Assignment mechanisms for many-to-one matching markets with preferences revolve around the key concept of stability. Using school choice as our matching market application, we introduce the problem of jointly allocating a school capacity expansion and finding the best stable allocation for the students in the expanded market. We theoretically analyze the problem, focusing on the trade-off behind the multiplicity of student-optimal assignments, the incentive properties, and the problem’s complexity. Due to the impossibility of efficiently solving the problem with classical methods, we generalize existent mathematical programming formulations of stability constraints to our setting, most of which result in integer quadratically-constrained programs. In addition, we propose a novel mixed-integer linear programming formulation that is exponentially-large on the problem size. We show that its stability constraints can be separated in linear time, leading to an effective cutting-plane method. We evaluate the performance of our approaches in a detailed computational study, and we find that our cutting-plane method outperforms MIP solvers applied to the formulations obtained by extending existing approaches. We also propose two heuristics that are effective for large instances of the problem. Finally, we use the Chilean school choice system data to demonstrate the impact of capacity planning under stability conditions. Our results show that each additional school seat can benefit multiple students. Moreover, our methodology can prioritize the assignment of previously unassigned students or improve the assignment of several students through improvement chains. These insights empower the decision-maker in tuning the matching algorithm to provide a fair application-oriented solution.

Motivated by online dating apps, we consider the problem of selecting the subset of profiles to show to each user in each period in a two-sided matching platform. Users on each side observe the profiles set by the platform and decide which of them to like. A match occurs if and only if two users mutually like each other, potentially in different periods. We study how platforms should make this decision to maximize the expected number of matches under different platform designs, varying (i) how users interact with each other, i.e., whether one or both sides of the market can initiate an interaction (one and two-directional, resp.), and (ii) the timing of matches, i.e., whether the platform allows non-sequential matches (i.e., when both users see and like each other in the same period) in addition to sequential ones. We focus on the case with two periods and study the performance of different approaches. First, we show that natural approaches in the online matching and assortment literature, including greedy and perfect matching, have worst-case performance arbitrarily close to zero. Second, we show that algorithms that exploit the submodularity of the problem and properties of its feasible region can achieve constant factor approximation guarantees that depend on the platform design, ranging from 1-1/e to 1/3. Finally, we show that the Dating Heuristic (DH) (Rios et al. 2023), which is commonly used and achieves good performance in practice, provides an approximation guarantee of 1-1/e for all platform designs. We show theoretically and empirically that the performance of the DH is robust to the platform design. Our simulation results---using real data from our industry partner---also show that platforms using a one-directional design should initiate interactions with the side that leads to the smallest expected backlog per profile displayed, balancing size and selectivity. Moreover, we find that a one-directional design can lead to at least half of the matches obtained with a two-directional design. Finally, our results show that avoiding non-sequential matches has no sizable effect, regardless of the platform design.

In this paper, we present the results of a multi-year collaboration with policy-makers to design and evaluate whether information policies implemented at scale can effectively improve students' outcomes. Using a series of nationwide surveys, we find that ~40% of students do not apply to their preferred college and major, and 10% of these students would have strictly benefited by including these programs. Upon these results, we implemented with the Ministry of Education of Chile a large-scale field experiment for college admissions, which included personalized information about program characteristics, students' admission probabilities, and alternative major recommendations. The intervention significantly reduced application mistakes, increasing the probability of assignment for unmatched students by 20% and the probability of improving the assignment of undermatched students by 38%. After scaling-up the policy, the intervention approximately doubled the matching probability for unmatched and undermatched students and tripled the enrollment likelihood for initially unmatched students.

We analyze the relevance of incorporating dynamic incentives and eliciting private information about students' preferences to improve their welfare and outcomes in dynamic centralized assignment systems. We show that the most common assignment mechanism, the Deferred Acceptance (DA) algorithm, can result in significant inefficiencies as it fails to elicit cardinal information on students' preferences. We collect novel data about students' preferences, their beliefs on admission chances, and their college outcomes for the Chilean college system. We analyze two main behavioral channels that explain students' dynamic decisions. First, by exploiting discontinuities on admission cutoffs, we show that not being assigned to ones' top-reported preference has a positive causal effect on the probability of re-applying to the centralized system and switching one's major/college, suggesting that students switch to more preferred programs due to initial mismatches. Second, we find that a significant fraction of students change their preferences during their college progression, and that these changes are correlated with their grades, suggesting that students may learn about their match-quality. Based on these facts, we build and estimate a structural model of students' college progression in the presence of a centralized admission system, allowing students to learn about their match-quality over time and re-apply to the system. We use the estimated model to disentangle how much of students' switching behavior is due to initial mismatches and learning, and we analyze the impact of changing the assignment mechanism and the re-application rules on the efficiency of the system. Our counterfactual results show that policies that provide score bonuses that elicit information on students' cardinal preferences and leverage dynamic incentives can significantly decrease switchings, dropouts, and increase students' overall welfare.

We study stable matching problems under contingent priorities, whereby the clearinghouse prioritizes some agents based on the allocation of others. Using school choice as a motivating example, we first introduce a stylized model of a many-to-one matching market where the clearinghouse aims to prioritize applicants with siblings assigned to the same school and match them together. We provide a series of guidelines to implement these contingent priorities and introduce two novel concepts of stability that account for them. We study some properties of the corresponding mechanisms, including the existence of a stable assignment under contingent priorities, its incentive properties, and the complexity of finding one if it exists. Moreover, we provide mathematical programming formulations to find such stable assignments whenever they exist. Finally, using data from the Chilean school choice system, we show that our framework can significantly increase the number of siblings assigned together while having no large effect on students without siblings.

We study the effects of incentive schemes and their interaction with team-building activities to reduce project delays. We introduce a stylized model of a project involving two sequential tasks performed by two workers, each responsible for one task. Workers get a fixed salary, pay a penalty that depends either on the delay of their task (individual incentives) or the delay of the project (group incentives), and they must choose between working on the project or an alternative that offers a private benefit but delays their task completion. We show that workers will complete their tasks as soon as possible provided a large enough penalty, regardless of the incentives scheme. We hypothesize that behavioral drivers like social preferences and strategic uncertainty may create distinctions among incentive schemes, potentially amplified by team-building activities fostering team identity and cooperation. To test these predictions, we conduct an experiment replicating the theoretical model, varying the incentives scheme (individual vs. group) and the initial activity that subjects participate in (individual investment game vs. team-building activity). First, we find no differences in delays in the absence of the team-building activity. Second, we show that the team-building activity significantly reduces delays when paired with group incentives, while it has no effect under individual incentives. Finally, we identify the main behavioral drivers of these effects, including social preferences, beliefs, and a higher interdependence on the time workers take to complete their tasks when group incentives are combined with the team-building activity.

Charitable donations are a vital source of funding for non-profit organizations, enabling them to carry out their mission of addressing social issues and providing support to those in need. To enhance donations, fundraisers employ various designs aimed at increasing donations. However, budgets are often limited and fundraisers must strategically decide on the optimal design choice that maximizes overall donations. This paper investigates the effectiveness of two design choices in the context of fundraising: (i) matching and (ii) gift unlock. We introduce a stylized game-theoretic model where a fundraiser decides the design choice and corresponding design parameters to maximize overall donations. Following the fundraiser’s decision, donors, endowed with a certain amount of wealth, make a one-time contribution to a charitable entity. We find the fundraisers’ optimal policy and characterize the equilibrium donation amount, for each design choice. We compare the overall contribution under the two design choices and find that given a fixed fundraising budget, the gift unlock design consistently leads to higher overall contributions. Furthermore, we conduct a numerical experiment to find that the difference in overall contributions increases with an increase in the fundraising budget and the number of donors. Our research findings underscore the importance of design choices in incentivizing donation behavior and offer insights for non-profits to maximize fundraising outcomes.

We analyze the application process in the Chilean College Admissions problem. Students can submit up to 10 preferences, but most of the students do not fill their entire application list ("short-list"). Even though students face no incentives to misreport, we find evidence of strategic behavior as students tend to omit programs if their admission probabilities are too low. To rationalize this behavior, we construct a portfolio problem where students maximize their expected utility of reporting a ROL given their preferences and beliefs over admission probabilities. We adapt the estimation procedure proposed by Agarwal and Somaini (2018) to solve a large portfolio problem. To simplify this task, we show that it is sufficient to compare a ROL with only a subset of ROLs ("one-shot swaps") to ensure its optimality without running into the curse of dimensionality. To better identify the model, we exploit a unique exogenous variation on the admission weights over time. We find that assuming truth-telling leads to biased results. Specifically, when students only include programs if it is strictly profitable to do so, assuming truth-telling underestimates how preferred selective programs are and overstates the value of being unassigned and the degree of preference heterogeneity in the system. In addition, ignoring the constraint on the length of the list can also result in biased estimates, even if the proportion of constrained ROLs is relatively small. Our estimation results strongly suggest that "short-list" students should not be interpret as truth-tellers, even in a seemingly strategy-proof environment.

We test the theoretical predictions of Designing Charity Donation Systems using a lab experiment.

We explore how the search environment influences users' search behavior and outcomes. Motivated by dating and home-servicing platforms, we focus on the effect of (i) the search mechanism, i.e., whether users evaluate options sequentially or simultnaeously; (ii) the number of options available, capturing scenarios of abundance and scarcity; and (iii) the search cost that agents incur for each option they evaluate.

We study the behavioral effects of process automation on human workers interacting with automated tasks. We introduce a stylized model with two workers who complete their tasks sequentially, working toward a joint project to obtain a fixed payment plus a variable bonus that depends on how early the project is completed. We show that workers will complete their tasks as soon as possible if the early completion bonus is high enough. Following the literature, we hypothesize that workers will suboptimally delay project completion. In addition, we predict that automation will alleviate this problem by reducing the uncertainty about task completion, leading to a higher project completion rate and worker productivity. To test these predictions, we conduct an experiment replicating the theoretical model, varying whether a worker collaborates with a coworker or robot. First, we find that workers largely deviate from the optimal policy, as they take longer than what the theory prescribes to complete their tasks or do not complete the project. Second, process automation increases the project completion rate and reduces the project completion time, confirming the benefits of process automation. Interestingly, workers who collaborate with robots take longer to complete their tasks, contradicting our initial hypothesis that process automation has a positive effect on the productivity of human workers. An additional treatment shows that the reduced uncertainty derived from process automation cannot be leveraged to improve workers' productivity in the same way as in a human-human setting and that social preferences are an important driver of this result.

We study settings in which a centralized clearinghouse organizes a market where agents sequentially search among different options under competition. We introduce a stylized model of sequential search, whereby agents are exogenously prioritized by the clearinghouse and must decide when to stop their search to maximize the chosen option's value. We focus on the effect of two market design choices that are motivated in the context of kidney transplants: (i) transparency, i.e., whether agents know their priority relative to the other agents searching; and (ii) the mechanism to collect decisions, namely, whether all agents make their decisions simultaneously or sequentially in decreasing order of priority. In each case, we characterize the optimal policy, which defines a sequence of thresholds that determine when each agent should accept an option depending on the information available. We find that, although the mechanism to collect agents' decisions does not affect the optimal policy, providing information about agents' priorities reduces the overall welfare and fairness of the allocation. We design and conduct a lab experiment that replicates our theoretical model to test these predictions. We find that agents significantly deviate from their corresponding optimal policies. Moreover, we find that the mechanism has a significant effect on their decisions, due primarily to two drivers: (i) saliency of competition and (ii) frustration in regard to accepting but not obtaining an option. Finally, we find that the benefits of opaqueness do not translate to practice, mainly because agents do not incorporate relevant information about the amount of competition.

We study how online platforms can leverage the behavioral considerations of their users to improve their assortment decisions. Motivated by dating markets, we consider a platform that must select an assortment of potential partners to show to each user in each day. Users can like/not like each potential partner presented to them, and a match is formed if two users (eventually) like each other. The platform's objective is to maximize the expected number of matches in a time horizon. Using data from a dating company, we estimate the main inputs of our model, namely, the like and log in probabilities, and find that the number of matches obtained in the recent past has a negative effect on the like behavior of users. Leveraging this finding, we propose a family of heuristics that decide the assortment to show to each user on each day. We show that these heuristics considerably improve the number of matches generated by the platform in markets simulated based on the real data and further identify the sources of improvement. Finally, we implemented a field experiment that confirms that the improvement achieved by our algorithms also translates into our partner's platform.

Motivated by recent initiatives to increase transparency in procurement, we study the effects of disclosing information about previous purchases in a setting where an organization delegates its purchasing decisions to its employees. When employees can use their own discretion-which may be influenced by personal preferences—to select a supplier, the incentives of the employees and the organization may be misaligned. Disclosing information about previous purchasing decisions made by other employees can reduce or exacerbate this misalignment, as peer effects may come into play. To understand the effects of transparency, we introduce a theoretical model that compares employees' actions in a setting where they cannot observe each other's choices, to a setting where they can observe the decision previously made by a peer before making their own. Two behavioral considerations are central to our model: that employees are heterogeneous in their reciprocity towards their employer, and that they experience peer effects in the form of income inequality aversion towards their peer. As a result, our model predicts the existence of negative spillovers as a reciprocal employee is more likely to choose the expensive supplier (which gives him a personal reward) when he observes that a peer did so. A laboratory experiment confirms the existence of negative spillovers and the main behavioral mechanisms described in our model. A surprising result not predicted by our theory, is that employees whose decisions are observed by their peers are less likely to choose the expensive supplier than the employees in the no transparency case. We show that observed employees’ preferences for compliance with the social norm of "appropriate purchasing behavior" explain our data well.

In this paper we present the design and implementation of a new system to solve the Chilean college admissions problem. We develop an algorithm that obtains all stable allocations when preferences are not strict and when all tied students in the last seat of a program (if any) must be allocated. We use this algorithm to determine which mechanism was used to perform the allocation, and we propose a new method to incorporate the affirmative action that is part of the system and correct the inefficiencies that arise from having double-assigned students. By unifying the regular admission with the affirmative action, we have improved the allocation of approximately 3% of students every year since 2016. From a theoretical standpoint, we show that some desired properties, such as strategy-proofness and monotonicity, cannot be guaranteed under flexible quotas. Nevertheless, we show that the mechanism is strategy-proof in the large, and therefore truthful reporting is approximately optimal.

Centralized school admission mechanisms are an attractive way of improving social welfare and fairness in large educational systems. In this paper we report the design and implementation of the newly established school choice mechanism in Chile, where over 274,000 students applied to more than 6,400 schools. The Chilean system presents unprecedented design challenges that make it unique. On the one hand, it is a simultaneous nationwide system, making it one of the largest school admission problems worldwide. On the other hand, the system runs at all school levels, from Pre-K to 12th grade, raising at least two issues of outmost importance; namely, the system needs to guarantee their current seat to students applying for a school change, and the system has to favor the assignment of siblings to the same school. As in other systems around the world, we develop a model based on the celebrated Deferred Acceptance algorithm. The algorithm deals not only with the aforementioned issues, but also with further practical features such as soft-bounds and overlapping types. In this context we analyze new stability definitions, present the results of its implementation and conduct simulations showing the benefits of the innovations of the implemented system.

Data for optimization problems often comes from (deterministic) forecasts, but it is naïve to consider a forecast as the only future possibility. A more sophisticated approach uses data to generate alternative future scenarios, each with an attached probability. The basic idea is to estimate the distribution of forecast errors and use that to construct the scenarios. Although sampling from the distribution of errors comes immediately to mind, we propose instead to approximate rather than sample. Benchmark studies show that the method we propose works well.

A new methodology is laid out for the modeling of commodity prices, it departs from the "standard" approach in that it makes a definite distinction between the analysis of the short term and long term regimes. In particular, this allows us to come up with an explicit drift term for the short-term process whereas the long-term process is primarily driftless due to inherent high volatility of commodity prices excluding an almost negligible mean reversion term. Not unexpectedly, the information used to build the short-term process relies on more than just historical prices but takes into account additional information about the state of the market. This work is done in the context of copper prices but a similar approach should be applicable to wide variety of commodities although certainly not all since commodities come with very distinct characteristics. In addition, our model also takes into account inflation which leads us to consider a multi-dimensional system for which one can generate explicit solutions.

We describe a multi-faceted effort to demonstrate the practical implementation of stochastic unit commitment at RTO scale. The inputs for the scheduling engine consist of multiple hourly trajectories of load and variable generation availability together with probabilities that accurately describe their likelihood of occurrence given information available on the day ahead. Preliminary computational results indicate that the methods have promise.

This paper analyses the effect of including high school grade rankings as a new factor in the admission process to Chilean universities. The paper evaluates the impact of different weighting strategies of the high school grade ranking and identifies socioeconomic and gender characteristics of the students who benefited and were harmed by the inclusion of this new factor. Starting with the weightings of the different factors considered in the Admission Process for 2012, we simulate, using a selection algorithm, alternative weightings for high school grade rankings in the 2013 Admission Process. We also evaluate the effect of the actual increase in the weighting of grade ranking in the 2014 admission process. Even though the impact on students' entrance and exit from the selection list is rather small, the introduction of the high school grade ranking into the admission process has an effect on the composition of the students selected, producing greater socioeconomic and gender equality.

We analyse how to deal with the uncertainty before solving a stochastic optimization problem and we apply it to a forestry management problem. In particular, we start from historical data to build a stochastic process for wood prices and for bounds on its demand. Then, we generate scenario trees considering different numbers of scenarios and different scenario-generation methods, and we describe a procedure to compare the solutions obtained with each approach. Finally, we show that the scenario tree used to obtain a candidate solution has a considerable impact in our decision model.

Unit commitment decisions made in the day-ahead market and during subsequent reliability assessments are critically based on forecasts of load. Traditional, deterministic unit commitment is based on point or expectation-based load forecasts. In contrast, stochastic unit commitment relies on multiple load scenarios, with associated probabilities, that in aggregate capture the range of likely load time-series. The shift from point-based to scenario-based forecasting necessitates a shift in forecasting technologies, to provide accurate inputs to stochastic unit commitment. In this paper, we discuss a novel scenario generation methodology for load forecasting in stochastic unit commitment, with application to real data associated with the Independent System Operator of New England (ISO-NE). The accuracy of the expected load scenario generated using our methodology is consistent with that of point forecasting methods. The resulting sets of realistic scenarios serve as input to rigorously test the scalability of stochastic unit commitment solvers, as described in the companion paper. The scenarios generated by our method are available as an online supplement to this paper, as part of a novel, publicly available large-scale stochastic unit commitment benchmark.

Fire has a significant impact on timber production on many forest landscapes. In this article we describe how we used the method of generating a discrete set of fire scars described in Kulhmann et al. (2015) to generate a set of fire scar scenarios which we incorporated in a two stage stochastic linear programming (SLP) timber harvest scheduling model. We solve the resulting SLP model to produce timber harvesting strategies which we evaluate by assessing how well they perform in a simulated forest management planning environment in which fire burns a portion of the forest each period. We explore how the quality of the SLP solution varies as the number of fire scar scenarios varies and the sensitivity of the solutions to some of the parameters of the fire simulator. We then compare the performance of the SLP solutions with those produced when fire is ignored and when a traditional burn probability model is used to estimate the probability that each stand will burn. We found that the SLP solutions produced only slightly better expected returns but significantly better performance with respect to risk measures.

We study an extension of the classical college admission problem where applicants have strict preferences but careers may include ties in their preference lists. We present an algorithm which enables us to find stable assignments without breaking ties rules, but considering flexible quotas. We investigate the properties of this algorithm-stability, optimality-and we show that the resulting algorithm is neither monotone nor strategy-proof. The mechanism is used to solve real instances of the Chilean college admission problem. Among our results, we show that the welfare of students is increased if flexible quotas and a student-optimal assignment are combined. Finally, we argue why such assignment may be desirable in the Chilean context.