This paper examines an adverse selection environment where a sender with private information (high or low ability) tries to convince a receiver of their high ability. Without commitment or costly signaling, market failure can occur. Certification intermediaries reduce these frictions by enabling signaling through hard information. This paper focuses on a monopolistic certifier and its impact on equilibrium welfare and certificate design. Key findings show that the certifier often provides minimal information, pooling senders of varying abilities and leaving low rents for high-type senders, which typically disadvantages the receiver. However, when precise information is demanded, the certifier screens the sender perfectly, benefiting the receiver. Thus, the monopolistic intermediary has an ambiguous effect on market efficiency. The results emphasize the importance of high certification standards, which drive low-ability senders out of the market. Conditions for such equilibria are characterized, showing how simple threshold strategies by the receiver induce first-best outcomes. Additionally, the relationship between the characteristics of offered certificates and welfare is identified.
{"title":"Certifying Lemons","authors":"Hershdeep Chopra","doi":"arxiv-2407.19814","DOIUrl":"https://doi.org/arxiv-2407.19814","url":null,"abstract":"This paper examines an adverse selection environment where a sender with\u0000private information (high or low ability) tries to convince a receiver of their\u0000high ability. Without commitment or costly signaling, market failure can occur.\u0000Certification intermediaries reduce these frictions by enabling signaling\u0000through hard information. This paper focuses on a monopolistic certifier and\u0000its impact on equilibrium welfare and certificate design. Key findings show\u0000that the certifier often provides minimal information, pooling senders of\u0000varying abilities and leaving low rents for high-type senders, which typically\u0000disadvantages the receiver. However, when precise information is demanded, the\u0000certifier screens the sender perfectly, benefiting the receiver. Thus, the\u0000monopolistic intermediary has an ambiguous effect on market efficiency. The\u0000results emphasize the importance of high certification standards, which drive\u0000low-ability senders out of the market. Conditions for such equilibria are\u0000characterized, showing how simple threshold strategies by the receiver induce\u0000first-best outcomes. Additionally, the relationship between the characteristics\u0000of offered certificates and welfare is identified.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862657","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}
Josue Ortega, Gabriel Ziegler, R. Pablo Arribillaga
The Efficiency-Adjusted Deferred Acceptance (EADA) mechanism corrects the Pareto-inefficiency of the celebrated Deferred Acceptance (DA) algorithm, assigning every student to a weakly more preferred school. Nonetheless, it is unclear which and how many students do not improve their DA placement under EADA. We show that, despite all its merits, EADA never benefits pupils who are either assigned to their worst-ranked schools or unmatched under DA. It also limits the placement improvement of marginalized students, preserving school segregation. The placement of the worst-off student under EADA may be unreasonably bad, even though significantly more egalitarian allocations are possible. Finally, we provide a bound on the expected number of unimprovable students using a random market approach. Our results help to understand why EADA fails to reduce the inequality generated by DA in empirical evaluations of school choice mechanisms.
经过效率调整的延迟录取（EADA）机制纠正了著名的延迟录取（DA）算法的帕累托效率低下问题，将每个学生分配到一个较弱的优先学校。尽管如此，目前还不清楚在 EADA 机制下，哪些学生以及有多少学生的 DA 排名没有得到改善。我们的研究表明，尽管 EADA 有很多优点，但它从未使那些被分配到排名最差的学校或未被 DA 匹配的学生受益。它还限制了边缘化学生的派位改善，维持了学校隔离。在 EADA 条件下，最差学生的派位可能是不合理的，即使有可能进行更平等的派位。最后，我们利用随机市场方法给出了未改善学生预期人数的约束。我们的研究结果有助于理解为什么在择校机制的实证评估中，"平等机会与发展 "无法减少 "发展议程 "所产生的不平等。
{"title":"Unimprovable Students and Inequality in School Choice","authors":"Josue Ortega, Gabriel Ziegler, R. Pablo Arribillaga","doi":"arxiv-2407.19831","DOIUrl":"https://doi.org/arxiv-2407.19831","url":null,"abstract":"The Efficiency-Adjusted Deferred Acceptance (EADA) mechanism corrects the\u0000Pareto-inefficiency of the celebrated Deferred Acceptance (DA) algorithm,\u0000assigning every student to a weakly more preferred school. Nonetheless, it is\u0000unclear which and how many students do not improve their DA placement under\u0000EADA. We show that, despite all its merits, EADA never benefits pupils who are\u0000either assigned to their worst-ranked schools or unmatched under DA. It also\u0000limits the placement improvement of marginalized students, preserving school\u0000segregation. The placement of the worst-off student under EADA may be\u0000unreasonably bad, even though significantly more egalitarian allocations are\u0000possible. Finally, we provide a bound on the expected number of unimprovable\u0000students using a random market approach. Our results help to understand why EADA fails to reduce the inequality\u0000generated by DA in empirical evaluations of school choice mechanisms.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862656","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}
For an ascending correspondence $F:Xto 2^X$ with chain-complete values on a complete lattice $X$, we prove that the set of fixed points is a complete lattice. This strengthens Zhou's fixed point theorem. For chain-complete posets that are not necessarily lattices, we generalize the Abian-Brown and the Markowsky fixed point theorems from single-valued maps to multivalued correspondences. We provide an application in game theory.
{"title":"Order-theoretical fixed point theorems for correspondences and application in game theory","authors":"Lu Yu","doi":"arxiv-2407.18582","DOIUrl":"https://doi.org/arxiv-2407.18582","url":null,"abstract":"For an ascending correspondence $F:Xto 2^X$ with chain-complete values on a\u0000complete lattice $X$, we prove that the set of fixed points is a complete\u0000lattice. This strengthens Zhou's fixed point theorem. For chain-complete posets\u0000that are not necessarily lattices, we generalize the Abian-Brown and the\u0000Markowsky fixed point theorems from single-valued maps to multivalued\u0000correspondences. We provide an application in game theory.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862659","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 examine the strategic interaction between an expert (principal) maximizing engagement and an agent seeking swift information. Our analysis reveals: When priors align, relative patience determines optimal disclosure -- impatient agents induce gradual revelation, while impatient principals cause delayed, abrupt revelation. When priors disagree, catering to the bias often emerges, with the principal initially providing signals aligned with the agent's bias. With private agent beliefs, we observe two phases: one engaging both agents, followed by catering to one type. Comparing personalized and non-personalized strategies, we find faster information revelation in the non-personalized case, but higher quality information in the personalized case.
{"title":"Getting the Agent to Wait","authors":"Maryam Saeedi, Yikang Shen, Ali Shourideh","doi":"arxiv-2407.19127","DOIUrl":"https://doi.org/arxiv-2407.19127","url":null,"abstract":"We examine the strategic interaction between an expert (principal) maximizing\u0000engagement and an agent seeking swift information. Our analysis reveals: When\u0000priors align, relative patience determines optimal disclosure -- impatient\u0000agents induce gradual revelation, while impatient principals cause delayed,\u0000abrupt revelation. When priors disagree, catering to the bias often emerges,\u0000with the principal initially providing signals aligned with the agent's bias.\u0000With private agent beliefs, we observe two phases: one engaging both agents,\u0000followed by catering to one type. Comparing personalized and non-personalized\u0000strategies, we find faster information revelation in the non-personalized case,\u0000but higher quality information in the personalized case.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"94 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862658","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 give two generalizations of the Zhou fixed point theorem. They weaken the subcompleteness condition of values, and relax the ascending condition of the correspondence. As an application, we derive a generalization of Topkis's theorem on the existence and order structure of the set of Nash equilibria of supermodular games.
{"title":"Generalization of Zhou fixed point theorem","authors":"Lu Yu","doi":"arxiv-2407.17884","DOIUrl":"https://doi.org/arxiv-2407.17884","url":null,"abstract":"We give two generalizations of the Zhou fixed point theorem. They weaken the\u0000subcompleteness condition of values, and relax the ascending condition of the\u0000correspondence. As an application, we derive a generalization of Topkis's\u0000theorem on the existence and order structure of the set of Nash equilibria of\u0000supermodular games.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782323","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}
Addiction is a major societal issue leading to billions in healthcare losses per year. Policy makers often introduce ad hoc quantity limits-limits on the consumption or possession of a substance-something which current economic models of addiction have failed to address. This paper enriches Bernheim and Rangel (2004)'s model of addiction driven by cue-triggered decisions by incorporating endogenous choice of how much of the addictive good to consume, instead of just whether or not consumption happens. Stricter quality limits improve welfare as long as they do not preclude the myopically optimal level of consumption.
{"title":"Quantity Limits on Addictive Goods","authors":"Eric Gao","doi":"arxiv-2407.16987","DOIUrl":"https://doi.org/arxiv-2407.16987","url":null,"abstract":"Addiction is a major societal issue leading to billions in healthcare losses\u0000per year. Policy makers often introduce ad hoc quantity limits-limits on the\u0000consumption or possession of a substance-something which current economic\u0000models of addiction have failed to address. This paper enriches Bernheim and\u0000Rangel (2004)'s model of addiction driven by cue-triggered decisions by\u0000incorporating endogenous choice of how much of the addictive good to consume,\u0000instead of just whether or not consumption happens. Stricter quality limits\u0000improve welfare as long as they do not preclude the myopically optimal level of\u0000consumption.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782330","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 present novel monotone comparative statics results for steady state behavior in a dynamic optimization environment with misspecified Bayesian learning. We consider a generalized framework, based on Esponda and Pouzo (2021), wherein a Bayesian learner facing a dynamic optimization problem has a prior on a set of parameterized transition probability functions (models) but is misspecified in the sense that the true process is not within this set. In the steady state, the learner infers the model that best-fits the data generated by their actions, and in turn, their actions are optimally chosen given their inferred model. We characterize conditions on the primitives of the environment, and in particular, over the set of models under which the steady state distribution over states and actions and inferred models exhibit monotonic behavior. Further, we offer a new theorem on the existence of a steady state on the basis of a monotonicity argument. Lastly, we provide an upper bound on the cost of misspecification, again in terms of the primitives of the environment. We demonstrate the utility of our results for several environments of general interest, including forecasting models, dynamic effort-task, and optimal consumption-savings problems.
{"title":"Robust Comparative Statics with Misspecified Bayesian Learning","authors":"Aniruddha Ghosh","doi":"arxiv-2407.17037","DOIUrl":"https://doi.org/arxiv-2407.17037","url":null,"abstract":"We present novel monotone comparative statics results for steady state\u0000behavior in a dynamic optimization environment with misspecified Bayesian\u0000learning. We consider a generalized framework, based on Esponda and Pouzo\u0000(2021), wherein a Bayesian learner facing a dynamic optimization problem has a\u0000prior on a set of parameterized transition probability functions (models) but\u0000is misspecified in the sense that the true process is not within this set. In\u0000the steady state, the learner infers the model that best-fits the data\u0000generated by their actions, and in turn, their actions are optimally chosen\u0000given their inferred model. We characterize conditions on the primitives of the\u0000environment, and in particular, over the set of models under which the steady\u0000state distribution over states and actions and inferred models exhibit\u0000monotonic behavior. Further, we offer a new theorem on the existence of a\u0000steady state on the basis of a monotonicity argument. Lastly, we provide an\u0000upper bound on the cost of misspecification, again in terms of the primitives\u0000of the environment. We demonstrate the utility of our results for several\u0000environments of general interest, including forecasting models, dynamic\u0000effort-task, and optimal consumption-savings problems.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782327","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}
Federico Echenique, Teddy Mekonnen, M. Bumin Yenmez
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 the standard notion of majorization in order to favor arbitrary distributional objectives, such as population-level distributions over race/ethnicity or socioeconomic 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. We compare our choice rule to the leading proposal in the literature, ``reserves and quotas,'' and find ours to be more flexible.
{"title":"Diversity in Choice as Majorization","authors":"Federico Echenique, Teddy Mekonnen, M. Bumin Yenmez","doi":"arxiv-2407.17589","DOIUrl":"https://doi.org/arxiv-2407.17589","url":null,"abstract":"We use majorization to model comparative diversity in school choice. A\u0000population of agents is more diverse than another population of agents if its\u0000distribution over groups is less concentrated: being less concentrated takes a\u0000specific mathematical meaning borrowed from the theory of majorization. We\u0000adapt the standard notion of majorization in order to favor arbitrary\u0000distributional objectives, such as population-level distributions over\u0000race/ethnicity or socioeconomic status. With school admissions in mind, we\u0000axiomatically characterize choice rules that are consistent with modified\u0000majorization, and constitute a principled method for admitting a diverse\u0000population of students into a school. Two important advantages of our approach\u0000is that majorization provides a natural notion of diversity, and that our\u0000axioms are independent of any exogenous priority ordering. We compare our\u0000choice rule to the leading proposal in the literature, ``reserves and quotas,''\u0000and find ours to be more flexible.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782324","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 gather many perspectives on Capital and synthesize their commonalities. We provide a characterization of Capital as a historical agential system and propose a model of Capital using tools from computer science. Our model consists of propositions which, if satisfied by a specific grounding, constitute a valid model of Capital. We clarify the manners in which Capital can evolve. We claim that, when its evolution is driven by quantitative optimization processes, Capital can possess qualities of Artificial Intelligence. We find that Capital may not uniquely represent meaning, in the same way that optimization is not intentionally meaningful. We find that Artificial Intelligences like modern day Large Language Models are a part of Capital. We link our readers to a web-interface where they can interact with a part of Capital.
{"title":"Capital as Artificial Intelligence","authors":"Cesare Carissimo, Marcin Korecki","doi":"arxiv-2407.16314","DOIUrl":"https://doi.org/arxiv-2407.16314","url":null,"abstract":"We gather many perspectives on Capital and synthesize their commonalities. We\u0000provide a characterization of Capital as a historical agential system and\u0000propose a model of Capital using tools from computer science. Our model\u0000consists of propositions which, if satisfied by a specific grounding,\u0000constitute a valid model of Capital. We clarify the manners in which Capital\u0000can evolve. We claim that, when its evolution is driven by quantitative\u0000optimization processes, Capital can possess qualities of Artificial\u0000Intelligence. We find that Capital may not uniquely represent meaning, in the\u0000same way that optimization is not intentionally meaningful. We find that\u0000Artificial Intelligences like modern day Large Language Models are a part of\u0000Capital. We link our readers to a web-interface where they can interact with a\u0000part of Capital.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785902","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}
In this paper, we reveal that the signal representation of information introduced by Gentzkow and Kamenica (2017) can be applied profitably to dynamic decision problems. We use this to characterize when one dynamic information structure is more valuable to an agent than another, irrespective of what other dynamic sources of information the agent may possess. Notably, this robust dominance is equivalent to an intuitive dynamic version of Brooks, Frankel, and Kamenica (2022)'s reveal-or-refine condition.
{"title":"Dynamic Signals","authors":"Mark Whitmeyer, Cole Williams","doi":"arxiv-2407.16648","DOIUrl":"https://doi.org/arxiv-2407.16648","url":null,"abstract":"In this paper, we reveal that the signal representation of information\u0000introduced by Gentzkow and Kamenica (2017) can be applied profitably to dynamic\u0000decision problems. We use this to characterize when one dynamic information\u0000structure is more valuable to an agent than another, irrespective of what other\u0000dynamic sources of information the agent may possess. Notably, this robust\u0000dominance is equivalent to an intuitive dynamic version of Brooks, Frankel, and\u0000Kamenica (2022)'s reveal-or-refine condition.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782325","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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