Session 8: Market Design

We consider screening through prices and ordeals in settings with allocative externalities. Agents care not only about how much they are given, but also about how many and which other agents are allocated to. We explore how allowing agents to engage in ordeals, such as waiting in line or filling out lengthy applications, can increase a seller’s profits by modifying consumer behavior and externalities associated with product consumption. We find that ordeals are useful in revenue optimal mechanisms by either filtering out consumers that lower others’ valuations or by attracting consumers with positive valuation impact on others. We also find conditions under which optimal mechanisms create two classes of customers: those who pay with money and those who pay with effort. Our results can be applied to model situations like concerts attendance or diversity in college admissions.

We use majorization to model comparative diversity in school choice. A population of agents is more diverse than another population of agents if its distribution over groups is less concentrated: being less concentrated takes a specific mathematical meaning borrowed from the theory of majorization. We adapt majorization to favor arbitrary distributional objectives, such as population-level distributions over race/ethnicity or socio-economic status. With school admissions in mind, we axiomatically characterize choice rules that are consistent with modified majorization, and constitute a principled method for admitting a diverse population of students into a school. Two important advantages of our approach is that majorization provides a natural notion of diversity, and that our axioms are independent of any exogenous priority ordering.

Path independence is arguably one of the most important choice rule properties in economic theory. We show that a choice rule is path independent if and only if it is rationalizable by a utility function satisfying ordinal concavity, a concept closely related to concavity notions in discrete mathematics. We also provide a rationalization result for choice rules that satisfy path independence and the law of aggregate demand.

We propose a measure of strategic complexity for a class of strategy-proof mechanisms, which includes all strategy-proof mechanisms used in practice. Our rankings are consistent with the coarser ones implied by the solution concepts of (strong) obvious strategy-proofness (Li, 2017b; Pycia and Troyan, 2023b). The added flexibility of our approach allows a designer to balance a mechanism’s simplicity with other objectives. Our measure characterizes the Ausubel (2004) auction as the simplest way to implement the VCG outcome in multi-unit allocation problems with transfers, and provides novel rankings of mechanisms that implement stable outcomes in matching problems. Finally, we characterize minimally complex mechanisms for a range of settings, and formalize the intuition that some mechanisms are as simple as if they were (strongly) obviously strategy- proof. We explain how this extension can be valuable for high-stakes applications such as the FCC incentive auction.

We show that achieving dominant strategy incentive compatibility often requires a designer to choose a mechanism of severely limited transparency. Since both properties have been shown to affect a mechanism’s performance, we propose as-if dominant strategy mechanisms to successfully balance transparency and straightforward strategic incentives. An as-if dominant strategy mechanism is such that, as long as all agents believe others play as if they were in a static mechanism: (i) They all have a strategy that is optimal no matter what others do, and (ii) rationality alone is enough to ensure that they always best respond to each other. We show that the auction format used by prominent online auction platforms—such as eBay—achieves maximal transparency within the set of as-if dominant strategy second-price auctions with decentralized bids. Furthermore, our approach reconciles theoretical predictions with experimental evidence in a range of settings, from matching to multi-unit auctions environments. Finally, we show that mechanisms satisfying a refinement of as-if dominance are also solvable by iterated elimination of weakly dominated strategies.

Personalizing policies can theoretically increase their effectiveness. However, personalization is difficult when individual types are unobservable and the preferences of policymakers and individuals are not aligned, which could cause individuals to mis- report their type. Mechanism design offers a strategy to overcome this issue: offer a menu of policy choices, and make it incentive-compatible for participants to choose the “right” variant. Using a field experiment that personalized incentives for exercise among 6,800 adults with diabetes and hypertension in urban India, we show that personalizing with an incentive-compatible choice menu substantially improves program performance, increasing the treatment e↵ect of incentives on exercise by 80% with- out increasing program costs relative to a one-size-fits-all benchmark. Personalizing with mechanism design also performs well relative to another potential strategy for personalization: assigning policy variants based on observables.

In many market-design applications, a new mechanism is introduced to reform an existing institution. Compared to the design of a mechanism in isolation, the presence of a status-quo system introduces both challenges and opportunities for the designer. We study this problem in the context of reforming the mechanism used to assign Child Protective Services (CPS) investigators to reported cases of child maltreatment in the U.S. CPS investigators make the consequential decision of whether to place a child in foster care when their safety at home is in question. We develop a design framework built on two sets of results: (i) an identification strategy that leverages the status-quo random assignment of investigators—and administrative data on previous assignments and outcomes—to estimate investigator performance; and (ii) mechanism-design results allowing us to elicit investigators’ preferences and efficiently allocate cases. Our proposed mechanism can be implemented by setting personalized non-linear rates at which each investigator can exchange various types of cases. In a policy simulation, we show that this mechanism reduces the number of investigators’ false positives (children placed in foster care who would have been safe in their homes) by 10% while also decreasing false negatives (children left at home who are subsequently maltreated) and overall foster care placements. Importantly, the reforming mechanism is designed so that no investigator is made worse-off relative to the status-quo. We show that a naive approach which ignores investigator preference heterogeneity would generate substantial welfare losses for investigators, with potential adverse effects on investigator recruitment and turnover.

School-choice clearinghouses often advise students to "rank their true preferences" despite not allowing students to express preferences over peers. We evaluate the consequences of doing so. Empirically, we find students have preferences over relative peer ability in the college admissions market in New South Wales, Australia. Theoretically, we show stable matchings exist even with peer preferences under mild conditions, but finding one via one-shot mechanisms is unlikely. The status quo procedure frequently employed by clearinghouses is to inform applicants about the assignment of students in the previous cohort, inducing a tâtonnement process which potentially provides useful information about likely peers in the current cohort. We theoretically argue this process likely leads to an unstable outcome, and we find instability in our empirical setting. We propose a mechanism that yields stability and incentivizes truthful reporting in the presence of peer preferences.

We compare cardinal-preference and ordinal-preference mechanisms for assignment problems such as school choice, with a focus on a variant of the pseudomarket mechanism of Hylland and Zeck-hauser (1979) as well as an envy-free mechanism related to Nguyen, Peivandi and Vohra (2015). We introduce and theoretically analyze a variant of the pseudomarket mechanism that has an equilibrium selection rule. We also introduce a computer algorithm to compute the implied stochastic assignment. The envy free mechanism is a linear program and hence simpler to compute. We estimate cardinal preferences over schools using data on student submissions of rank ordered lists of schools in Seattle. Using these estimated preferences, we measure the welfare gains from using the pseudomarket and envy-free mechanisms instead of the ordinally-efficient probabilistic serial mechanism. We find that the psuedomarket captures 19% of the possible gains over the ordinal mechanism using a utilitarian benchmark. The envy-free mechanism captures 58% of the possible gains over the ordinal mechanism.

We examine the design of optimal rating systems in the presence of moral hazard. First, an intermediary commits to a rating scheme. Then, a decision-maker chooses an action that generates value for the buyer. The intermediary then observes a noisy signal of the decision-maker’s choice and sends the buyer a signal consistent with the rating scheme. We fully characterize the set of allocations that can arise in equilibrium under any arbitrary rating system. We use this characterization to study various design aspects of optimal rating systems. Specifically, we examine scenarios in which the intermediary can observe a noisy outcome of the decision-maker’s efforts and when the decision-maker can manipulate what the intermediary observes. In presence of manipulation, rating uncertainty should be used fairly robustly. A decline in the cost of manipulation leads to more informative optimal ratings which use a mixture of full revelation and rating uncertainty.

This paper studies the strategic implications of online advertisers adopting attribution-based automated bidding algorithms. Online advertisers typically advertise on multiple publishers to increase their reach. These advertisers face an attribution problem of measuring the effectiveness of each campaign, which serves as a key input for the automated bidding algorithms to determine future bids. However, publishers often have access to more information, such as user behavior on their sites. This information asymmetry, interacting with the algorithm dynamics, can lead to a moral hazard problem: Publishers can exploit the information advantage to target advertisements in ways not aligned with advertisers’ interests. I therefore cast the attribution problem as an incentive design problem, and use a team compensation framework to study the advertiser’s optimal strategy. As in the existing literature, I model publishers as having more information about the incremental effect of an advertisement. More novel, I also model publishers as having more information about the opportunity cost of displaying an advertisement. I find that, if the publishers’ opportunity costs are affiliated, the advertiser’s optimal strategy is, for each publisher respectively, to compensate that publisher only when a user’s desired action (e.g., a visit or a purchase) is preceded by a single advertisement impression by that publisher. I discuss how such incentives can be implemented directly through pay-per-action mechanisms and indirectly through attribution-based automated bidding algorithms. I carry out a field experiment and verify empirically that the opportunity costs are affiliated across publishers. Counterfactual simulations reveal that the optimal strategy increases the advertiser’s ROI by 37% compared to a pay-per-impression strategy. Notably, this suggests a Pareto improvement, as I hold the publisher payoff constant in the comparison. Moreover, I characterize the incentives created by prevalent attribution algorithms and show that single-touch algorithms, which are based on simple rules, yield higher profits than multi-touch algorithms, which are based on the measurement of marginal causal effects. The findings reveal that compensating publishers solely based on the marginal causal effects can be suboptimal, emphasizing the importance of considering the dynamic incentives that measurement tools generate.

In a single-item auction, a duplicitous seller may masquerade as one or more bidders in order to manipulate the clearing price. This paper characterizes auction formats that are shill-proof : a profit-maximizing seller has no incentive to submit any shill bids. We distinguish between strong shill-proofness, in which a seller with full knowledge of bidders’ valuations can never profit from shilling, and weak shill-proofness, which requires only that the expected equilibrium profit from shilling is nonpositive. The Dutch auction (with suitable reserve) is the unique optimal and strongly shill-proof auction. Moreover, the Dutch auction (with no reserve) is the unique prior-independent auction that is both efficient and weakly shill-proof. While there are a multiplicity of strategy-proof, weakly shill-proof, and optimal auctions; any optimal auction can satisfy only two properties in the set {static,strategy-proof, weakly shill-proof}.

The allocation of services and goods often involves both stochastic supply and demand, a feature not captured by the classic auction model. Motivated by applications such as cloud computing, gig platforms, and blockchain auctions, we study the optimal design of mechanisms in an M/M/1 queueing model where buyers have private valuations and incur waiting costs. We derive the dynamically optimal screening mechanism, which strategically manages buyer participation and competition through a reserve price that increases with queue length and an auction to allocate the good. The mechanism balances efficiency and revenue, offering insights into the design of queueing systems in various settings where supply and demand fluctuate over time.

We consider the robust pricing problem of an advertising platform that charges a producer for dis- closing hard evidence of product quality to a consumer before trading. Multiple equilibria arise since consumer beliefs and producer’s contingent advertisement purchases are interdependent. To tackle strategic uncertainty, the platform offers each producer’s quality type a menu of disclosure- probability-and-price plans to maximize its revenue guaranteed across all equilibria. The optimal menus offer a continuum of plans with strictly increasing marginal prices for higher disclosure prob-abilities. Full disclosure is implemented in the unique equilibrium. All partial-disclosure plans, though off-path, preclude bad equilibrium play. This solution admits a tractable price function that suggests volume-based pricing can outperform click-based pricing when strategic uncertainty is accounted for. Moreover, the platform prioritizes attracting higher types into service and offers them higher rents despite symmetric information between the platform and the producer.