Session 2: Market Design

The Combinatorial Multi-Round Auction (CMRA) is a new auction format which has already been used in several recent European spectrum auctions. We characterize equilibria in the CMRA that feature auction-specific forms of truthful bidding, demand expansion, and demand reduction for settings in which bidders have either decreasing or non-decreasing marginal values. In particular, we establish sufficient conditions for riskless collusion. Overall, our results suggest that the CMRA might be an attractive auction design in the presence of highly complementary goods on sale. We discuss to what extent our theory is consistent with outcomes data in Danish spectrum auctions and how our predictions can be tested using bidding data.

Regulated banks have traditionally dominated Treasury markets. More recently, less regulated institutions, such as hedge funds, have entered these markets. We document steady bank exit and rising, yet volatile hedge fund participation in the Canadian primary market. To understand hedge fund entry and to trade-off the benefits of greater competition against the costs of higher market volatility, we introduce and estimate a model with multi-unit auctions and endogenous entry. A counterfactual analysis suggests that hedge fund entry was partially driven by bank exit, and that competition benefits may be small compared to volatility costs. This trade-off is likely present in other markets with regular and irregular participants, which can be studied in our framework.

We study the optimal execution problem in a principal-agent setting. A client contracts to purchase a large position from a dealer at a future date. The dealer first buys the position from the market, creating temporary and permanent price impact. The client chooses a contract, which specifies payment as a function of market prices; hidden action precludes her from conditioning on the dealer’s trade sequence. Weighted-average-price contracts are commonly-used. We explicitly characterize the optimal weights: they are symmetric and generally U-shaped over time. Back-of-the-envelope calculations suggest that switching to our optimal contract significantly reduces transaction costs.

We study when a principal’s difficulty in describing payoff-relevant outcomes leads contracts to be optimally incomplete. Our setting is a general principal-agent model in which agents’ actions are partially contractible and the principal can choose the extent of contractibility at a cost. We first characterize implementable and optimal incomplete contracts for any fixed extent of contractibility. We next show that, if costs of contractibility satisfy a generalized notion of having a strictly positive marginal cost, then contracts are optimally coarse: they specify finitely many outcomes out of a continuum of possibilities. This provides a general foundation for incomplete contracts: even with arbitrarily small costs of contractibility, optimal contracts leave almost all outcomes unspecified. We apply these results to study when and why monopoly pricing takes the form of coarse quality tiers.

We study optimal bundling when consumers differ in one dimension. We introduce a partial order on the set of bundles defined by (i) set inclusion and (ii) sales volumes (if sold alone and priced optimally). We show that if the undominated bundles with respect to this partial order are nested, then nested bundling (tiered pricing) is optimal. We characterize which nested menu is optimal: Selling a given menu of nested bundles is optimal if a smaller bundle in (out of) the menu sells more (less)
than a bigger bundle in the menu. We present three applications of these insights: the first two connect optimal bundling and quality design to price elasticities and cost structures; the last one establishes a necessary and sufficient condition for costly screening to be optimal when a principal can use both price and nonprice screening instruments.

Auto-bidding has recently become a popular feature in ad auctions. This feature enables advertisers to simply provide high-level constraints and goals to an automated agent, which optimizes their auction bids on their behalf. These auto-bidding intermediaries interact in a decentralized manner in the underlying auctions, leading to new interesting practical and
theoretical questions on auction design, for example, in understanding the bidding equilibrium properties between auto-bidder intermediaries for different auctions. In this paper, we examine the effect of different auctions on the incentives of advertisers to report their constraints to the auto-bidder intermediaries. More precisely, we study whether canonical auctions such as first price auction (FPA) and second price auction (SPA) are auto-bidding incentive compatible (AIC): whether an advertiser can gain by misreporting their constraints to the autobidder.

We consider value-maximizing advertisers in two important settings: when they have a budget constraint and when they have a target cost-per-acquisition constraint. The main result of our work is that for both settings, FPA and SPA are not AIC. This contrasts with FPA being AIC when auto-bidders are constrained to bid using a (sub-optimal) uniform bidding policy. We further extend our main result and show that any (possibly randomized) auction that is truthful (in the classic profit-maximizing sense), scale-invariant and symmetric is not AIC. Finally, to complement our findings, we provide sufficient market conditions for FPA and SPA to become AIC for two advertisers. These conditions require advertisers’ valuations to be well-aligned. This suggests that when the competition is intense for all queries, advertisers have less incentive to misreport their constraints.

From a methodological standpoint, we develop a novel continuous model of queries. This model provides tractability to study equilibrium with auto-bidders, which contrasts with the standard discrete query model, which is known to be hard. Through the analysis of this model, we uncover a surprising result: in auto-bidding with two advertisers, FPA and SPA are auction equivalent.

Centralized matching markets that are designed by policymakers to prioritize specific participants and achieve specific policy goals are common in practice, but priority is often assigned using endogenous characteristics of participants. I study this in the context of the heart transplant waitlist in the United States where the treatment that a patient receives is used to assign waitlist priority. Policy makers recently changed the prioritization in an attempt to reduce waitlist mortality by assigning higher priority to patients receiving specific treatments previously associated with high waitlist mortality. First, I document a significant response to waitlist incentives in treatments given and transplants that take place. Then, I develop a framework to evaluate the expected life-years gained by a patient from entering a waitlist with a given design that accounts for how doctors select patients into treatments and transplants. Results from the model demonstrate that patients that select into receiving high priority treatments have lower expected life-years under the current design, despite attempts to improve outcomes by responding to priority. Meanwhile patients that would have received these treatments under either design experience a significant increase in expected life-years.

A buyer trades with a group of sellers whose heterogeneous willingness to trade is private information. She must trade with all sellers or none and must offer sellers identical terms of trade. We characterize the optimal mechanism: trade occurs if and only if the buyer’s benefit of trade exceeds a weighted average of sellers’ virtual values. These weights are endogenous, with sellers who are ex ante less inclined to trade being given greater influence. This mechanism always outperforms posted-price mechanisms, using the entire profile of sellers’ values to set the terms of trade. An extension characterizes the entire Pareto frontier.

In many matching markets, matches are formed after costly interviews. We analyze the welfare implications of costly interviewing in a model of worker-firm matching. We use our model to understand the trade-offs between a centralized matching system and a decentralized one, where matches can occur at any time. Centralized matching with a common offer date leads to coordination issues in the interview stage. Each firm must incorporate the externality imposed by the interview decisions of the firms ranked above it when deciding on its interview list. As a result, low-ranked firms often fail to interview some candidates that ex-ante have high match quality. A decentralized setting with exploding offers generates, at a minimum, the same welfare as the centralized setting, though the set of candidates who receive interviews is different. Total welfare is generally maximized with a system that ensures firms interview and match in sequence, clearing the market for the next firm. Such asynchronicity reduces interview congestion. This system can be implemented by encouraging top firms to interview and match early and allowing candidates to renege on offers.

Designed markets often rely on carefully crafted descriptions of mechanisms. By and large, these descriptions implicitly attempt to convey as directly as possible how outcomes are calculated. Are there principled, alternative theories of how to construct descriptions to expose different properties of mechanisms? Recently-proposed menu descriptions aim to provide such a theory towards exposing the strategyproofness of real-world mechanisms such as Deferred Acceptance. We design an incentivized experiment to test the ability of a menu description (compared to a traditional description) to affect participants' understanding of strategyproofness and behavior. We also design treatments conveying the definition of strategyproofness itself rather than the full details of the mechanism, with one treatment following the menu approach, and one using a common mechanism-design definition of strategyproofness.

We present evidence from a randomized trial of the impact of matching workers to jobs using the deferred acceptance (DA) algorithm. Our setting is the U.S. Army’s annual many-to-one marketplace that matches over 14,000 officers to units. Officers and jobs are partitioned into over 100 distinct markets, our unit of randomization. Matching with DA reduced officers’ attrition in their first year in their new match by 16.9 percent, but these gains disappear in the second year. We can rule out a 1.5 pp reduction in attrition within two years. Matching with DA had no impact on performance evaluations or promotions. Although matching with DA increased truthful preference reporting by a statistically significant 10 percent, many officers matched by DA misreport their true preferences. We present new evidence suggesting that communication and coordination of preferences may limit the benefits of strategyproofness in matching markets where each side actively ranks the other.

We provide optimal solutions to an institution that has dual goals of diversity and meritocracy when choosing from a set of applications. For example, in college admissions, administrators may want to admit a diverse class in addition to choosing students with the highest qualifications. We provide a family of choice rules that maximize merit subject to attaining a diversity level. We study the desirable properties of choice rules in this family and use them to find all subsets of applications on the diversity-merit Pareto frontier. In addition, we provide two novel characterizations of matroids.

College admissions in many countries are based on a centrally administered test. Applicants invest a great deal of resources to improve their performance on the test, and there is growing concern about the large costs associated with these activities. We consider modifying such tests by introducing performance-disclosure policies that pool intervals of performance rankings, and investigate how such policies can improve students’ welfare in a Pareto sense. Pooling affects the equilibrium allocation of students.

The Covid-19 pandemic has accelerated the trend of many colleges moving to test-optional, and in some cases test-blind, admissions policies. A frequent claim is that by not seeing standardized test scores, a college is able to admit a student body that it prefers, such as one with more diversity. But how can observing less information allow a college to improve its decisions? We argue that test-optional policies may be driven by social pressure on colleges’ admission decisions. We propose a model of college admissions in which a college disagrees with society on which students should be admitted. We show how the college can use a test-optional policy to reduce its “disagreement cost” with society, regardless of whether this results in a preferred student pool. We discuss which students either benefit from or are harmed by a test-optional policy. In an application, we study how a ban on using race in admissions may result in more colleges going test optional or test blind.

Equal pay laws increasingly require that workers doing “similar” work are paid equal wages within a firm. We study such “equal pay for similar work” (EPSW) policies theoretically and empirically. In our model, we show that when EPSW restricts firms by protected class (e.g. no woman can be paid less than any similar man, and vice versa) firms segregate their workforce by gender in equilibrium. This endogenously lowers competition for workers, as it becomes costly for firms to poach from one another–doing so exposes them to the bite of the policy. When there are more men than women, EPSW leads to an increase in the equilibrium gender wage gap. For a sufficiently high ratio of men to women, there exist equilibria with arbitrarily low wages for women, leading to a particularly large wage gap. By contrast, EPSW that is not based on protected class can decrease the equilibrium wage gap. We test our model predictions using a difference-in-difference approach to analyze a gender-based EPSW enacted in Chile in 2009. We find that the EPSW increases the share of employees working at gender-segregated firms by 3% and increases the gender wage gap by 3%.