.
With Yu Zhou. (2021). New version, February 20.
We investigate menu mechanisms: dynamic mechanisms where at each history, an agent selects from a menu of his possible assignments. We provide general conditions guaranteeing that these provide robust implementations, including dominant strategy implementations. We also formalize the insight that these generally improve upon the privacy of direct mechanisms. Applications include elections, marriage, college admissions, auctions, labor markets, matching with contracts, and object allocation.
9. "Fairly taking turns." Submitted.
With Vilmos Komornik. (2020). New version, December 21.
We investigate the fair allocation of a sequence of time slots when each agent is sufficiently patient. We consider several notions of fairness, and propose several procedures for constructing fair allocations.
(2020). Under revision.
I revisit Savage's model of choice under uncertainty with a finite number of outcomes n, and prove that Savage's first five postulates, monotone continuity, (8n-7)th-order atom-swarming, and a weak sophistication axiom together guarantee a subjective expected utility representation. Because this result allows for a countably infinite collection of atoms, it applies to intertemporal choice.
With Christian Trudeau. (2020). Revise and resubmit, Theoretical Economics.
Standard mechanism design objectives are compatible when allocating an object, but incompatible when providing a public good. Why? We provide an answer in a general model of costly inclusion that covers these environments and many others.
WORK IN PROGRESS
"Mechanisms for one-sided collusion in two-sided markets."
With Christian Trudeau. (2019).
We investigate mechanisms by which a cartel can divide surplus among its members at the expense of the other side of the market. This involves our characterization of the envy-free Groves mechanisms for this problem, which can be found in our older manuscript here.
(2020). Forthcoming, Economic Theory Bulletin.
Using a theorem of Luce, I provide a new proof of my result about representing beliefs with probabilities. The new proof involves almost all of the same techniques, but it avoids constructing a structure that I designed, essentially because Luce constructs something similar.
(2020). Games and Economic Behavior 124, 512-533.
For obviously strategy-proof implementation, it is safe, in a very strong sense, to restrict attention to extensive game forms where the administrator randomizes once at the start of play, then agents take turns making public announcements about their types.
(2020). Economic Theory 69, 713-743.
Using historical documents and axiomatic analysis, I recommend that the Roman Catholic Church overturn the changes of Pope Pius XII to reinstate the papal election format of Pope Gregory XV. I also present some arguments in favor of randomization in the case of deadlock.
(2019). Theoretical Economics 14, 709-778.
When can beliefs, which rank events on the basis of relative likelihood, be represented by a probability measure? I provide a new answer that allows for atoms.
This paper was presented at the Jaffray Memorial Lecture at the 2016 Risk, Uncertainty, and Decision (RUD) Conference.
(2015). Games and Economic Behavior 94, 15-28.
When peers nominate one another for a prize (which may be awarded randomly), the voters are the candidates---so what does it mean to treat everyone symmetrically? I propose several symmetry notions, and give two characterizations using impartiality: the requirement that no agent's report should impact whether or not he wins, removing incentives for strategic nomination.
We consider voting rules that can be administered using physical machines: by casting a vote, an agent exerts a pull on the outcome. In particular, we compare new rules involving weights and strings to familiar rules involving rubber bands in order to explore the tradeoffs between resistance to manipulation, decisiveness, and responsiveness.