Pub Date : 2026-01-19DOI: 10.1016/j.jmateco.2026.103216
R. Pablo Arribillaga , Jordi Massó , Alejandro Neme
We introduce the concept of group obvious strategy-proofness, an extension of Li (2017)’s notion of obvious strategy-proofness, by requiring that truth-telling remains an obviously dominant strategy for any group of agents in the extensive game form implementing the social choice function. We show that this stronger condition is no more restrictive: the set of all group obviously strategy-proof social choice functions coincides with the set of all obviously strategy-proof social choice functions. Building on this equivalence result and on existing results on obvious strategy-proofness via extensive game forms with perfect information, we derive additional equivalences concerning the implementability of social choice functions: in this class of games, strategy-proofness, group strategy-proofness, obvious strategy-proofness, and group obvious strategy-proofness are all equivalent.
{"title":"Group obvious strategy-proofness: Definition and characterization","authors":"R. Pablo Arribillaga , Jordi Massó , Alejandro Neme","doi":"10.1016/j.jmateco.2026.103216","DOIUrl":"10.1016/j.jmateco.2026.103216","url":null,"abstract":"<div><div>We introduce the concept of group obvious strategy-proofness, an extension of Li (2017)’s notion of obvious strategy-proofness, by requiring that truth-telling remains an obviously dominant strategy for any group of agents in the extensive game form implementing the social choice function. We show that this stronger condition is no more restrictive: the set of all group obviously strategy-proof social choice functions coincides with the set of all obviously strategy-proof social choice functions. Building on this equivalence result and on existing results on obvious strategy-proofness <em>via</em> extensive game forms with perfect information, we derive additional equivalences concerning the implementability of social choice functions: in this class of games, strategy-proofness, group strategy-proofness, obvious strategy-proofness, and group obvious strategy-proofness are all equivalent.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"123 ","pages":"Article 103216"},"PeriodicalIF":0.7,"publicationDate":"2026-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-16DOI: 10.1016/j.jmateco.2026.103214
Gil Bar Castellon Koltun , Ehud Lehrer , Eilon Solan
We study two-player zero-sum repeated games with incomplete information on one side, where the payoff function is tail measurable (and not necessarily the long-run average payoff). We show that the maxmin value equals the concavification of the value function of the non-revealing game. In addition, we provide an example demonstrating that, under tail-measurable payoffs, the value of the game may fail to exist.
{"title":"The maxmin value of repeated games with incomplete information on one side and tail-measurable payoffs","authors":"Gil Bar Castellon Koltun , Ehud Lehrer , Eilon Solan","doi":"10.1016/j.jmateco.2026.103214","DOIUrl":"10.1016/j.jmateco.2026.103214","url":null,"abstract":"<div><div>We study two-player zero-sum repeated games with incomplete information on one side, where the payoff function is tail measurable (and not necessarily the long-run average payoff). We show that the maxmin value equals the concavification of the value function of the non-revealing game. In addition, we provide an example demonstrating that, under tail-measurable payoffs, the value of the game may fail to exist.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"123 ","pages":"Article 103214"},"PeriodicalIF":0.7,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145993587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-14DOI: 10.1016/j.jmateco.2026.103215
Makoto Hagiwara , Goro Ochiai , Hirofumi Yamamura
We investigate strategy-proof rules defined over the set of single-peaked preference profiles whose range may not be an interval. We define the class of “minmax rules with a family of upper-set tie-breaking rules”, and show that it is characterized by strategy-proofness. This class is broader than that of “disturbed minmax rules” introduced by Massó and Moreno de Barreda (2011), because, under the domain of all single-peaked preferences, the alternative selected by a strategy-proof rule whose range is not an interval may be affected by asymmetric single-peaked preferences over alternatives lying outside its range.
我们研究了在单峰偏好曲线集合上定义的策略证明规则，其范围可能不是一个区间。我们定义了一类“带有一组上集破局规则的极小极大规则”，并证明了它具有策略证明性。这一类比Massó和Moreno de Barreda（2011）引入的“扰动最小最大值规则”更广泛，因为在所有单峰偏好域下，由范围不是区间的策略证明规则选择的替代方案可能会受到非对称单峰偏好对其范围之外的替代方案的影响。
{"title":"On strategy-proofness and single peakedness: A full characterization","authors":"Makoto Hagiwara , Goro Ochiai , Hirofumi Yamamura","doi":"10.1016/j.jmateco.2026.103215","DOIUrl":"10.1016/j.jmateco.2026.103215","url":null,"abstract":"<div><div>We investigate <em>strategy-proof</em> rules defined over the set of single-peaked preference profiles whose range may not be an interval. We define the class of “minmax rules with a family of upper-set tie-breaking rules”, and show that it is characterized by <em>strategy-proofness</em>. This class is broader than that of “disturbed minmax rules” introduced by Massó and Moreno de Barreda (2011), because, under the domain of all single-peaked preferences, the alternative selected by a <em>strategy-proof</em> rule whose range is not an interval may be affected by asymmetric single-peaked preferences over alternatives lying outside its range.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"123 ","pages":"Article 103215"},"PeriodicalIF":0.7,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146039492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-09DOI: 10.1016/j.jmateco.2026.103213
Yihang Zhou , David Sibley
A seller bargains with two buyers to make a deal with each of them, using an alternating-offer protocol (“AO”). The bargaining begins with one buyer, with the second entering at a future date. The seller has a concave utility function, defined over total payments made by the two buyers. Hence, the bargain made with one buyer affects the outcome of the bargain made with the second buyer. The curvature properties of the seller utility and the arrival date of the second buyer decide how bargains affect each other. We derive dynamic properties of the negotiated prices. These prices exhibit unusual comparative statics. The price paid by the first buyer can be non-monotone in the discount factor used in the AO bargaining. This is because the bargaining between the seller and the first buyer anticipates the arrival of the second buyer. We extend the model to include downstream competition between the two buyers. We obtain results on first-mover and second-mover advantage.
{"title":"Interdependent Bargains","authors":"Yihang Zhou , David Sibley","doi":"10.1016/j.jmateco.2026.103213","DOIUrl":"10.1016/j.jmateco.2026.103213","url":null,"abstract":"<div><div>A seller bargains with two buyers to make a deal with each of them, using an alternating-offer protocol (“AO”). The bargaining begins with one buyer, with the second entering at a future date. The seller has a concave utility function, defined over total payments made by the two buyers. Hence, the bargain made with one buyer affects the outcome of the bargain made with the second buyer. The curvature properties of the seller utility and the arrival date of the second buyer decide how bargains affect each other. We derive dynamic properties of the negotiated prices. These prices exhibit unusual comparative statics. The price paid by the first buyer can be non-monotone in the discount factor used in the AO bargaining. This is because the bargaining between the seller and the first buyer anticipates the arrival of the second buyer. We extend the model to include downstream competition between the two buyers. We obtain results on first-mover and second-mover advantage.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"122 ","pages":"Article 103213"},"PeriodicalIF":0.7,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-24DOI: 10.1016/j.jmateco.2025.103211
Erik Lillethun
Consumer welfare may be higher when platforms sometimes conceal product quality information, because this can incentivize firms to invest more in quality. I study an infinite horizon model in which a long-run firm with a persistent type interacts with a sequence of short-run consumers. The focus is on the case where there are frequent consumer purchases. When a designer commits in advance to an information policy to maximize average consumer welfare, the approximately optimal policy and the resulting welfare depend on whether the policy may condition on the full history or only the publicly observable history. An approximately optimal full history policy approximates the upper bound welfare that is consistent with firm participation. It may do so by privately keeping track of a firm rating, threatening a hypothetical punishment (revealing firm type) off the path of play, while never giving consumers information on the path of play. However, learning must occur on the path of play in an approximately optimal public history policy. A public history policy can only achieve the upper bound welfare conditional on beliefs being above some cutoff. The approximately optimal public history policy features a learning cutoff: The firm must pass an initial test, driving beliefs up to the cutoff, which is essential for rewarding the firm.
{"title":"Information design and reputations in the frequent-interaction limit","authors":"Erik Lillethun","doi":"10.1016/j.jmateco.2025.103211","DOIUrl":"10.1016/j.jmateco.2025.103211","url":null,"abstract":"<div><div>Consumer welfare may be higher when platforms sometimes conceal product quality information, because this can incentivize firms to invest more in quality. I study an infinite horizon model in which a long-run firm with a persistent type interacts with a sequence of short-run consumers. The focus is on the case where there are frequent consumer purchases. When a designer commits in advance to an information policy to maximize average consumer welfare, the approximately optimal policy and the resulting welfare depend on whether the policy may condition on the full history or only the publicly observable history. An approximately optimal full history policy approximates the upper bound welfare that is consistent with firm participation. It may do so by privately keeping track of a firm rating, threatening a hypothetical punishment (revealing firm type) off the path of play, while never giving consumers information on the path of play. However, learning must occur on the path of play in an approximately optimal public history policy. A public history policy can only achieve the upper bound welfare conditional on beliefs being above some cutoff. The approximately optimal public history policy features a learning cutoff: The firm must pass an initial test, driving beliefs up to the cutoff, which is essential for rewarding the firm.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"122 ","pages":"Article 103211"},"PeriodicalIF":0.7,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145839283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper explores the dynamics of learning in a multi-sector general equilibrium model where firms operate under incomplete information about their production returns to scale. Firms iteratively update their beliefs using maximum a-posteriori estimation, derived from observed production outcomes, to refine their knowledge of their returns to scale. The implications of these learning dynamics for market equilibrium and the conditions under which firms can effectively learn their true returns to scale are the key objects of this study. Our results shed light on how idiosyncratic shocks influence the learning process and demonstrate that input decisions encode all pertinent information for belief updates. Additionally, we show that a long-memory (path-dependent) learning which keeps track of all past estimations ends up having a worse performance than a short-memory (path-independent) approach.
{"title":"Learning paths to multi-sector equilibrium: Belief dynamics under uncertain returns to scale","authors":"Stefano Nasini , Rabia Nessah , Bertrand Wigniolle","doi":"10.1016/j.jmateco.2025.103212","DOIUrl":"10.1016/j.jmateco.2025.103212","url":null,"abstract":"<div><div>This paper explores the dynamics of learning in a multi-sector general equilibrium model where firms operate under incomplete information about their production returns to scale. Firms iteratively update their beliefs using maximum a-posteriori estimation, derived from observed production outcomes, to refine their knowledge of their returns to scale. The implications of these learning dynamics for market equilibrium and the conditions under which firms can effectively learn their true returns to scale are the key objects of this study. Our results shed light on how idiosyncratic shocks influence the learning process and demonstrate that input decisions encode all pertinent information for belief updates. Additionally, we show that a long-memory (path-dependent) learning which keeps track of all past estimations ends up having a worse performance than a short-memory (path-independent) approach.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"122 ","pages":"Article 103212"},"PeriodicalIF":0.7,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145839284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-03DOI: 10.1016/j.jmateco.2025.103209
Christian Trudeau , Edward C. Rosenthal
We consider a set of users who are located along a pipeline with a single source. These users consume a good that is extracted from the source and flows downstream, with diminishing marginal returns for each user. In addition, flows along each edge in the pipeline create negative externalities, which are nondecreasing as a function of flow. The users cooperate toward obtaining group welfare maximization. In both the continuous and discrete cases, we obtain the group optimal solutions, and we then use cooperative game theory to determine how best to allocate the damages, using optimistic and pessimistic formulations for the characteristic function. Using core stability as our guiding principle, we provide a set of stable allocations that apportions the damages at a location among the set of downstream users, notably an average damage allocation and a marginal damage allocation. Given that the joint optimization forces agents to reduce (unequally) their consumption, we also examine the Shapley value of the optimistic game, also in the core, that allows to compensate agents who have sacrificed their consumption for the benefit of the group. Finally, we show that our pipeline externalities model generalizes some well-known problems from the literature, including the river sharing problem of Ambec and Sprumont 2002 and the joint production problem of Moulin and Shenker 1992.
{"title":"The pipeline externalities problem","authors":"Christian Trudeau , Edward C. Rosenthal","doi":"10.1016/j.jmateco.2025.103209","DOIUrl":"10.1016/j.jmateco.2025.103209","url":null,"abstract":"<div><div>We consider a set of users who are located along a pipeline with a single source. These users consume a good that is extracted from the source and flows downstream, with diminishing marginal returns for each user. In addition, flows along each edge in the pipeline create negative externalities, which are nondecreasing as a function of flow. The users cooperate toward obtaining group welfare maximization. In both the continuous and discrete cases, we obtain the group optimal solutions, and we then use cooperative game theory to determine how best to allocate the damages, using optimistic and pessimistic formulations for the characteristic function. Using core stability as our guiding principle, we provide a set of stable allocations that apportions the damages at a location among the set of downstream users, notably an average damage allocation and a marginal damage allocation. Given that the joint optimization forces agents to reduce (unequally) their consumption, we also examine the Shapley value of the optimistic game, also in the core, that allows to compensate agents who have sacrificed their consumption for the benefit of the group. Finally, we show that our pipeline externalities model generalizes some well-known problems from the literature, including the river sharing problem of Ambec and Sprumont 2002 and the joint production problem of Moulin and Shenker 1992.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"122 ","pages":"Article 103209"},"PeriodicalIF":0.7,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145736756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-02DOI: 10.1016/j.jmateco.2025.103210
Zijia Wang
We study a three-stage sequential elimination contest with repechage. In the first stage, all the contestants compete against each other, and some advance directly to the third stage while the others enter the second stage to compete for the opportunity to proceed to the third stage. The finalists in the third stage then compete against each other for the final prize. Compared to a sequential elimination contest without repechage, the contest with repechage induces a strictly higher overall contest effort as well as a higher expected total effort from the prize winner. This result helps to explain the prevalence of repechage in some real-world tournaments or competitions.
{"title":"Sequential elimination contests with repechage","authors":"Zijia Wang","doi":"10.1016/j.jmateco.2025.103210","DOIUrl":"10.1016/j.jmateco.2025.103210","url":null,"abstract":"<div><div>We study a three-stage sequential elimination contest with repechage. In the first stage, all the contestants compete against each other, and some advance directly to the third stage while the others enter the second stage to compete for the opportunity to proceed to the third stage. The finalists in the third stage then compete against each other for the final prize. Compared to a sequential elimination contest without repechage, the contest with repechage induces a strictly higher overall contest effort as well as a higher expected total effort from the prize winner. This result helps to explain the prevalence of repechage in some real-world tournaments or competitions.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"122 ","pages":"Article 103210"},"PeriodicalIF":0.7,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145684363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-28DOI: 10.1016/j.jmateco.2025.103205
Aggey Simons Semenov
This paper characterizes optimal contracts under adverse selection when the principal faces a general linear constraint involving both the quantity produced and the transfer paid. These constraints capture enforcement limits, budget restrictions, and minimum quality standards. Using optimal control techniques, we establish existence and continuity of the optimal quantity schedule and derive a three-region structure: under regularity conditions, the optimal contract splits the type space into at most three connected intervals (slack and binding intervals), where binding intervals generically induce endogenous bunching of quantities. Our unifying framework, along with novel analytical assumptions, provides rigorous foundations for understanding how optimal mechanisms behave under such smooth constraints and offers a toolkit for analyzing a broad class of constrained contracting problems.
{"title":"Optimal contracts under general mixed constraints: Continuity, structure, and applications","authors":"Aggey Simons Semenov","doi":"10.1016/j.jmateco.2025.103205","DOIUrl":"10.1016/j.jmateco.2025.103205","url":null,"abstract":"<div><div>This paper characterizes optimal contracts under adverse selection when the principal faces a general linear constraint involving both the quantity produced and the transfer paid. These constraints capture enforcement limits, budget restrictions, and minimum quality standards. Using optimal control techniques, we establish existence and continuity of the optimal quantity schedule and derive a three-region structure: under regularity conditions, the optimal contract splits the type space into at most three connected intervals (slack and binding intervals), where binding intervals generically induce endogenous bunching of quantities. Our unifying framework, along with novel analytical assumptions, provides rigorous foundations for understanding how optimal mechanisms behave under such smooth constraints and offers a toolkit for analyzing a broad class of constrained contracting problems.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"122 ","pages":"Article 103205"},"PeriodicalIF":0.7,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145684366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-27DOI: 10.1016/j.jmateco.2025.103208
Toan Le
Two mechanisms are equivalent if they share the same allocation rules and interim transfer rules, carrying incentive properties from one mechanism to the other. I prove the generalized d’Aspremont-Gérard-Varet (AGV) mechanism achieves minimal liquidity risk. It uniquely minimizes total transfer variance among all ex post budget-balanced mechanisms equivalent to an initial mechanism that balances the budget in expectation. Motivated by the contrast between ex ante and ex post fairness, I characterize the optimal mechanism minimizing payoff volatility. Finally, I show that in single-item auctions, a first-price auction with the optimal reserve price jointly maximizes expected revenue and minimizes revenue variance.
{"title":"AGV mechanism balances the budget with minimum total transfer variance","authors":"Toan Le","doi":"10.1016/j.jmateco.2025.103208","DOIUrl":"10.1016/j.jmateco.2025.103208","url":null,"abstract":"<div><div>Two mechanisms are <em>equivalent</em> if they share the same allocation rules and interim transfer rules, carrying incentive properties from one mechanism to the other. I prove the generalized d’Aspremont-Gérard-Varet (AGV) mechanism achieves minimal liquidity risk. It uniquely minimizes total transfer variance among all ex post budget-balanced mechanisms equivalent to an initial mechanism that balances the budget in expectation. Motivated by the contrast between ex ante and ex post fairness, I characterize the optimal mechanism minimizing payoff volatility. Finally, I show that in single-item auctions, a first-price auction with the optimal reserve price jointly maximizes expected revenue and minimizes revenue variance.</div></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"122 ","pages":"Article 103208"},"PeriodicalIF":0.7,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145684365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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