The Colonel Blotto game and its variants are a common approach to study competitive allocation of interchangeable resources (e.g., soldiers, money, or votes). We introduce a new variant of Blotto, which we call the Derby game, to study competitive allocation of non-interchangeable resources, such as campaign surrogates in politics or skilled workers in companies, and analyze its Nash equilibria. While Derby games unsurprisingly admit no pure Nash equilibria, our main results surprisingly show that Nash equilibria generically exist where one player plays a pure strategy, and we give necessary and sufficient conditions for such equilibria.
{"title":"The Derby Game: An Ordering-based Colonel Blotto Game","authors":"Akash Gaonkar, Divya Raghunathan, S. Weinberg","doi":"10.1145/3490486.3538367","DOIUrl":"https://doi.org/10.1145/3490486.3538367","url":null,"abstract":"The Colonel Blotto game and its variants are a common approach to study competitive allocation of interchangeable resources (e.g., soldiers, money, or votes). We introduce a new variant of Blotto, which we call the Derby game, to study competitive allocation of non-interchangeable resources, such as campaign surrogates in politics or skilled workers in companies, and analyze its Nash equilibria. While Derby games unsurprisingly admit no pure Nash equilibria, our main results surprisingly show that Nash equilibria generically exist where one player plays a pure strategy, and we give necessary and sufficient conditions for such equilibria.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122044023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Classical frameworks in mechanism design often specify an objective function and maximize it by choosing allocation. We extend these frameworks by allowing maximizing an objective function (such as expected revenue in an auction) subject to additional constraints (such as lower bounds on efficiency or welfare). The additional complexity arising due to each additional constraint manifests in the reduced form of the optimal mechanism as at most one jump discontinuity in an "ironed" interval. We apply our results to demonstrate the simplicity of optimal mechanisms despite the presence of a side constraint in common economic applications such as contract and auction design. We also introduce a regularity condition under which the general structure of optimal mechanisms bears no additional complexity due to the presence of a side constraint. The analysis builds on the findings of Kleiner et al. (2021) by considering optimal mechanisms as extreme points of function spaces.
{"title":"Constrained Majorization: Applications in Mechanism Design","authors":"Afshin Nikzad","doi":"10.1145/3490486.3538257","DOIUrl":"https://doi.org/10.1145/3490486.3538257","url":null,"abstract":"Classical frameworks in mechanism design often specify an objective function and maximize it by choosing allocation. We extend these frameworks by allowing maximizing an objective function (such as expected revenue in an auction) subject to additional constraints (such as lower bounds on efficiency or welfare). The additional complexity arising due to each additional constraint manifests in the reduced form of the optimal mechanism as at most one jump discontinuity in an \"ironed\" interval. We apply our results to demonstrate the simplicity of optimal mechanisms despite the presence of a side constraint in common economic applications such as contract and auction design. We also introduce a regularity condition under which the general structure of optimal mechanisms bears no additional complexity due to the presence of a side constraint. The analysis builds on the findings of Kleiner et al. (2021) by considering optimal mechanisms as extreme points of function spaces.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133263574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We extend a number of classic results for finite one-to-one matching markets, such as group strategy-proofness, entry comparative statics, and respect for unambiguous improvements, to infinite markets via the compactness theorem of propositional logic. In addition, we show that two versions of the lattice structure of finite one-to-one matching markets carry over to infinite markets. At the same time, we prove that other results, such as weak Pareto optimality and strong stability property, do not extend to infinite markets.
{"title":"On Two-sided Matching in Infinite Markets","authors":"Yunseo Choi","doi":"10.1145/3490486.3538325","DOIUrl":"https://doi.org/10.1145/3490486.3538325","url":null,"abstract":"We extend a number of classic results for finite one-to-one matching markets, such as group strategy-proofness, entry comparative statics, and respect for unambiguous improvements, to infinite markets via the compactness theorem of propositional logic. In addition, we show that two versions of the lattice structure of finite one-to-one matching markets carry over to infinite markets. At the same time, we prove that other results, such as weak Pareto optimality and strong stability property, do not extend to infinite markets.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115042759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
When allocating indivisible items across agents, it is desirable for the allocation to be envy-free, which means that each agent prefers their own bundle over every other bundle. Even though envy-free allocations are not guaranteed to exist for worst-case utilities, they frequently exist in practice. To explain this phenomenon, prior work has shown that, if utilities are drawn from certain probability distributions, then envy-free allocations exist with high probability (as long as the number of items is sufficiently large relative to the number of agents). In this paper, we study a more general setting, a smoothed model of utilities, in which utility profiles are mainly worst-case, but are slightly perturbed at random to avoid brittle counter-examples. Specifically, we start from a worst-case profile of utilities and, with some small probability, increase an agent's value for an item by adding a random amount, where the probability of perturbation and the distribution of perturbations are parameters of the model. If the probability of such perturbations is sufficiently large relative to the number of agents and items, we show that envy-free allocations exist with high probability and can be found efficiently. This analysis is tight up to constant factors. We also give an efficient algorithm for finding allocations that are simultaneously proportional and Pareto-optimal, which succeeds with high probability in the smoothed model.
{"title":"Fair Allocations for Smoothed Utilities","authors":"Yushi Bai, U. Feige, Paul Gölz, A. Procaccia","doi":"10.1145/3490486.3538285","DOIUrl":"https://doi.org/10.1145/3490486.3538285","url":null,"abstract":"When allocating indivisible items across agents, it is desirable for the allocation to be envy-free, which means that each agent prefers their own bundle over every other bundle. Even though envy-free allocations are not guaranteed to exist for worst-case utilities, they frequently exist in practice. To explain this phenomenon, prior work has shown that, if utilities are drawn from certain probability distributions, then envy-free allocations exist with high probability (as long as the number of items is sufficiently large relative to the number of agents). In this paper, we study a more general setting, a smoothed model of utilities, in which utility profiles are mainly worst-case, but are slightly perturbed at random to avoid brittle counter-examples. Specifically, we start from a worst-case profile of utilities and, with some small probability, increase an agent's value for an item by adding a random amount, where the probability of perturbation and the distribution of perturbations are parameters of the model. If the probability of such perturbations is sufficiently large relative to the number of agents and items, we show that envy-free allocations exist with high probability and can be found efficiently. This analysis is tight up to constant factors. We also give an efficient algorithm for finding allocations that are simultaneously proportional and Pareto-optimal, which succeeds with high probability in the smoothed model.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128668553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Atanasov, Jens Witkowski, B. Mellers, P. Tetlock
Crowd prediction systems, such as prediction markets, provide the infrastructure to elicit and combine the predictions from a group (“crowd”) of forecasters. In contrast to data-driven approaches, crowd predictions are especially useful in settings with little historical data, such as in new product development, vaccine trials, pandemics, or geopolitical events. Our contributions in this area are threefold. First, we provide an experimental evaluation of two popular types of prediction market architectures: continuous double auction (CDA) markets and logarithmic market scoring rules (LMSR) markets. To the best of our knowledge, we are the first to study these methods in a large, randomized experiment. Prior research reporting on CDA and LMSR market performance did not compare the two designs directly but had separate sets of questions for each [2]. Using data from over 1300 forecasters and 147 forecasting questions, we find that the LMSR market achieves higher accuracy than the CDA market. The LMSR market achieves 14% lower Brier scores (MCDA = 0.245, SDCDA = 0.327 versus MLMSR = 0.211, SDLMSR = 0.280; t(146) = 2.28, p = 0.024). In exploratory analyses, we find that the better performance of the LMSR market appears particularly pronounced for questions that attracted few traders as well as early in a question when only few traders had placed orders on the question. Relative to LMSR, the CDA market underperformed in thin-market settings, consistent with Robin Hanson’s motivation for the LMSR market mechanism. Second, we quantify the impact of prediction system architecture and individual forecaster track record on aggregate performance. Previous research studied how the performance of CDA prediction markets and prediction polls compares when populated by sub-elite forecasters [1] while most previous work on elite forecasters has only examined their individual performance [3]. We are the first to compare the aggregate performance of small, elite forecaster crowds across two prediction systems: LMSR prediction markets and team prediction polls. Moreover, we compare the aggregate accuracy of elite forecaster crowds to larger, sub-elite crowds using the same prediction
{"title":"Crowd Prediction Systems: Markets, Polls, and Elite Forecasters","authors":"P. Atanasov, Jens Witkowski, B. Mellers, P. Tetlock","doi":"10.1145/3490486.3538265","DOIUrl":"https://doi.org/10.1145/3490486.3538265","url":null,"abstract":"Crowd prediction systems, such as prediction markets, provide the infrastructure to elicit and combine the predictions from a group (“crowd”) of forecasters. In contrast to data-driven approaches, crowd predictions are especially useful in settings with little historical data, such as in new product development, vaccine trials, pandemics, or geopolitical events. Our contributions in this area are threefold. First, we provide an experimental evaluation of two popular types of prediction market architectures: continuous double auction (CDA) markets and logarithmic market scoring rules (LMSR) markets. To the best of our knowledge, we are the first to study these methods in a large, randomized experiment. Prior research reporting on CDA and LMSR market performance did not compare the two designs directly but had separate sets of questions for each [2]. Using data from over 1300 forecasters and 147 forecasting questions, we find that the LMSR market achieves higher accuracy than the CDA market. The LMSR market achieves 14% lower Brier scores (MCDA = 0.245, SDCDA = 0.327 versus MLMSR = 0.211, SDLMSR = 0.280; t(146) = 2.28, p = 0.024). In exploratory analyses, we find that the better performance of the LMSR market appears particularly pronounced for questions that attracted few traders as well as early in a question when only few traders had placed orders on the question. Relative to LMSR, the CDA market underperformed in thin-market settings, consistent with Robin Hanson’s motivation for the LMSR market mechanism. Second, we quantify the impact of prediction system architecture and individual forecaster track record on aggregate performance. Previous research studied how the performance of CDA prediction markets and prediction polls compares when populated by sub-elite forecasters [1] while most previous work on elite forecasters has only examined their individual performance [3]. We are the first to compare the aggregate performance of small, elite forecaster crowds across two prediction systems: LMSR prediction markets and team prediction polls. Moreover, we compare the aggregate accuracy of elite forecaster crowds to larger, sub-elite crowds using the same prediction","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134423537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We document the response of bidders to a change in auction pricing rules by a platform selling online advertising impressions. The platform switched from a second-price auction to a first-price auction in 2019. We analyze the transition and ask three questions: Did the bids by the same bidder bidding to show the same creative in the same location on the same webpage fall? If yes, did the bids fall enough? And if the bids fell enough, how long did the transition take? To answer our questions, we study 11 long-running creatives with sufficient volume of bids for a month before the switch and three months after the switch. We find that bids on these long-running creatives indeed declined after the switch, but this decline was not sufficient. To detect insufficient shading, we propose a simple nonparametric estimator of the lower bound on advertiser valuations in first-price sealed-bid auctions. Unlike standard econometric approaches to first-price auctions, our bound estimator does not assume equilibrium and it can accommodate affiliated private values. The identifying assumption is that each bidder prefers his actual bid to an even lower bid given the hyper-local competition the bidder is facing at the moment. This assumption implies a lower bound on a rationalizable valuation of the bidder in a first-price auction. Comparing the post-switch valuation lower bounds to the pre-switch valuation magnitudes allows us to detect insufficient adjustment whenever the former exceeds the latter. And we indeed find that the bid shading was insufficient for a vast majority of bidders and creatives included in our study: observed bids on the median creative imply that the bidder bid as if the switch from second-price to first-price rules increased his valuation of an impression at least 30 percent. We also find evidence of an incomplete and slow downward adjustment in bid magnitude over the period of months, whereby bids remain insufficiently shaded for about half of the creatives even three months after the switch. The full paper is available at: https://ssrn.com/abstract=4036006
{"title":"Adjustment of Bidding Strategies After a Switch to First-Price Rules","authors":"Miguel Alcobendas, Robert Zeithammer","doi":"10.1145/3490486.3538236","DOIUrl":"https://doi.org/10.1145/3490486.3538236","url":null,"abstract":"We document the response of bidders to a change in auction pricing rules by a platform selling online advertising impressions. The platform switched from a second-price auction to a first-price auction in 2019. We analyze the transition and ask three questions: Did the bids by the same bidder bidding to show the same creative in the same location on the same webpage fall? If yes, did the bids fall enough? And if the bids fell enough, how long did the transition take? To answer our questions, we study 11 long-running creatives with sufficient volume of bids for a month before the switch and three months after the switch. We find that bids on these long-running creatives indeed declined after the switch, but this decline was not sufficient. To detect insufficient shading, we propose a simple nonparametric estimator of the lower bound on advertiser valuations in first-price sealed-bid auctions. Unlike standard econometric approaches to first-price auctions, our bound estimator does not assume equilibrium and it can accommodate affiliated private values. The identifying assumption is that each bidder prefers his actual bid to an even lower bid given the hyper-local competition the bidder is facing at the moment. This assumption implies a lower bound on a rationalizable valuation of the bidder in a first-price auction. Comparing the post-switch valuation lower bounds to the pre-switch valuation magnitudes allows us to detect insufficient adjustment whenever the former exceeds the latter. And we indeed find that the bid shading was insufficient for a vast majority of bidders and creatives included in our study: observed bids on the median creative imply that the bidder bid as if the switch from second-price to first-price rules increased his valuation of an impression at least 30 percent. We also find evidence of an incomplete and slow downward adjustment in bid magnitude over the period of months, whereby bids remain insufficiently shaded for about half of the creatives even three months after the switch. The full paper is available at: https://ssrn.com/abstract=4036006","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134257929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maxwell Allman, I. Ashlagi, Irene Lo, J. Love, Katherine Mentzer, Lulabel Ruiz-Setz, Henry O'Connell
More than 65 years after the "Brown v. Board of Education" ruling that school segregation is unconstitutional, public schools across the U.S. are resegregating. In attempts to disentangle school segregation from neighborhood segregation, many cities have adopted policies for district-wide choice. However, these policies have largely not improved patterns of segregation. From 2018-2020, we worked with the San Francisco Unified School District (SFUSD) to design a new policy for student assignment system that meets the district's goals of diversity, predictability, and proximity. To develop potential policies, we used optimization techniques to augment and operationalize the district's proposal of restricting choice to zones. We compared these to approaches typically suggested by the school choice literature. Using predictive choice models developed using historical choice data, we find that appropriately-designed zones with minority reserves can achieve all the district's goals, at the expense of choice, and choice can resegregate diverse zones. A zone-based policy can decrease the percentage of racial minorities in high-poverty schools from 29% to 11%, decrease the average travel distance from 1.39 miles to 1.29 miles, and improve predictability, but reduce the percentage of students assigned to one of their top 3 programs from 80% to 59%. Existing approaches in the school choice literature can improve diversity at lesser expense to choice, and present a trade-off between diversity, proximity, distributional effects, and ease of understanding and implementation. Our work informed the design and approval of a zone-based policy for use starting the 2024-25 school year.
{"title":"Designing School Choice for Diversity in the San Francisco Unified School District","authors":"Maxwell Allman, I. Ashlagi, Irene Lo, J. Love, Katherine Mentzer, Lulabel Ruiz-Setz, Henry O'Connell","doi":"10.1145/3490486.3538271","DOIUrl":"https://doi.org/10.1145/3490486.3538271","url":null,"abstract":"More than 65 years after the \"Brown v. Board of Education\" ruling that school segregation is unconstitutional, public schools across the U.S. are resegregating. In attempts to disentangle school segregation from neighborhood segregation, many cities have adopted policies for district-wide choice. However, these policies have largely not improved patterns of segregation. From 2018-2020, we worked with the San Francisco Unified School District (SFUSD) to design a new policy for student assignment system that meets the district's goals of diversity, predictability, and proximity. To develop potential policies, we used optimization techniques to augment and operationalize the district's proposal of restricting choice to zones. We compared these to approaches typically suggested by the school choice literature. Using predictive choice models developed using historical choice data, we find that appropriately-designed zones with minority reserves can achieve all the district's goals, at the expense of choice, and choice can resegregate diverse zones. A zone-based policy can decrease the percentage of racial minorities in high-poverty schools from 29% to 11%, decrease the average travel distance from 1.39 miles to 1.29 miles, and improve predictability, but reduce the percentage of students assigned to one of their top 3 programs from 80% to 59%. Existing approaches in the school choice literature can improve diversity at lesser expense to choice, and present a trade-off between diversity, proximity, distributional effects, and ease of understanding and implementation. Our work informed the design and approval of a zone-based policy for use starting the 2024-25 school year.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130566202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I incorporate computational constraints into decision theory in order to capture how cognitive limitations affect behavior. I impose an axiom of computational tractability that only rules out behaviors that are thought to be fundamentally hard. I use this framework to better understand common behavioral heuristics: if choices are tractable and consistent with the expected utility axioms, then they are observationally equivalent to forms of choice bracketing. Then I show that a computationally-constrained decisionmaker can be objectively better off if she is willing to use heuristics that would not appear rational to an outside observer. The full paper is available at https://mkcamara.github.io/ctc.pdf.
{"title":"Computationally Tractable Choice","authors":"Modibo K. Camara","doi":"10.1145/3490486.3538256","DOIUrl":"https://doi.org/10.1145/3490486.3538256","url":null,"abstract":"I incorporate computational constraints into decision theory in order to capture how cognitive limitations affect behavior. I impose an axiom of computational tractability that only rules out behaviors that are thought to be fundamentally hard. I use this framework to better understand common behavioral heuristics: if choices are tractable and consistent with the expected utility axioms, then they are observationally equivalent to forms of choice bracketing. Then I show that a computationally-constrained decisionmaker can be objectively better off if she is willing to use heuristics that would not appear rational to an outside observer. The full paper is available at https://mkcamara.github.io/ctc.pdf.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120916325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The increasing availability of data in credit markets may appear to make adverse selection concerns less relevant. However, when there is adverse selection, more information does not necessarily increase welfare. We provide tools for making better use of the data that is collected from potential borrowers, formulating and solving the optimal disclosure problem of an intermediary with commitment that seeks to maximize the probability of successful transactions, weighted by the size of the gains of these transactions. We show that any optimal disclosure policy needs to satisfy some simple conditions in terms of local sufficient statistics. These conditions relate prices to the price elasticities of the expected value of the loans for the investors. Empirically, we apply our method to the data from the Townsend Thai Project, which is a long panel dataset with rich information on credit histories, balance sheets, and income statements, to evaluate whether it can help develop the particularly thin formal rural credit markets in Thailand, finding economically meaningful gains from adopting optimal information disclosure policies.
{"title":"Optimal Credit Scores Under Adverse Selection","authors":"Nicole Immorlica, Andre Sztutman, R. Townsend","doi":"10.1145/3490486.3538331","DOIUrl":"https://doi.org/10.1145/3490486.3538331","url":null,"abstract":"The increasing availability of data in credit markets may appear to make adverse selection concerns less relevant. However, when there is adverse selection, more information does not necessarily increase welfare. We provide tools for making better use of the data that is collected from potential borrowers, formulating and solving the optimal disclosure problem of an intermediary with commitment that seeks to maximize the probability of successful transactions, weighted by the size of the gains of these transactions. We show that any optimal disclosure policy needs to satisfy some simple conditions in terms of local sufficient statistics. These conditions relate prices to the price elasticities of the expected value of the loans for the investors. Empirically, we apply our method to the data from the Townsend Thai Project, which is a long panel dataset with rich information on credit histories, balance sheets, and income statements, to evaluate whether it can help develop the particularly thin formal rural credit markets in Thailand, finding economically meaningful gains from adopting optimal information disclosure policies.","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131479479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Statistical discrimination results when a decision-maker observes an imperfect estimate of the quality of each candidate dependent on which demographic group they belong to [1,8]. Imperfect estimates have been modelled via noise, where the variance depends on the candidate's group ([4,6,7]). Prior literature, however, is limited to simple selection problems, where a single decision-maker tries to choose the best candidates among the applications they received. In this paper, we initiate the study of statistical discrimination in matching, where multiple decision-makers are simultaneously facing selection problems from the same pool of candidates. We consider the college admission problem as first introduced in [5] and recently extended to a model with a continuum of students [3]. We propose a model where two colleges A and B observe noisy estimates of each candidate's quality, where Ws, the vector of estimates for student s, is assumed to be a bivariate normal random variable. In this setting, the estimation noise controls a new key feature of the problem, namely correlation, ρ, between the estimates of the two colleges: if the noise is high, the correlation is low and if the noise is low the correlation is high. We assume that the population of students is divided into two groups G1 and G2, and that members of these two groups are subject to different correlation levels between their grades at colleges A and B. Concretely, for each student s, their grade vector (WAs, WBs) is drawn according to a centered bivariate normal distribution with variance 1 and covariance ρGs, where Gs is the group student s belongs to. We consider the stable matching induced by this distribution and characterize how key outcome characteristics vary with the parameters, in particular with the group-dependent correlation coefficient. Our results summarize as follows: We show that the probability that a student is assigned to their first choice is independent of the student's group, but that it decreases when the correlation of either group decreases. This means that higher measurement noise (inducing lower correlation) on one group hurts not only the students of that group, but the students of all groups. We show that the probability that a student is assigned to their second choice and the probability that they remain unassigned both depend on the student's group, which reveals the presence of statistical discrimination coming from the correlation effect alone. Specifically, we find that the probability that a student remains unmatched is decreasing when the correlation of their group decreases (higher measurement noise) and when the correlation of the other group increases. In other words, the higher the measurement noise of their own group, the better off students are with regard to getting assigned a college at all. This is somewhat counter-intuitive, but is explained by the observation that with high noise (i.e., low correlation) the fact that a student is rejected
{"title":"Statistical Discrimination in Stable Matchings","authors":"Rémi Castera, P. Loiseau, Bary S. R. Pradelski","doi":"10.1145/3490486.3538364","DOIUrl":"https://doi.org/10.1145/3490486.3538364","url":null,"abstract":"Statistical discrimination results when a decision-maker observes an imperfect estimate of the quality of each candidate dependent on which demographic group they belong to [1,8]. Imperfect estimates have been modelled via noise, where the variance depends on the candidate's group ([4,6,7]). Prior literature, however, is limited to simple selection problems, where a single decision-maker tries to choose the best candidates among the applications they received. In this paper, we initiate the study of statistical discrimination in matching, where multiple decision-makers are simultaneously facing selection problems from the same pool of candidates. We consider the college admission problem as first introduced in [5] and recently extended to a model with a continuum of students [3]. We propose a model where two colleges A and B observe noisy estimates of each candidate's quality, where Ws, the vector of estimates for student s, is assumed to be a bivariate normal random variable. In this setting, the estimation noise controls a new key feature of the problem, namely correlation, ρ, between the estimates of the two colleges: if the noise is high, the correlation is low and if the noise is low the correlation is high. We assume that the population of students is divided into two groups G1 and G2, and that members of these two groups are subject to different correlation levels between their grades at colleges A and B. Concretely, for each student s, their grade vector (WAs, WBs) is drawn according to a centered bivariate normal distribution with variance 1 and covariance ρGs, where Gs is the group student s belongs to. We consider the stable matching induced by this distribution and characterize how key outcome characteristics vary with the parameters, in particular with the group-dependent correlation coefficient. Our results summarize as follows: We show that the probability that a student is assigned to their first choice is independent of the student's group, but that it decreases when the correlation of either group decreases. This means that higher measurement noise (inducing lower correlation) on one group hurts not only the students of that group, but the students of all groups. We show that the probability that a student is assigned to their second choice and the probability that they remain unassigned both depend on the student's group, which reveals the presence of statistical discrimination coming from the correlation effect alone. Specifically, we find that the probability that a student remains unmatched is decreasing when the correlation of their group decreases (higher measurement noise) and when the correlation of the other group increases. In other words, the higher the measurement noise of their own group, the better off students are with regard to getting assigned a college at all. This is somewhat counter-intuitive, but is explained by the observation that with high noise (i.e., low correlation) the fact that a student is rejected ","PeriodicalId":209859,"journal":{"name":"Proceedings of the 23rd ACM Conference on Economics and Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131675392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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