Lotteries are a common way to resolve ties in assignment mechanisms that ration resources. We consider a model with a continuum of agents and a finite set of resources with heterogeneous qualities, where the agents' preferences are generated from a multinomial‐logit (MNL) model based on the resource qualities. We show that all agents prefer a common lottery to independent lotteries at each resource if every resource is popular, meaning that the mass of agents ranking that resource as their first choice exceeds its capacity. We then prove a stronger result where the assumption that every resource is popular is not required and agents' preferences are drawn from a (more general) nested MNL model. By appropriately adapting the notion of popularity to resource types, we show that a hybrid tie‐breaking rule in which the objects in each popular type share a common lottery dominates independent lotteries at each resource.
{"title":"On rank dominance of tie‐breaking rules","authors":"Maxwell Allman, I. Ashlagi, Afshin Nikzad","doi":"10.3982/te4762","DOIUrl":"https://doi.org/10.3982/te4762","url":null,"abstract":"Lotteries are a common way to resolve ties in assignment mechanisms that ration resources. We consider a model with a continuum of agents and a finite set of resources with heterogeneous qualities, where the agents' preferences are generated from a multinomial‐logit (MNL) model based on the resource qualities. We show that all agents prefer a common lottery to independent lotteries at each resource if every resource is popular, meaning that the mass of agents ranking that resource as their first choice exceeds its capacity. We then prove a stronger result where the assumption that every resource is popular is not required and agents' preferences are drawn from a (more general) nested MNL model. By appropriately adapting the notion of popularity to resource types, we show that a hybrid tie‐breaking rule in which the objects in each popular type share a common lottery dominates independent lotteries at each resource.","PeriodicalId":46923,"journal":{"name":"Theoretical Economics","volume":"7 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75157629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The founder of a start‐up (principal) who has a project with uncertain returns must retain and incentivize an agent using promise of future payments and information gathering. The agent's effort incrementally advances production and such advance is a prerequisite for gathering new information. The principal decides how much information to gather based on these incremental advancements. The principal faces cash constraints. The agent's outside option is large relative to his effort cost. Equilibrium features one of two outcomes: immediate learning , whereby the agent's compensation is low, learning is immediate and retention is possible only conditional on the project being of high quality; or gradual learning , whereby the agent's compensation is high, learning is gradual, the agent never quits and effort is inefficiently high.
{"title":"Paying with information","authors":"Ayça Kaya","doi":"10.3982/te4465","DOIUrl":"https://doi.org/10.3982/te4465","url":null,"abstract":"The founder of a start‐up (principal) who has a project with uncertain returns must retain and incentivize an agent using promise of future payments and information gathering. The agent's effort incrementally advances production and such advance is a prerequisite for gathering new information. The principal decides how much information to gather based on these incremental advancements. The principal faces cash constraints. The agent's outside option is large relative to his effort cost. Equilibrium features one of two outcomes: immediate learning , whereby the agent's compensation is low, learning is immediate and retention is possible only conditional on the project being of high quality; or gradual learning , whereby the agent's compensation is high, learning is gradual, the agent never quits and effort is inefficiently high.","PeriodicalId":46923,"journal":{"name":"Theoretical Economics","volume":"216 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135734300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper develops a framework for studying repeated matching markets. The model departs from the Gale–Shapley matching model by having a fixed set of long‐lived players (firms) match with a new generation of short‐lived players (workers) in every period. I define history‐dependent and self‐enforcing matching processes in this repeated matching environment and characterize the firms' payoffs. Firms fall into one of two categories: some firms must obtain the same payoff as they would in static stable matchings, and this holds at every patience level; meanwhile, repetition and history dependence can enlarge the set of sustainable payoffs for the other firms, provided that the firms are sufficiently patient. In large matching markets with correlated preferences, the first kind of firms corresponds to “elite” firms that make up at most a vanishingly small fraction of the market. The vast majority of firms fall into the second category.
{"title":"Stability in repeated matching markets","authors":"Ce Liu","doi":"10.3982/te4898","DOIUrl":"https://doi.org/10.3982/te4898","url":null,"abstract":"This paper develops a framework for studying repeated matching markets. The model departs from the Gale–Shapley matching model by having a fixed set of long‐lived players (firms) match with a new generation of short‐lived players (workers) in every period. I define history‐dependent and self‐enforcing matching processes in this repeated matching environment and characterize the firms' payoffs. Firms fall into one of two categories: some firms must obtain the same payoff as they would in static stable matchings, and this holds at every patience level; meanwhile, repetition and history dependence can enlarge the set of sustainable payoffs for the other firms, provided that the firms are sufficiently patient. In large matching markets with correlated preferences, the first kind of firms corresponds to “elite” firms that make up at most a vanishingly small fraction of the market. The vast majority of firms fall into the second category.","PeriodicalId":46923,"journal":{"name":"Theoretical Economics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback–Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman's (1990) uniform convergence result to, e.g., priors that have finite support, are constrained by independence assumptions, or have a parametric form that cannot match some probability distributions. The concentration result lets us provide a rate of convergence for Berk's (1966) result on the limiting behavior of posterior beliefs when the prior is misspecified. We provide a bound on approximation errors in “anticipated‐utility” models, and extend our analysis to outcomes that are perceived to follow a Markov process.
{"title":"Pathwise concentration bounds for Bayesian beliefs","authors":"Drew Fudenberg, Giacomo Lanzani, Philipp Strack","doi":"10.3982/te5206","DOIUrl":"https://doi.org/10.3982/te5206","url":null,"abstract":"We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback–Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman's (1990) uniform convergence result to, e.g., priors that have finite support, are constrained by independence assumptions, or have a parametric form that cannot match some probability distributions. The concentration result lets us provide a rate of convergence for Berk's (1966) result on the limiting behavior of posterior beliefs when the prior is misspecified. We provide a bound on approximation errors in “anticipated‐utility” models, and extend our analysis to outcomes that are perceived to follow a Markov process.","PeriodicalId":46923,"journal":{"name":"Theoretical Economics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135561058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.52342/2587-7666vte_2023_1_46_59
R. Nureev, Yury V. Latov, I. Surkhaev
{"title":"INTERFERENCE OF VOTING MEANS AND POLITICAL RELATIONS IN PERSPECTIVE FROM PRE-INDUSTRIAL TO POST-INDUSTRIAL SOCIETY","authors":"R. Nureev, Yury V. Latov, I. Surkhaev","doi":"10.52342/2587-7666vte_2023_1_46_59","DOIUrl":"https://doi.org/10.52342/2587-7666vte_2023_1_46_59","url":null,"abstract":"","PeriodicalId":46923,"journal":{"name":"Theoretical Economics","volume":"31 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84434553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I study how the arrival of new private information affects bargaining outcomes. A seller makes offers to a buyer. The buyer is privately informed about her valuation and the seller privately observes her stochastically changing cost of delivering the good. Prices fall gradually at the early stages of negotiations, and trade is inefficiently delayed. The first‐best is implementable via a mechanism, whereas all equilibrium outcomes of the bargaining game are inefficient.
{"title":"Bargaining with evolving private information","authors":"Juan Ortner","doi":"10.3982/te4841","DOIUrl":"https://doi.org/10.3982/te4841","url":null,"abstract":"I study how the arrival of new private information affects bargaining outcomes. A seller makes offers to a buyer. The buyer is privately informed about her valuation and the seller privately observes her stochastically changing cost of delivering the good. Prices fall gradually at the early stages of negotiations, and trade is inefficiently delayed. The first‐best is implementable via a mechanism, whereas all equilibrium outcomes of the bargaining game are inefficient.","PeriodicalId":46923,"journal":{"name":"Theoretical Economics","volume":"9 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81826458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.52342/2587-7666vte_2023_1_21_31
L. Tsedilin
{"title":"UNDERSTANDING ECONOMIC SECURITY IN RUSSIA: OFFICIAL DOCTRINE AND ALTERNATIVE APPROACHES","authors":"L. Tsedilin","doi":"10.52342/2587-7666vte_2023_1_21_31","DOIUrl":"https://doi.org/10.52342/2587-7666vte_2023_1_21_31","url":null,"abstract":"","PeriodicalId":46923,"journal":{"name":"Theoretical Economics","volume":"59 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75994935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
With the goal of maximizing expected gains from trade, this paper analyzes the jointly optimal information structure and mechanism in a bilateral trade setting. The difference in gains from trade between the optimal information structure and first best constitutes the minimal loss due to asymmetric information. With binary underlying types it is shown that more than 95% of first best can be achieved while the optimal mechanism without information design may achieve less than 90% of first best. For more general type distributions, the optimal information structure is a monotone partition of the type space and the optimal mechanism is deterministic. Necessary conditions for the optimal information structure are derived and a closed form solution is given for the binary type case.
{"title":"Optimal information structures in bilateral trade","authors":"Christoph Schottmüller","doi":"10.3982/te4074","DOIUrl":"https://doi.org/10.3982/te4074","url":null,"abstract":"With the goal of maximizing expected gains from trade, this paper analyzes the jointly optimal information structure and mechanism in a bilateral trade setting. The difference in gains from trade between the optimal information structure and first best constitutes the minimal loss due to asymmetric information. With binary underlying types it is shown that more than 95% of first best can be achieved while the optimal mechanism without information design may achieve less than 90% of first best. For more general type distributions, the optimal information structure is a monotone partition of the type space and the optimal mechanism is deterministic. Necessary conditions for the optimal information structure are derived and a closed form solution is given for the binary type case.","PeriodicalId":46923,"journal":{"name":"Theoretical Economics","volume":"7 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82077667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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