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On a class of strategy-proof social choice correspondences with single-peaked utility functions 关于一类具有单峰效用函数的策略证明社会选择对应关系
IF 1.3 4区 经济学
Journal of Mathematical Economics Pub Date : 2023-11-04 DOI: 10.1016/j.jmateco.2023.102912
Chinmay Ingalagavi , Soumyarup Sadhukhan
{"title":"On a class of strategy-proof social choice correspondences with single-peaked utility functions","authors":"Chinmay Ingalagavi ,&nbsp;Soumyarup Sadhukhan","doi":"10.1016/j.jmateco.2023.102912","DOIUrl":"https://doi.org/10.1016/j.jmateco.2023.102912","url":null,"abstract":"<div><p>We consider the problem of constructing strategy-proof rules that choose sets of alternatives based on the preferences of voters, modelled as Social Choice Correspondences (SCCs) in the literature. We focus on two domain restrictions inspired by Barberà et al. (2001) in the context of single-peaked utility functions. We find that for the narrower domain, the set of tops-only, unanimous, and strategy-proof SCCs coincides with the class of unions of two min–max rules (Moulin, 1980). For the broader domain, the set of SCCs coincides with the class of unions of two ‘adjacent’ min–max rules, meaning the corresponding parameters for the two rules must be either the same or consecutive alternatives.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72249481","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}
引用次数: 0
Correlated play in weakest-link and best-shot group contests 在最弱的环节和最好的投篮小组比赛中相互关联
IF 1.3 4区 经济学
Journal of Mathematical Economics Pub Date : 2023-11-04 DOI: 10.1016/j.jmateco.2023.102917
Stefano Barbieri , Iryna Topolyan
{"title":"Correlated play in weakest-link and best-shot group contests","authors":"Stefano Barbieri ,&nbsp;Iryna Topolyan","doi":"10.1016/j.jmateco.2023.102917","DOIUrl":"https://doi.org/10.1016/j.jmateco.2023.102917","url":null,"abstract":"<div><p>We explore public randomization (Harris et al., 1995) in group contests and introduce group public randomization equilibria (GPRE). We consider group all-pay auctions with weakest-link and best-shot impact functions. While best-shot contests without public randomization are known for their multiplicity of equilibria, introducing public randomization results in a unique GPRE in which only one of the strongest players in each group is active. However, in the weakest-link case, the well-known multiplicity of equilibria becomes even more pronounced with public randomization. Despite this multiplicity, a refinement that selects GPRE immune to coalitional deviations reduces the gamut of GPRE to a unique equilibrium group-effort distribution, which, for identical groups composed of identical agents, features the highest expected total effort among all equilibria of the full information game without correlation devices. The (weak) increase in expected efforts due to correlated strategies is also observed in the best-shot case.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92051302","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}
引用次数: 0
An α-MaxMin utility representation for close and distant future preferences with temporal biases 具有时间偏差的近期和远期偏好的α-MaxMin效用表示
IF 1.3 4区 经济学
Journal of Mathematical Economics Pub Date : 2023-10-31 DOI: 10.1016/j.jmateco.2023.102916
Jean-Pierre Drugeon , Thai Ha-Huy
{"title":"An α-MaxMin utility representation for close and distant future preferences with temporal biases","authors":"Jean-Pierre Drugeon ,&nbsp;Thai Ha-Huy","doi":"10.1016/j.jmateco.2023.102916","DOIUrl":"https://doi.org/10.1016/j.jmateco.2023.102916","url":null,"abstract":"<div><p>This paper provides a framework for understanding preferences over utility streams across different time periods. We analyze preferences for the close future, for the distant future, and a synthesis of both, establishing a representation involving weights over time periods. Examining scenarios where two utility streams cannot be robustly compared to each other, we introduce notions in which one has more “potential” to be preferred over another, which lead to MaxMin, MaxMax, and <span><math><mi>α</mi></math></span><span>-MaxMin representations. Finally, we consider temporal bias in the form of violations of stationarity. For close future preferences, we obtain a generalization of quasi-hyperbolic discounting. For distant future preferences, we obtain Banach limits and discuss the relationship with exponential discounting.</span></p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91959837","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}
引用次数: 0
The Sure-Thing Principle 确定原则
IF 1.3 4区 经济学
Journal of Mathematical Economics Pub Date : 2023-10-31 DOI: 10.1016/j.jmateco.2023.102915
Jean Baccelli , Lorenz Hartmann
{"title":"The Sure-Thing Principle","authors":"Jean Baccelli ,&nbsp;Lorenz Hartmann","doi":"10.1016/j.jmateco.2023.102915","DOIUrl":"https://doi.org/10.1016/j.jmateco.2023.102915","url":null,"abstract":"<div><p>The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to a dominance condition; that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe-Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304406823001088/pdfft?md5=553741f4c2e07c71bc882d9bcf66edd0&pid=1-s2.0-S0304406823001088-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92136329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A multidimensional, nonconvex model of optimal growth 最优增长的多维非凸模型
IF 1.3 4区 经济学
Journal of Mathematical Economics Pub Date : 2023-10-31 DOI: 10.1016/j.jmateco.2023.102914
Stefano Bosi, Thai Ha-Huy
{"title":"A multidimensional, nonconvex model of optimal growth","authors":"Stefano Bosi,&nbsp;Thai Ha-Huy","doi":"10.1016/j.jmateco.2023.102914","DOIUrl":"https://doi.org/10.1016/j.jmateco.2023.102914","url":null,"abstract":"<div><p><span>In this article, we consider a multidimensional economy where the standard supermodularity property fails. We generalize the notion of net gain of investment, introduced by Kamihigashi and Roy (2007) and applied to one-sector growth models, to the case of multiple capital stocks. We prove the convergence to the set of steady states without relying on the monotonicity of optimal path. Our approach differs from the standard </span>dynamic programming based on convexity or supermodularity. We find that preferences are key to shape the economy in the long run.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72249482","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}
引用次数: 0
Context-sensitive rationality: Choice by salience 语境敏感理性：突出的选择
IF 1.3 4区 经济学
Journal of Mathematical Economics Pub Date : 2023-10-30 DOI: 10.1016/j.jmateco.2023.102913
Alfio Giarlotta , Angelo Petralia , Stephen Watson
{"title":"Context-sensitive rationality: Choice by salience","authors":"Alfio Giarlotta ,&nbsp;Angelo Petralia ,&nbsp;Stephen Watson","doi":"10.1016/j.jmateco.2023.102913","DOIUrl":"https://doi.org/10.1016/j.jmateco.2023.102913","url":null,"abstract":"<div><p>We describe a context-sensitive approach to individual choice, in which the explanation is provided by a family of linear orders indexed by all available items. Selection from a menu is then recovered by the classical maximization paradigm, subject to the constraint that the justifying rationale must be indexed by an item of the menu. This approach allows us to pursue two complementary goals: (1) a fine classification of all possible choices into classes of rationality, and (2) a bounded rationality model based on an ordinal notion of salience. Concerning (1), we refine the context-free model of <em>rationalization by multiple rationales</em>, partitioning the class of all choice functions on <span><math><mi>n</mi></math></span> items into <span><math><mi>n</mi></math></span> classes of rationality. The least rational class is expressive of a moody behavior, which is rare for small <span><math><mi>n</mi></math></span>, but prevailing for large <span><math><mi>n</mi></math></span>. Concerning (2), we enrich our framework by a binary relation of salience, which guides the selection process. Upon requiring that all rationales associated to equally salient items coincide, choice is explained by appealing to the unique linear order indexed by a maximally salient item of the menu. Choice by salience is a specification of <em>choice with limited attention</em>. Numerical estimates show the sharp selectivity of this model of bounded rationality.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304406823001064/pdfft?md5=389083d0d7f43630a9658f69ede0247c&pid=1-s2.0-S0304406823001064-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72250160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-stage elimination games 两阶段淘汰赛
IF 1.3 4区 经济学
Journal of Mathematical Economics Pub Date : 2023-10-29 DOI: 10.1016/j.jmateco.2023.102911
Aner Sela
{"title":"Two-stage elimination games","authors":"Aner Sela","doi":"10.1016/j.jmateco.2023.102911","DOIUrl":"https://doi.org/10.1016/j.jmateco.2023.102911","url":null,"abstract":"<div><p>We study two-stage elimination games with four heterogeneous players. In the first stage, the players are allocated into two contests, each of which includes two players competing against each other in an all-pay auction. The winners of the two contests then interact with each other in the second stage. The outcomes of the interaction in the second stage are given by a general form of the players’ payoffs as functions of their types (abilities). Then, we examine the effect of the timing of the competitions in the first stage on the players’ expected payoffs and their total effort. In particular, we show that if the players’ payoff functions in the second stage are separable in the players’ types, then the timing of play in the first stage of either simultaneous or sequential contests has no effect on the players’ expected payoff as well as their total effort in the elimination games.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92047001","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}
引用次数: 0
The general equilibrium effects of localised technological progress: A Classical approach 局部技术进步的一般均衡效应:经典方法
IF 1.3 4区 经济学
Journal of Mathematical Economics Pub Date : 2023-10-13 DOI: 10.1016/j.jmateco.2023.102904
Naoki Yoshihara , Roberto Veneziani
{"title":"The general equilibrium effects of localised technological progress: A Classical approach","authors":"Naoki Yoshihara ,&nbsp;Roberto Veneziani","doi":"10.1016/j.jmateco.2023.102904","DOIUrl":"https://doi.org/10.1016/j.jmateco.2023.102904","url":null,"abstract":"<div><p><span>We study the general equilibrium<span> effects of localised technical progress à la Atkinson–Stiglitz in economies in which capital is a vector of reproducible and heterogeneous goods. We show that there is no obvious relation between ex-ante profitable innovations and the functional distribution of income that actually emerges in equilibrium. Unlike in the standard macroeconomic approach to technical progress, localised innovations may lead to indeterminacy in equilibrium factor prices, and individually rational choices of technique do not necessarily lead to optimal outcomes. Innovations may even cause the disappearance of </span></span><em>all</em> equilibria.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92136328","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}
引用次数: 0
Symmetric mechanism design: Comment 对称机制设计:注释
IF 1.3 4区 经济学
Journal of Mathematical Economics Pub Date : 2023-10-12 DOI: 10.1016/j.jmateco.2023.102910
Bo Chen , Dmitriy Knyazev
{"title":"Symmetric mechanism design: Comment","authors":"Bo Chen ,&nbsp;Dmitriy Knyazev","doi":"10.1016/j.jmateco.2023.102910","DOIUrl":"https://doi.org/10.1016/j.jmateco.2023.102910","url":null,"abstract":"<div><p>In an earlier paper published in this journal, Azrieli and Jain (2018) claim that a social choice function (SCF) is symmetrically implementable in a dominant strategy equilibrium only if the SCF is symmetric. This result crucially relies on their notion of dominant strategy, which is used in the game theory literature and is stronger than the one traditionally used in the mechanism design literature. We discuss the limitation of using their notion in mechanism design and provide a set of characterizations of symmetric mechanism design using the (weaker) standard notion that differ from their findings.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304406823001039/pdfft?md5=99e7a0a373466ec5ec00db0a266b1ecc&pid=1-s2.0-S0304406823001039-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92136245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A dual approach to agency problems 解决代理问题的双重方法
IF 1.3 4区 经济学
Journal of Mathematical Economics Pub Date : 2023-10-10 DOI: 10.1016/j.jmateco.2023.102909
Chang Koo Chi , Kyoung Jin Choi
{"title":"A dual approach to agency problems","authors":"Chang Koo Chi ,&nbsp;Kyoung Jin Choi","doi":"10.1016/j.jmateco.2023.102909","DOIUrl":"https://doi.org/10.1016/j.jmateco.2023.102909","url":null,"abstract":"<div><p>This paper presents a dual approach to the standard model of moral hazard. We formulate the dual of the principal–agent problem under the assumption that the incentive constraint can be replaced by a local constraint (the first-order approach), to examine whether the <em>relaxed</em><span> agency problem yields a candidate solution. The dual formulation generates a convex conjugate, which transforms the agent’s utility from compensation into a dual functional. The dual problem features a simple convex structure, which enables us to perform a comprehensive analysis for the agency problem. We derive novel and more tractable conditions for existence and uniqueness of a solution to the problem with the dual elements. Furthermore, the approach to the dual problem provides illuminating insights into the previous nonexistence results.</span></p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49881236","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}
引用次数: 0
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