Pub Date : 2023-12-21DOI: 10.22574/jmid.2023.12.001
Zhan Wang, Jinpeng Ma, Hongwei Zhang
Affordable housing lotteries often enforce a rule preventing duplicate lottery entries that makes the model in Hylland & Zeckhauser (1979) (HZ) inapplicable. We revisit HZ and propose a new individually stable (IS) allocation that can be achieved by a Tickets algorithm and accommodate the rule. A strictly envy-free (SEF) allocation is shown to be the unique IS and Pareto-optimal allocation, the outcome of the unique strong Nash equilibrium of a congestion game, and the unique Pseudo market equilibrium allocation in HZ. The algorithm always obtains the unique SEF allocation (if any) and fixes a designed flaw of existing lotteries.
经济适用房抽签通常会执行一项防止重复抽签的规则，这使得 Hylland & Zeckhauser（1979）（HZ）中的模型不适用。我们重新审视了 HZ 模型，并提出了一种新的个体稳定（IS）分配，这种分配可以通过 Tickets 算法实现，并能适应规则。严格无嫉妒（SEF）分配被证明是唯一的 IS 和帕累托最优分配，是拥挤博弈中唯一强纳什均衡的结果，也是 HZ 中唯一的伪市场均衡分配。该算法总是能获得唯一的 SEF 分配（如果有的话），并修正了现有彩票的一个设计缺陷。
{"title":"Stable and envy-free lottery allocations for affordable housing","authors":"Zhan Wang, Jinpeng Ma, Hongwei Zhang","doi":"10.22574/jmid.2023.12.001","DOIUrl":"https://doi.org/10.22574/jmid.2023.12.001","url":null,"abstract":"Affordable housing lotteries often enforce a rule preventing duplicate lottery entries that makes the model in Hylland & Zeckhauser (1979) (HZ) inapplicable. We revisit HZ and propose a new individually stable (IS) allocation that can be achieved by a Tickets algorithm and accommodate the rule. A strictly envy-free (SEF) allocation is shown to be the unique IS and Pareto-optimal allocation, the outcome of the unique strong Nash equilibrium of a congestion game, and the unique Pseudo market equilibrium allocation in HZ. The algorithm always obtains the unique SEF allocation (if any) and fixes a designed flaw of existing lotteries.","PeriodicalId":32451,"journal":{"name":"Journal of Mechanism and Institution Design","volume":"65 45","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138950701","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}
Pub Date : 2023-12-21DOI: 10.22574/jmid.2023.12.004
Pathikrit Basu
We consider a setting in which a mechanism designer must choose the appropriate social alternative depending on the state of nature. We study the problem of optimal design and demonstrate that a mechanism which allocates resources so as to achieve the social optimum and assigns payments equal to the posterior expected utility of the agent at the social optimum, is an epsilon-optimal mechanism for environments with many players.
{"title":"Optimal mechanism design with approximate incentive compatibility and many players","authors":"Pathikrit Basu","doi":"10.22574/jmid.2023.12.004","DOIUrl":"https://doi.org/10.22574/jmid.2023.12.004","url":null,"abstract":"We consider a setting in which a mechanism designer must choose the appropriate social alternative depending on the state of nature. We study the problem of optimal design and demonstrate that a mechanism which allocates resources so as to achieve the social optimum and assigns payments equal to the posterior expected utility of the agent at the social optimum, is an epsilon-optimal mechanism for environments with many players.","PeriodicalId":32451,"journal":{"name":"Journal of Mechanism and Institution Design","volume":"6 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138948575","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}
Pub Date : 2023-12-21DOI: 10.22574/jmid.2023.12.005
Braulio Calagua
This paper studies screening problems with quasilinear preferences, where agents' private information is two-dimensional and the allocation instrument is one-dimensional. We define a preorder to compare types based on their marginal valuation to the instrument, which facilitates the reduction of incentive compatibility constraints that must be checked. With this approach, the discretized problem becomes computationally tractable. As an application, we numerically solve a problem introduced by Lewis & Sappington (1988)
本文研究的是具有准线性偏好的筛选问题，即代理人的私人信息是二维的，而分配工具是一维的。我们定义了一个前序，根据类型对工具的边际估值对其进行比较，这有助于减少必须检查的激励相容约束。通过这种方法，离散化问题在计算上变得简单易行。作为应用，我们用数值方法解决了 Lewis & Sappington（1988）提出的一个问题
{"title":"Reducing incentive constraints in bidimensional screening","authors":"Braulio Calagua","doi":"10.22574/jmid.2023.12.005","DOIUrl":"https://doi.org/10.22574/jmid.2023.12.005","url":null,"abstract":"This paper studies screening problems with quasilinear preferences, where agents' private information is two-dimensional and the allocation instrument is one-dimensional. We define a preorder to compare types based on their marginal valuation to the instrument, which facilitates the reduction of incentive compatibility constraints that must be checked. With this approach, the discretized problem becomes computationally tractable. As an application, we numerically solve a problem introduced by Lewis & Sappington (1988)","PeriodicalId":32451,"journal":{"name":"Journal of Mechanism and Institution Design","volume":"43 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138949937","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}
Pub Date : 2023-12-21DOI: 10.22574/jmid.2023.12.002
S. Flåm
This paper considers common use of natural, renewable resources. It identifies good prospects for efficiency and welfare. To be precise, a core outcome -- hence cooperation -- can be secured over time by principal planning of total quotas, and in time by agents who share these in short-term markets. Information flows in two directions: to the principal as market prices and from him as total quantities. Of particular interest is eventual convergence to a golden-rule, steady state.
{"title":"Golden rule in cooperative commons","authors":"S. Flåm","doi":"10.22574/jmid.2023.12.002","DOIUrl":"https://doi.org/10.22574/jmid.2023.12.002","url":null,"abstract":"This paper considers common use of natural, renewable resources. It identifies good prospects for efficiency and welfare. To be precise, a core outcome -- hence cooperation -- can be secured over time by principal planning of total quotas, and in time by agents who share these in short-term markets. Information flows in two directions: to the principal as market prices and from him as total quantities. Of particular interest is eventual convergence to a golden-rule, steady state.","PeriodicalId":32451,"journal":{"name":"Journal of Mechanism and Institution Design","volume":"48 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138950031","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}
Pub Date : 2022-12-03DOI: 10.22574/jmid.2022.12.002
P. Csóka, P. Herings
We consider financial networks where agents are linked to each other by financial contracts. A centralized clearing mechanism collects the initial endowments, the liabilities and the division rules of the agents and determines the payments to be made. A division rule specifies how the assets of the agents should be rationed. Since payments made depend on payments received, we are looking for solutions to a system of equations. The set of solutions is known to have a lattice structure, leading to the existence of a least and a greatest clearing payment matrix. Previous research has shown how decentralized clearing selects the least clearing payment matrix. We present a centralized approach towards clearing in order to select the greatest clearing payment matrix. To do so, we formulate the determination of the greatest clearing payment matrix as a programming problem. When agents use proportional division rules, this programming problem corresponds to a linear programming problem. We show that for other common division rules, it can be written as an integer linear programming problem.
{"title":"Centralized clearing mechanisms: A programming approach","authors":"P. Csóka, P. Herings","doi":"10.22574/jmid.2022.12.002","DOIUrl":"https://doi.org/10.22574/jmid.2022.12.002","url":null,"abstract":"We consider financial networks where agents are linked to each other by financial contracts. A centralized clearing mechanism collects the initial endowments, the liabilities and the division rules of the agents and determines the payments to be made. A division rule specifies how the assets of the agents should be rationed. Since payments made depend on payments received, we are looking for solutions to a system of equations. The set of solutions is known to have a lattice structure, leading to the existence of a least and a greatest clearing payment matrix. Previous research has shown how decentralized clearing selects the least clearing payment matrix. We present a centralized approach towards clearing in order to select the greatest clearing payment matrix. To do so, we formulate the determination of the greatest clearing payment matrix as a programming problem. When agents use proportional division rules, this programming problem corresponds to a linear programming problem. We show that for other common division rules, it can be written as an integer linear programming problem.","PeriodicalId":32451,"journal":{"name":"Journal of Mechanism and Institution Design","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41919577","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}
Pub Date : 2021-12-07DOI: 10.22574/jmid.2021.12.001
Oliver J. Board, Kim-Sau Chung
This paper provides foundations for a model of unawareness, called object-based unawareness (OBU) structures, that can be used to distinguish between what an agent is unaware of and what she simply does not know. At an informal level, this distinction plays a key role in a number of papers such as Tirole (2009) and Chung & Fortnow (2016). In this paper, we give the model-theoretic description of OBU structures by showing how they assign truth conditions to every sentence of the formal language used. We then prove a model-theoretic sound and completeness theorem, which characterizes OBU structures in terms of a system of axioms. We then verify that agents in OBU structures do not violate any of the introspection axioms that are generally considered to be necessary conditions for a plausible notion of unawareness. Applications are provided in our companion paper.
{"title":"Object-based unawareness: Axioms","authors":"Oliver J. Board, Kim-Sau Chung","doi":"10.22574/jmid.2021.12.001","DOIUrl":"https://doi.org/10.22574/jmid.2021.12.001","url":null,"abstract":"This paper provides foundations for a model of unawareness, called object-based unawareness (OBU) structures, that can be used to distinguish between what an agent is unaware of and what she simply does not know. At an informal level, this distinction plays a key role in a number of papers such as Tirole (2009) and Chung & Fortnow (2016). In this paper, we give the model-theoretic description of OBU structures by showing how they assign truth conditions to every sentence of the formal language used. We then prove a model-theoretic sound and completeness theorem, which characterizes OBU structures in terms of a system of axioms. We then verify that agents in OBU structures do not violate any of the introspection axioms that are generally considered to be necessary conditions for a plausible notion of unawareness. Applications are provided in our companion paper.","PeriodicalId":32451,"journal":{"name":"Journal of Mechanism and Institution Design","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44818083","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}
Pub Date : 2021-12-07DOI: 10.22574/jmid.2021.12.003
Tobias Reischmann, Thilo Klein, Sven Giegerich
We design and implement a program-proposing deferred acceptance mechanism with ties (DAT) and apply it to childcare assignment in two German cities. The mechanism can accommodate complementarities in providers' preferences, is fast to terminate even in larger cities, is difficult to manipulate in practice, and produces stable allocations. It can be further sped up by introducing two new features. First, allowing for an arbitrary share of facilities who participate in a centralized manner by submitting a rank-order-list over applicants. Second, by breaking ties in applicants' rank-order-lists on a first-come-first-serve basis, which sets incentives for programs to propose faster. We provide and evaluate simulation results.
{"title":"A deferred acceptance mechanism for decentralized, fast, and fair childcare assignment","authors":"Tobias Reischmann, Thilo Klein, Sven Giegerich","doi":"10.22574/jmid.2021.12.003","DOIUrl":"https://doi.org/10.22574/jmid.2021.12.003","url":null,"abstract":"We design and implement a program-proposing deferred acceptance mechanism with ties (DAT) and apply it to childcare assignment in two German cities. The mechanism can accommodate complementarities in providers' preferences, is fast to terminate even in larger cities, is difficult to manipulate in practice, and produces stable allocations. It can be further sped up by introducing two new features. First, allowing for an arbitrary share of facilities who participate in a centralized manner by submitting a rank-order-list over applicants. Second, by breaking ties in applicants' rank-order-lists on a first-come-first-serve basis, which sets incentives for programs to propose faster. We provide and evaluate simulation results.","PeriodicalId":32451,"journal":{"name":"Journal of Mechanism and Institution Design","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46720105","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}
Pub Date : 2021-12-07DOI: 10.22574/jmid.2021.12.002
Y. Chun
We consider 2-person bargaining situations in which the feasible set is known, but the disagreement point is uncertain. We investigate the implications of various axioms concerning uncertain disagreement points and characterize the family of linear solutions, which includes the egalitarian, lexicographic egalitarian, Nash, and Kalai-Rosenthal solutions. We also show that how the important subfamilies (or members) of this family can be singled out by imposing additional axioms or strengthening the axioms used in the characterizations.
{"title":"Axioms concerning uncertain disagreement points in 2-person bargaining problems","authors":"Y. Chun","doi":"10.22574/jmid.2021.12.002","DOIUrl":"https://doi.org/10.22574/jmid.2021.12.002","url":null,"abstract":"We consider 2-person bargaining situations in which the feasible set is known, but the disagreement point is uncertain. We investigate the implications of various axioms concerning uncertain disagreement points and characterize the family of linear solutions, which includes the egalitarian, lexicographic egalitarian, Nash, and Kalai-Rosenthal solutions. We also show that how the important subfamilies (or members) of this family can be singled out by imposing additional axioms or strengthening the axioms used in the characterizations.","PeriodicalId":32451,"journal":{"name":"Journal of Mechanism and Institution Design","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41458943","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}
Pub Date : 2020-12-07DOI: 10.22574/jmid.2020.12.003
Simon Hoof
We consider n-person pure bargaining games in which the space of feasible payoffs is constructed via a normal form differential game. At the beginning of the game the agents bargain over strategies to be played over an infinite time horizon. An initial cooperative solution (a strategy tuple) is called subgame individually rational (SIR) if it remains individually rational throughout the entire game and time consistent (TC) if renegotiating it at a later time instant yields the original solution. For a class of linear-state differential games we show that any solution which is individually rational at the beginning of the game satisfies SIR and TC if the space of admissible cooperative strategies is restricted to constants. We discuss an application from environmental economics.
{"title":"On a class of linear-state differential games with subgame individually rational and time consistent bargaining solutions","authors":"Simon Hoof","doi":"10.22574/jmid.2020.12.003","DOIUrl":"https://doi.org/10.22574/jmid.2020.12.003","url":null,"abstract":"We consider n-person pure bargaining games in which the space of feasible payoffs is constructed via a normal form differential game. At the beginning of the game the agents bargain over strategies to be played over an infinite time horizon. An initial cooperative solution (a strategy tuple) is called subgame individually rational (SIR) if it remains individually rational throughout the entire game and time consistent (TC) if renegotiating it at a later time instant yields the original solution. For a class of linear-state differential games we show that any solution which is individually rational at the beginning of the game satisfies SIR and TC if the space of admissible cooperative strategies is restricted to constants. We discuss an application from environmental economics.","PeriodicalId":32451,"journal":{"name":"Journal of Mechanism and Institution Design","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41795723","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}
Pub Date : 2019-11-01DOI: 10.22574/JMID.2019.11.001
Kim-Sau Chung, Jeffrey C. Ely
In auction environments in which agents have private values, the Vickrey auction induces agents to truthfully reveal their preferences and selects the efficient allocation accordingly. When the agents' valuations are interdependent, various generalizations of the Vickrey auction have been found which provide incentives for truthful revelation of all private information and preserve efficiency. However, these mechanisms generally do not provide the bidders with dominant strategies. The existing literature has therefore used a stronger equilibrium solution concept. In this paper we show that while the generalized VCG mechanism admits a multiplicity of equilibria, many of which are inefficient. We give conditions under which the efficiency equilibrium is the unique outcome of iterative elimination of ex post weakly dominated strategies. With two bidders, the standard single-crossing condition is sufficient. With more than two bidders, we show by example that a strengthening of the single-crossing condition is necessary.
{"title":"Efficient and Dominance Solvable Auctions with Interdependent Valuations","authors":"Kim-Sau Chung, Jeffrey C. Ely","doi":"10.22574/JMID.2019.11.001","DOIUrl":"https://doi.org/10.22574/JMID.2019.11.001","url":null,"abstract":"In auction environments in which agents have private values, the Vickrey auction induces agents to truthfully reveal their preferences and selects the efficient allocation accordingly. When the agents' valuations are interdependent, various generalizations of the Vickrey auction have been found which provide incentives for truthful revelation of all private information and preserve efficiency. However, these mechanisms generally do not provide the bidders with dominant strategies. The existing literature has therefore used a stronger equilibrium solution concept. In this paper we show that while the generalized VCG mechanism admits a multiplicity of equilibria, many of which are inefficient. We give conditions under which the efficiency equilibrium is the unique outcome of iterative elimination of ex post weakly dominated strategies. With two bidders, the standard single-crossing condition is sufficient. With more than two bidders, we show by example that a strengthening of the single-crossing condition is necessary.","PeriodicalId":32451,"journal":{"name":"Journal of Mechanism and Institution Design","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47658420","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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