{"title":"Sensitivity of fair prices in assignment markets","authors":"Tamás Solymosi","doi":"10.1016/j.mathsocsci.2023.09.003","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2023.09.003","url":null,"abstract":"<div><p>It is well known that in assignment markets competitive prices always exist, but no price mechanism is strategy-proof for all agents. We investigate the extent a single agent can influence three special competitive price vectors by misreporting his/her reservation values. We provide an exact formula how the minimum, the maximum, and the fair competitive price vectors change, and show that at the fair prices no agent can gain more than half of the deviation from the true values. We also derive the analogous results for the corresponding core payoffs of the associated assignment game via graph-theoretic characterizations of the two side-optimal core payoffs.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"126 ","pages":"Pages 1-12"},"PeriodicalIF":0.6,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50187458","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":"Unrealized arbitrage opportunities in naive equilibria with non-Bayesian belief processes","authors":"Alexander Zimper","doi":"10.1016/j.mathsocsci.2023.07.001","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2023.07.001","url":null,"abstract":"<div><p>A non-Bayesian decision maker forms posterior beliefs through an – ever so slightly – violation of Bayes’ rule. A naive equilibrium is a competitive equilibrium for a multiperiod complete markets economy such that every economic agent – Bayesian or non-Bayesian – assumes that all economic agents are Bayesian decision makers. If all agents are indeed Bayesian decision makers, the naive equilibrium coincides with the standard concept of an arbitrage-free equilibrium for which dynamic price ratios are comprehensively pinned down as the equilibrium price ratios of Arrow–Debreu securities in a static economy. If at least one agent is a non-Bayesian decision maker, however, some equilibrium price ratios will change over time. These changing price ratios imply the existence of unrealized dynamic arbitrage opportunities in a naive equilibrium with non-Bayesian decision makers.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"125 ","pages":"Pages 27-41"},"PeriodicalIF":0.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50190974","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":"When to seek expert advice? A simple model of borrowers with limited liability","authors":"Ratul Das Chaudhury , Sukanta Bhattacharya","doi":"10.1016/j.mathsocsci.2023.05.001","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2023.05.001","url":null,"abstract":"<div><p><span>We model the situation where a borrower can choose to acquire costly information about the outcome before implementing a risky project. The borrower is resource-constrained and faces a trade-off between incurring the cost of information or putting effort into the project. We provide novel insights about the type of project the borrower chooses and identify the conditions under which the borrower acquires information. We characterize the optimality conditions for the </span>interest rate charged by a socially-motivated as well as a profit-motivated lender. We find that if the interest rate is high, the borrower is likely to choose riskier projects and acquire information about the outcome. If capital is moderately expensive for the lender, even the socially-motivated lender charges a higher interest and makes a positive profit. This provides an alternate explanation for the prevalence of high-interest rates in the rural credit market, despite the presence of socially-motivated lenders.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"125 ","pages":"Pages 113-120"},"PeriodicalIF":0.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50191279","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":"Characterization of optimal durations of unemployment benefits in a nonstationary job search model","authors":"Gilles Joseph , Paul-Emile Maingé","doi":"10.1016/j.mathsocsci.2023.07.005","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2023.07.005","url":null,"abstract":"<div><p>This paper studies the optimal duration of unemployment insurance (UI) benefits in a job search model where a risk neutral UI agency cannot monitor the search effort of risk-averse workers. Unemployment assistance benefits for noneligible unemployed are taken as exogenous by the unemployment agency which chooses optimally the constant level of UI benefits, the date of their exhaustion and the constant level of the financing tax. So, due to possible finite values of the duration of unemployment benefits, the resulting agency’s problem involves nonstationarities that appears somewhat difficult to solve from the analytical viewpoint. Based upon the geometric properties of the incentive and budget constraints, we successfully provide two explicit sufficient conditions regarding the parameters of the model for obtaining a positive and finite optimal duration of UI. We then give a theoretical rationale for most unemployment insurance systems.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"125 ","pages":"Pages 76-93"},"PeriodicalIF":0.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50191274","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":"The disclosure decision game: Subsidies and incentives for R&D activity","authors":"Domenico Buccella , Luciano Fanti , Luca Gori","doi":"10.1016/j.mathsocsci.2023.06.002","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2023.06.002","url":null,"abstract":"<div><p>This article presents a three-stage non-cooperative disclosure decision game (DDG), in which R&D-investing firms choose whether to disclose R&D-related information to the rival in a Cournot-like environment. Though firms have no (private) incentive to disclose information unilaterally on their cost-reducing R&D activity to prevent a rival from engaging in free appropriation, this work reveals opportunity for the government to design an optimal policy aimed at incentivising R&D disclosure. Following this welfare-improving path, sharing R&D-related information becomes a Pareto-efficient Nash equilibrium strategy. These findings suggest that using public subsidies to R&D disclosure can lead to a win-win result, eliminating the unpleasant non-disclosing outcome from a societal perspective.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"125 ","pages":"Pages 11-26"},"PeriodicalIF":0.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50190946","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":"Implementing optimal scholarship assignments via backward induction","authors":"Pablo Amorós","doi":"10.1016/j.mathsocsci.2023.06.001","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2023.06.001","url":null,"abstract":"<div><p>A group of students who have applied for scholarships must be ranked. The committee responsible for determining this ranking consists of the students’ advisors. While impartial towards other students, the advisors are biased towards favoring their students. This paper examines the implementation of the deserving ranking via backward induction. Some of the best-known sequential mechanisms utilized in the real world are ineffective. We present two simple and natural sequential mechanisms that prove to be effective. The first mechanism is suitable for when there are precisely three students, and the second is for four or more students.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"125 ","pages":"Pages 1-10"},"PeriodicalIF":0.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50190973","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}
Cuong Le Van , Ngoc-Sang Pham , Thi Kim Cuong Pham
{"title":"Effects of development aid (grants and loans) on the economic dynamics of the recipient country","authors":"Cuong Le Van , Ngoc-Sang Pham , Thi Kim Cuong Pham","doi":"10.1016/j.mathsocsci.2023.06.003","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2023.06.003","url":null,"abstract":"<div><p>This paper investigates the nexus between foreign aid (in both forms: grant and loan), poverty trap, and economic development in a recipient country by using a Solow model<span> with two new ingredients: a development loan and a fixed cost in the production process. The presence of this fixed cost generates a poverty trap. We show that foreign aid may help the country to escape from the poverty trap and converge to a stable steady state in the long run, but only if (i) the country’s characteristics, such as saving rate, initial capital, governance quality, and productivity are good enough, (ii) the fixed cost is relatively low, and (iii) the loan rule is generous enough. We also show that our model with foreign aid has room for endogenous cycles, unlike the standard Solow model.</span></p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"125 ","pages":"Pages 101-112"},"PeriodicalIF":0.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50190947","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":"Experiments versus distributions of posteriors","authors":"Stefan Terstiege , Cédric Wasser","doi":"10.1016/j.mathsocsci.2023.07.003","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2023.07.003","url":null,"abstract":"<div><p>A fundamental result in Bayesian persuasion and information design states that a distribution of posterior beliefs can be induced by an experiment if and only if the posterior beliefs average to the prior belief. We present a general version of this result that applies to infinite state and signal spaces.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"125 ","pages":"Pages 58-60"},"PeriodicalIF":0.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50191277","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":"Proportional resource allocation in dynamic n-player Blotto games","authors":"Nejat Anbarci , Kutay Cingiz , Mehmet S. Ismail","doi":"10.1016/j.mathsocsci.2023.07.002","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2023.07.002","url":null,"abstract":"<div><p>In this note, we introduce a general model of dynamic <span><math><mi>n</mi></math></span>-player multi-battle Blotto contests in which asymmetric resources and non-homogeneous battlefield prizes are possible. Each player’s probability of winning the prize in a battlefield is governed by a ratio-form contest success function and players’ resource allocation on that battlefield. We show that there exists a pure subgame perfect equilibrium in which players allocate their resources in proportion to the battlefield prizes for every history. We also give a sufficient condition that if there are two players and the contest success function is of Tullock type, then the subgame perfect equilibrium is unique.</p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"125 ","pages":"Pages 94-100"},"PeriodicalIF":0.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50190948","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":"When is frugality optimal?","authors":"Bertrand Crettez , Naila Hayek , Georges Zaccour","doi":"10.1016/j.mathsocsci.2023.07.006","DOIUrl":"https://doi.org/10.1016/j.mathsocsci.2023.07.006","url":null,"abstract":"<div><p>We consider an optimal growth model in which the decision maker<span> chooses the consumption path that maximizes her utility over a finite planning horizon. At each instant of time, she can opt for a regular product that pollutes the environment, or a non-polluting frugal product, which procures, however, lower utility. Depending on the parameter values, different optimal paths can materialize, including some where a frugal lifestyle is on the rise, and others where polluting persists during the planning horizon.</span></p></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"125 ","pages":"Pages 65-75"},"PeriodicalIF":0.6,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50191275","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}