Peter Troyan
Job Market Candidate

Stanford University
Department of Economics
579 Serra Mall
Stanford, CA 94305
313-377-0512
petetroy@stanford.edu

Curriculum Vitae

Fields:
Microeconomic Theory, Market Design, Game Theory, Mechanism Design
Expected Graduation Date:
June, 2014

Thesis Committee:
Fuhito Kojima (Primary):
fkojima@stanford.edu

Alvin Roth:
alroth@stanford.edu

Muriel Niederle:
niederle@stanford.edu

Job Market Paper

Market Design under Distributional Constraints: Diversity in School Choice and Other Applications (with Daniel Fragiadakis)
Distributional constraints are important in many market design settings. Prominent examples include the minimum manning requirements at each branch in military cadet matching and diversity in school choice, whereby school districts impose constraints on the demographic distribution of students at each school. Standard assignment mechanisms implemented in practice are unable to accommodate all of these constraints. This leads policymakers to resort to ad-hoc solutions that eliminate blocks of seats ex-ante (before agents submit their preferences) to ensure that all constraints are satisfied ex-post.

We show that these solutions ignore important information contained in the submitted preferences, resulting in avoidable inefficiency. We introduce a new class of dynamic quotas mechanisms that allow the institutional quotas to dynamically adjust to the submitted preferences of the agents. We show how a wide class of mechanisms commonly used in the field can be adapted to our dynamic quotas framework. Focusing in particular on a new dynamic quotas deferred acceptance (DQDA) mechanism, we show that DQDA Pareto dominates current solutions. While it may seem that allowing the quotas to depend on the submitted preferences would compromise the strategyproofness of deferred acceptance, we show that this is not the case: as long as the order in which the quotas are adjusted is determined exogenously to the preferences, DQDA remains strategyproof. Thus, policymakers can be confident that efficiency will be improved without introducing perverse incentives. Simulations with school choice data are used to quantify the potential efficiency gains.

Publications

Comparing School Choice Mechanisms by Interim and Ex-Ante Welfare, Games and Economic Behavior (2012), vol. 75, pp. 936-947
The Boston mechanism and deferred acceptance (DA) are two competing mechanisms widely used in school choice problems across the United States. Recent work has highlighted welfare gains from the use of the Boston mechanism, in particular finding that when cardinal utility is taken into account, Boston interim Pareto dominates DA in certain incomplete information environments with no school priorities. We show that these previous interim results are not robust to the introduction of nontrivial (weak) priorities. However, we partially restore the earlier results by showing that from an ex-ante utility perspective, the Boston mechanism once again Pareto dominates any strategyproof mechanism (including DA), even allowing for arbitrary priority structures. Thus, we advocate ex-ante Pareto dominance as a criterion by which to compare school choice mechanisms. This criterion may be of interest to school district leaders, as they can be thought of as social planners whose goal is to maximize the overall ex-ante welfare of the students. From a policy perspective, school districts may want to use the Boston mechanism over a strategyproof alternative, even with nontrivial priority structures.

Matching and Market Design: An Introduction to Selected Topics (with Fuhito Kojima), Japanese Economic Review (2011), vol. 62, pp. 82-98 [refereed survey article]
Other Research Papers

Collusive Agreements in Auctions: Design and Execution by an Informed Principal (with Alejandro Francetich).
The standard approach in mechanism design by an informed principal assumes that an uninformed, disinterested third party executes the mechanism the principal designs. In auctions where collusion is illegal, collusive agreements are informal, and therefore likely to be designed and executed by the involved parties. In these cases, the standard approach neglects information leakages and minimizes frictions. We model collusion in a second-price auction as a contract-design problem by an informed principal who runs the mechanism: She collects information and then picks the outcome. Valuations are interdependent, and signals are affiliated. We show that all equilibria are monotonic and involve partial pooling at the top. In a pure common-value example, we find a first-mover disadvantage: The proposer is worse off than the receiver, even though both are better off than without collusion. Outside competition for the bidders can also undermine the gains from collusion.

Strategyproof Matching with Minimum Quotas (with Daniel Fragiadakis, Atsushi Iwasaki, Suguru Ueda, and Makoto Yokoo). Under Review.
(A preliminary version appeared as an extended abstract in the Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2012).)
We study matching markets in which institutions may have minimum (in addition to the more standard maximum) quotas. We introduce two new classes of strategyproof mechanisms that allow for minimum quotas as an explicit input, and show that our mechanisms improve welfare relative to current approaches. Because of an incompatibility between standard fairness and nonwastefulness axioms in the presence of minimum quotas, we introduce new second-best axioms and show that they are satisfied by our mechanisms. Last, we use computer simulations to quantify (i) the number of agents who will strictly prefer our mechanisms and (ii) how far they are from the first-best axioms of fairness and nonwastefulness. Combining both the theoretical and simulation results, we argue that our mechanisms should improve the performance of matching markets with minimum quota constraints in practice.

Improving Welfare in Assignment Problems: An Experimental Investigation (with Daniel Fragiadakis)
Many institutions face the task of allocating objects (such as university dormitories) to individuals (students) without the use of monetary transfers. A common solution to this problem is the Random Serial Dictatorship (RSD): agents are ordered randomly, and one at a time, each is assigned her favorite good according to her submitted preferences. While RSD provides each agent with a dominant strategy of ranking objects truthfully, it may produce socially undesirable outcomes whereby it is possible to make some agents substantially better off at only a small cost to others. In this paper, we study the prospect of raising welfare in assignment problems by incentivizing agents to report goods they value similarly as indifferent. Specifically, we modify RSD by ordering agents earlier who report more indifference, a method similar to that used by the Stanford Graduate School of Business to assign MBA students to educational trips abroad. While theory predicts weak welfare gains in equilibrium, this requires agents to calculate nontrivial best response strategies that deviate from simple truth-telling. In practice, it is unknown whether agents will be able to find these equilibria and, if they cannot, what the welfare implications of using such mechanisms will be. Motivated by these observations, we run a lab experiment where we find that many agents follow natural heuristics that entail reporting indifferences between objects that are similar in value. Average earnings increase significantly compared to RSD, but the way in which indifference is rewarded can alter the variance in earnings. This suggests that institutions that use RSD can benefit by rewarding indifference, but should choose how to do so carefully.

Network Formation with Private Information (with Alejandro Francetich).
Statistical network models (in which links form according to some predetermined stochastic procedure) are important tools for analyzing many social and economic phenomena. However, many social and economic networks are in fact the outcome of deliberate decisions by agents who weigh the costs of forming a link against its potential benefits, both direct and indirect. We connect models of random network formation with those of strategic interaction by introducing private information over link values into a basic network formation game. We model agents who choose which links to form, but the presence of private information gives rise to equilibrium outcomes that are random networks. We characterize a family of symmetric cut-off equilibria that provides a strategic foundation for the canonical Erdos-Renyi random network model. We also study different distributional assumptions and analyze asymmetric equilibria that give rise to random networks with different probability distributions. Finally, we advance extensions of the concepts of strong efficiency and pairwise stability to random networks.

Research in Progress

Optimal Collusion without Transfers: A Theory of Price Floors (with Manuel Amador and Kyle Bagwell).
We study a static duopoly game where firms sell differentiated products, set prices, face linear demands and are privately informed about their respective constant costs of production. Colluding firms select a set of permissible prices, where each firm then chooses a price from this set after observing its private cost realization. All transfers between firms are assumed infeasible. The resulting model can be understood as a delegation game with multiple agents, where the objective of the principal is to maximize the agents' ex ante joint welfare. We establish conditions under which optimal collusion is characterized by "price floors."

Teaching

Teaching Evaluations

For teaching materials I have developed for my classes, please see my other website.