{"title":"From local utility to neural networks","authors":"Shaowei Ke , Chen Zhao","doi":"10.1016/j.jmateco.2024.103003","DOIUrl":"https://doi.org/10.1016/j.jmateco.2024.103003","url":null,"abstract":"<div><p>We introduce and analyze two preference-based notions of local linearity in the spirit of Machina (1982). We show how the weaker among the two extends Machina’s local utility analysis, and that the stronger among the two characterizes continuous finite piecewise linear (CFPL) utility functions. We introduce a representation of the decision maker’s preference called the neural-network utility representation that is equivalent to the CFPL representation, in which the decision maker evaluates an alternative through a neural network.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"113 ","pages":"Article 103003"},"PeriodicalIF":1.3,"publicationDate":"2024-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141324219","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}
Raouf Boucekkine , Shankha Chakraborty , Aditya Goenka , Lin Liu
{"title":"Economic epidemiological modelling: A progress report","authors":"Raouf Boucekkine , Shankha Chakraborty , Aditya Goenka , Lin Liu","doi":"10.1016/j.jmateco.2024.103011","DOIUrl":"10.1016/j.jmateco.2024.103011","url":null,"abstract":"<div><p>Prior to the Covid-19 crisis, the integration of epidemiology and economics that is, economic epidemiology modelling (epi-econ), was relatively limited. The emergence of the Covid-19 crisis has prompted an unprecedented surge in this literature. This paper identifies and develops the main conceptual and modelling challenges involved in the expanding epi-econ stream, with a particular attention to the mathematical issues due, in particular, to the non-convex nature of epi-econ models. Recent extensions are also examined and a few future areas of research highlighted.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"113 ","pages":"Article 103011"},"PeriodicalIF":1.3,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304406824000703/pdfft?md5=f5af5592a06ab2cda81a69021f0a4081&pid=1-s2.0-S0304406824000703-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141402166","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}
{"title":"Bayesian equilibrium: From local to global","authors":"Yehuda John Levy","doi":"10.1016/j.jmateco.2024.103012","DOIUrl":"https://doi.org/10.1016/j.jmateco.2024.103012","url":null,"abstract":"<div><p>We study Bayesian games with a continuum of states which partition into a continuum of components, each of which is common knowledge, such that equilibria exist on each component. A canonical case is when each agent’s information consists of both public and private information, and conditional on each possible public signal, equilibria exist. We show that under some regularity conditions on the partition, measurable Bayesian equilibria exist for the game in its entirety. The results extend to pure equilibria, as well as to non-compact state-dependent action sets, uncommon priors, and non-bounded payoffs; the results also apply to several notions of approximate equilibria.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"113 ","pages":"Article 103012"},"PeriodicalIF":1.3,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304406824000727/pdfft?md5=871b6f52ebb8ac7e3357e6bcee15c1db&pid=1-s2.0-S0304406824000727-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141297846","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}
Alain Chateauneuf , José Heleno Faro , Jean-Marc Tallon , Vassili Vergopoulos
{"title":"Alpha-maxmin as an aggregation of two selves","authors":"Alain Chateauneuf , José Heleno Faro , Jean-Marc Tallon , Vassili Vergopoulos","doi":"10.1016/j.jmateco.2024.103006","DOIUrl":"https://doi.org/10.1016/j.jmateco.2024.103006","url":null,"abstract":"<div><p>This paper offers a novel perspective on the <span><math><mi>α</mi></math></span>-maxmin model, taking its components as originating from distinct selves within the decision maker. Drawing from the notion of multiple selves prevalent in inter-temporal decision-making contexts, we present an aggregation approach where each self possesses its own preference relation. Contrary to existing interpretations, these selves are not merely a means to interpret the decision maker’s overall utility function but are considered as primitives. Through consistency requirements, we derive an <span><math><mi>α</mi></math></span>-maxmin representation as an outcome of a convex combination of the preferences of two distinct selves. We first explore a setting involving objective information and then move on to a fully subjective derivation.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"113 ","pages":"Article 103006"},"PeriodicalIF":1.3,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141324223","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}
{"title":"NPV, IRR, PI, PP, and DPP: A unified view","authors":"Mikhail V. Sokolov","doi":"10.1016/j.jmateco.2024.102992","DOIUrl":"10.1016/j.jmateco.2024.102992","url":null,"abstract":"<div><p>This paper introduces a class of investment project's profitability metrics that includes the net present value (NPV) criterion (which labels a project as weakly profitable if its NPV is nonnegative), internal rate of return (IRR), profitability index (PI), payback period (PP), and discounted payback period (DPP) as special cases. We develop an axiomatic characterization of this class, as well as of the mentioned conventional metrics within the class. The proposed approach offers several key contributions. First, it provides a unified interpretation of profitability metrics as indicators of a project's financial stability across various economic scenarios. Second, it reveals that, except for the NPV criterion, a profitability metric is inherently undefined for some projects. In particular, this implies that any extension of IRR to the space of all projects does not meet a set of reasonable conditions. A similar conclusion is valid for the other mentioned conventional metrics. For each of these metrics, we offer a characterization of the pairs of comparable projects and identify the largest set of projects to which the metric can be unequivocally extended. Third, our study identifies conditions under which the application of one metric is superior to others, helping to guide decision-makers in selecting the most appropriate metric for specific investment contexts.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"114 ","pages":"Article 102992"},"PeriodicalIF":1.0,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141868737","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}
{"title":"Globally and universally convergent price adjustment processes","authors":"P. Jean-Jacques Herings","doi":"10.1016/j.jmateco.2024.103007","DOIUrl":"https://doi.org/10.1016/j.jmateco.2024.103007","url":null,"abstract":"<div><p>We discuss three processes of price adjustment in an exchange economy, proposed by Smale (1976), van der Laan and Talman (1987), and Kamiya (1990), respectively. Under a regularity condition on the economy, the first process is guaranteed to converge to a competitive equilibrium for almost every initial price system such that one of the prices is equal to zero. The process of Kamiya (1990) is guaranteed to converge to the set of competitive equilibria for almost every initial price system, under a condition on the boundary behavior of the excess demand function of the economy. The (van der Laan and Talman 1987) process was shown by Herings (1997) to converge to a competitive equilibrium for a generic set of exchange economies for any initial price system. The simplest way to describe these processes is by characterizing the path of prices that they generate. Convergence proofs then rely on results from differential topology and establish that these paths have a manifold structure. The required tools, involving regular constraint sets and manifolds with generalized boundary, are explained in detail and can be fruitfully applied in other domains as well. The paper concludes with an overview of globally and universally convergent processes in other environments like production economies, economies with price rigidities, and game theory.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"113 ","pages":"Article 103007"},"PeriodicalIF":1.3,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304406824000685/pdfft?md5=883c81deeb976bbc333bc3efc8670694&pid=1-s2.0-S0304406824000685-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141324221","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}
{"title":"Multidimensional screening after 37 years","authors":"Jean-Charles Rochet","doi":"10.1016/j.jmateco.2024.103010","DOIUrl":"https://doi.org/10.1016/j.jmateco.2024.103010","url":null,"abstract":"<div><p>This expository article surveys the literature that has followed my paper “A Necessary and Sufficient Condition for Rationalizability in a Quasi-linear Context” that was published in the Journal of Mathematical Economics in 1987.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"113 ","pages":"Article 103010"},"PeriodicalIF":1.3,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304406824000715/pdfft?md5=f26484c585ecbadca0efd2b0b1a81fbc&pid=1-s2.0-S0304406824000715-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141297845","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}
{"title":"Recent advances on uniqueness of competitive equilibrium","authors":"Alexis Akira Toda , Kieran James Walsh","doi":"10.1016/j.jmateco.2024.103008","DOIUrl":"https://doi.org/10.1016/j.jmateco.2024.103008","url":null,"abstract":"<div><p>This article reviews the recent advances in the uniqueness and multiplicity of competitive equilibria in models arising in mathematical economics, finance, macroeconomics, and trade.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"113 ","pages":"Article 103008"},"PeriodicalIF":1.3,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304406824000697/pdfft?md5=e4d7a800d0fe3c4786ccf79a73805637&pid=1-s2.0-S0304406824000697-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141263923","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}
{"title":"Strategic complementarity in games","authors":"Xavier Vives , Orestis Vravosinos","doi":"10.1016/j.jmateco.2024.103005","DOIUrl":"https://doi.org/10.1016/j.jmateco.2024.103005","url":null,"abstract":"<div><p>The lattice-theoretic approach has had a significant impact in all fields of economics, being progressively incorporated into the standard toolbox. This paper presents a selective survey with an emphasis on basic tools, some important results, and applications in industrial organization, dynamic games, games of incomplete information, and mechanism design. Frontier theoretical research employing lattice-theoretic methods continues to be developed in areas such as mean-field games and information design.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"113 ","pages":"Article 103005"},"PeriodicalIF":1.3,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304406824000673/pdfft?md5=fbe2415e2fb9c599b6c12a00abca0e33&pid=1-s2.0-S0304406824000673-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141290351","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}
{"title":"Dynamic games on arbitrary networks with two types of players","authors":"Shan Pei , Ross Cressman , Boyu Zhang","doi":"10.1016/j.jmateco.2024.102990","DOIUrl":"10.1016/j.jmateco.2024.102990","url":null,"abstract":"<div><p>We focus on asymmetric games on networks with two types of players characterized by their different intrinsic preferences. In general, it is NP-hard to calculate a pure strategy Nash equilibrium (PNE) for an asymmetric network game, which makes us difficult to predict the evolutionary outcome. In this paper, we study the asymptotic behavior of the tempered best response dynamics (tBRD). We develop an approximate approach that can transform the tBRD into a system of deterministic ordinary differential equations (ODE) for 2 × 2 asymmetric games with arbitrary payoff values and network structures. This then allows us to evaluate the effect of network structure on the evolutionary outcome without calculating the PNE. We highlight the importance of the network homophily index in the strategy evolution. For games with strategic complements, a lower homophily index promotes coordination. In contrast, games with strategic substitutes have a unique stable equilibrium for a higher homophily index and have two stable equilibria for a low homophily index. Finally, for games with a mixture of strategic complements and strategic substitutes, a lower homophily index in general promote cyclic behaviors and inhibits the existence of stable equilibrium. We then apply our approach to analyze the influence of social networks on the election and discuss the electoral strategies for the majority and minority parties.</p></div>","PeriodicalId":50145,"journal":{"name":"Journal of Mathematical Economics","volume":"113 ","pages":"Article 102990"},"PeriodicalIF":1.3,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304406824000521/pdfft?md5=8bd98aeea9ff742a3b0ddff8aca853eb&pid=1-s2.0-S0304406824000521-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141130658","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}
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