Pub Date : 2026-03-01Epub Date: 2026-02-17DOI: 10.1016/j.mathsocsci.2026.102516
Daniele Caliari , Davide Carpentiere
In this paper, we provide a constructive proof for threshold representations of partial orderings in a finite setting and extend the construction to arbitrary sets. This contributes to a long-standing open problem posed in Nakamura (2002) and Aleskerov et al. (2007). We identify and discuss aspects of our proof that do not directly generalize to an infinite setting and, for each, provide intuitive sufficient conditions.
{"title":"On the threshold representation of partial orderings","authors":"Daniele Caliari , Davide Carpentiere","doi":"10.1016/j.mathsocsci.2026.102516","DOIUrl":"10.1016/j.mathsocsci.2026.102516","url":null,"abstract":"<div><div>In this paper, we provide a constructive proof for threshold representations of partial orderings in a finite setting and extend the construction to arbitrary sets. This contributes to a long-standing open problem posed in Nakamura (2002) and Aleskerov et al. (2007). We identify and discuss aspects of our proof that do not directly generalize to an infinite setting and, for each, provide intuitive sufficient conditions.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102516"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147397470","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 : 2026-03-01Epub Date: 2025-12-30DOI: 10.1016/j.mathsocsci.2025.102493
Urs Schweizer
In this paper, a game-theoretic setting with transferable utility serves to explore the scope of damages rules for internalizing multidirectional external effects. From the legal perspective, damages rules aim at compensating victims for the wrongdoing of others (compensation requirement). Yet, to be held liable, it must be an agent’s wrongdoing that has caused harm to the victim (causation requirement). The two requirements can be at conflict when causation is meant in the sense of the but-for test. The paper proposes a causation test that resolves this conflict quite generally. It combines the legal idea of the NESS test with the Shapley value of a suitable characteristic function. The resulting damages rules fully internalize externalities even if they are of multidirectional nature.
{"title":"The conceivable scope of negligence rules for internalizing multidirectional externalities","authors":"Urs Schweizer","doi":"10.1016/j.mathsocsci.2025.102493","DOIUrl":"10.1016/j.mathsocsci.2025.102493","url":null,"abstract":"<div><div>In this paper, a game-theoretic setting with transferable utility serves to explore the scope of damages rules for internalizing multidirectional external effects. From the legal perspective, damages rules aim at compensating victims for the wrongdoing of others (compensation requirement). Yet, to be held liable, it must be an agent’s wrongdoing that has caused harm to the victim (causation requirement). The two requirements can be at conflict when causation is meant in the sense of the but-for test. The paper proposes a causation test that resolves this conflict quite generally. It combines the legal idea of the NESS test with the Shapley value of a suitable characteristic function. The resulting damages rules fully internalize externalities even if they are of multidirectional nature.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102493"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886247","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 : 2026-03-01Epub Date: 2026-01-08DOI: 10.1016/j.mathsocsci.2026.102502
Shohei Yanagita
This paper characterizes a simple model of belief updating in response to recommendations from black boxes, recommenders whose information-generating processes are complex and opaque. In particular, we focus on two types of reactions to recommendations. The first is a skeptical response, in which individuals receive recommendations that are highly inconsistent with their prior beliefs and respond skeptically by updating their beliefs conservatively. The second is a credulous response, in which individuals readily accept recommendations that are aligned with their prior beliefs. These two contrasting reactions are jointly captured under the resulting updating rule.
{"title":"Skeptical and credulous belief updating under black box recommendations","authors":"Shohei Yanagita","doi":"10.1016/j.mathsocsci.2026.102502","DOIUrl":"10.1016/j.mathsocsci.2026.102502","url":null,"abstract":"<div><div>This paper characterizes a simple model of belief updating in response to recommendations from black boxes, recommenders whose information-generating processes are complex and opaque. In particular, we focus on two types of reactions to recommendations. The first is a skeptical response, in which individuals receive recommendations that are highly inconsistent with their prior beliefs and respond skeptically by updating their beliefs conservatively. The second is a credulous response, in which individuals readily accept recommendations that are aligned with their prior beliefs. These two contrasting reactions are jointly captured under the resulting updating rule.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102502"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940473","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 : 2026-03-01Epub Date: 2026-01-16DOI: 10.1016/j.mathsocsci.2026.102507
Gonzalo F. de-Córdoba , Gonzalo Galiano
This paper develops the concept of poverty core, a novel framework that extends the traditional notion of poverty traps by incorporating the dynamics of irreversibility and complete capital depletion. While poverty traps describe self-reinforcing cycles of deprivation that hinder economic mobility, a poverty core emerges when an already vulnerable system experiences a random exogenous shock—such as a natural disaster, armed conflict, financial collapse, or health crisis—that destroys natural, physical, and human capital beyond the threshold required for recovery. Unlike poverty traps, which may be escaped through gradual investment or policy intervention, a poverty core represents an absorbing state of destitution where normal economic mechanisms are no longer sufficient to restore livelihoods.
To formally model the transition from poverty traps to poverty cores, we extend the Solow growth framework by incorporating divergence operators and introducing a nonlinear depreciation function that accounts for capital depletion under extreme shocks. This modification captures how spatial and structural economic vulnerabilities amplify depreciation rates beyond sustainable levels, leading to economic divergence instead of convergence. The model demonstrates that under specific conditions—where capital loss surpasses a critical threshold—economic collapse becomes irreversible, mathematically distinguishing poverty cores from conventional poverty traps.
Our findings contribute to the literature on economic fragility, disaster-induced poverty, and sustainability by providing a new theoretical and mathematical framework to identify cases where poverty becomes irreversible. Recognizing poverty cores as distinct from traditional traps is essential for designing effective interventions in post-shock environments, ensuring that affected communities are not left in perpetual economic collapse.
{"title":"Geographical poverty core formation in a spatial Solow growth model","authors":"Gonzalo F. de-Córdoba , Gonzalo Galiano","doi":"10.1016/j.mathsocsci.2026.102507","DOIUrl":"10.1016/j.mathsocsci.2026.102507","url":null,"abstract":"<div><div>This paper develops the concept of poverty core, a novel framework that extends the traditional notion of poverty traps by incorporating the dynamics of irreversibility and complete capital depletion. While poverty traps describe self-reinforcing cycles of deprivation that hinder economic mobility, a poverty core emerges when an already vulnerable system experiences a random exogenous shock—such as a natural disaster, armed conflict, financial collapse, or health crisis—that destroys natural, physical, and human capital beyond the threshold required for recovery. Unlike poverty traps, which may be escaped through gradual investment or policy intervention, a poverty core represents an absorbing state of destitution where normal economic mechanisms are no longer sufficient to restore livelihoods.</div><div>To formally model the transition from poverty traps to poverty cores, we extend the Solow growth framework by incorporating divergence operators and introducing a nonlinear depreciation function that accounts for capital depletion under extreme shocks. This modification captures how spatial and structural economic vulnerabilities amplify depreciation rates beyond sustainable levels, leading to economic divergence instead of convergence. The model demonstrates that under specific conditions—where capital loss surpasses a critical threshold—economic collapse becomes irreversible, mathematically distinguishing poverty cores from conventional poverty traps.</div><div>Our findings contribute to the literature on economic fragility, disaster-induced poverty, and sustainability by providing a new theoretical and mathematical framework to identify cases where poverty becomes irreversible. Recognizing poverty cores as distinct from traditional traps is essential for designing effective interventions in post-shock environments, ensuring that affected communities are not left in perpetual economic collapse.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102507"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979661","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 : 2026-03-01Epub Date: 2026-01-08DOI: 10.1016/j.mathsocsci.2026.102503
Hirokazu Sakane
Although it is extremely rare for real markets to adjust excess demand through the Walrasian tâtonnement, the standard in market adjustment theory, it is also true that excess demand is eventually eliminated. This gap suggests that some other factors, besides the price mechanism, contribute to adjusting excess demand. We hypothesize that consumers and firms, and therefore excess demand, spill over into neighboring markets in response to price differences that arise between markets. This motion must contribute to ameliorating excess demand. It is rational for some consumers (firms) to shift to markets where the prices of commodities are lower (higher) if price differences arise beyond those due to the characteristics of the commodities. Furthermore, excess demand fluctuates depending on the actions of consumers and firms. Thus, we study an economy in which excess demand advects and diffuses owing to price gradients. The application of partial differential equations is appropriate for this type of analysis.
Specifically, we model market price adjustment and the way consumers and firms respond by shifting toward other markets, thus causing excess demand to spill over and disperse. We represent these flows as advection and diffusion driven by price gradients and formalize their dynamics using partial differential equations. We prove that the competitive equilibrium price is locally and exponentially stable under certain conditions.
{"title":"Market adjustment with advection and diffusion in excess demand","authors":"Hirokazu Sakane","doi":"10.1016/j.mathsocsci.2026.102503","DOIUrl":"10.1016/j.mathsocsci.2026.102503","url":null,"abstract":"<div><div>Although it is extremely rare for real markets to adjust excess demand through the Walrasian tâtonnement, the standard in market adjustment theory, it is also true that excess demand is eventually eliminated. This gap suggests that some other factors, besides the price mechanism, contribute to adjusting excess demand. We hypothesize that consumers and firms, and therefore excess demand, spill over into neighboring markets in response to price differences that arise between markets. This motion must contribute to ameliorating excess demand. It is rational for some consumers (firms) to shift to markets where the prices of commodities are lower (higher) if price differences arise beyond those due to the characteristics of the commodities. Furthermore, excess demand fluctuates depending on the actions of consumers and firms. Thus, we study an economy in which excess demand advects and diffuses owing to price gradients. The application of partial differential equations is appropriate for this type of analysis.</div><div>Specifically, we model market price adjustment and the way consumers and firms respond by shifting toward other markets, thus causing excess demand to spill over and disperse. We represent these flows as advection and diffusion driven by price gradients and formalize their dynamics using partial differential equations. We prove that the competitive equilibrium price is locally and exponentially stable under certain conditions.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102503"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979658","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 : 2026-03-01Epub Date: 2026-01-29DOI: 10.1016/j.mathsocsci.2026.102510
Takaaki Abe
This paper investigates fairness principles in cooperative games with communication graphs. We show that several axioms – fairness for neighbors (Béal et al., 2012), splitting (Casajus, 2009), and a new axiom called gap preservation – are equivalent. Moreover, we show that fairness for neighbors, combined with either component efficiency or a weaker locality condition, guarantees the existence of a pairwise stable communication graph.
{"title":"From neighbors to components: The equivalence of fairness for neighbors and gap preservation","authors":"Takaaki Abe","doi":"10.1016/j.mathsocsci.2026.102510","DOIUrl":"10.1016/j.mathsocsci.2026.102510","url":null,"abstract":"<div><div>This paper investigates fairness principles in cooperative games with communication graphs. We show that several axioms – fairness for neighbors (Béal et al., 2012), splitting (Casajus, 2009), and a new axiom called gap preservation – are equivalent. Moreover, we show that fairness for neighbors, combined with either component efficiency or a weaker locality condition, guarantees the existence of a pairwise stable communication graph.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102510"},"PeriodicalIF":0.7,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078326","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 : 2026-01-01Epub Date: 2025-12-03DOI: 10.1016/j.mathsocsci.2025.102489
Yassine Badra , Bertrand Chopard , Huizhong Liu
This paper examines the strategic implications of research joint ventures (RJVs) in an oligopolistic setting with R&D spillovers, focusing on their impact on social welfare. Using the well-known R&D model of d’Aspremont–Jacquemin (AJ), we analyze different R&D cooperation structures: the non-cooperative regime, the R&D cartel regime, the cartelized RJV, and the non-cooperative RJV. Our findings challenge conventional views on the efficiency of RJVs. While the model of Kamien–Muller–Zang (KMZ) consistently predicts that RJVs lead to lower social welfare, we show that in the AJ framework, an RJV can outperform both the standard non-cooperative and cartel regimes when spillovers remain below a certain threshold. This result underscores the importance of model-specific assumptions in assessing R&D cooperation policies and offers valuable insights for industrial policy and antitrust regulation in innovation-driven markets.
{"title":"R&D cooperation and spillovers: When do research joint ventures improve welfare?","authors":"Yassine Badra , Bertrand Chopard , Huizhong Liu","doi":"10.1016/j.mathsocsci.2025.102489","DOIUrl":"10.1016/j.mathsocsci.2025.102489","url":null,"abstract":"<div><div>This paper examines the strategic implications of research joint ventures (RJVs) in an oligopolistic setting with R&D spillovers, focusing on their impact on social welfare. Using the well-known R&D model of d’Aspremont–Jacquemin (AJ), we analyze different R&D cooperation structures: the non-cooperative regime, the R&D cartel regime, the cartelized RJV, and the non-cooperative RJV. Our findings challenge conventional views on the efficiency of RJVs. While the model of Kamien–Muller–Zang (KMZ) consistently predicts that RJVs lead to lower social welfare, we show that in the AJ framework, an RJV can outperform both the standard non-cooperative and cartel regimes when spillovers remain below a certain threshold. This result underscores the importance of model-specific assumptions in assessing R&D cooperation policies and offers valuable insights for industrial policy and antitrust regulation in innovation-driven markets.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"139 ","pages":"Article 102489"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145748444","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 : 2026-01-01Epub Date: 2025-11-21DOI: 10.1016/j.mathsocsci.2025.102477
Noëmi Jacober, Luís Santos-Pinto
In many competitive settings, players must decide not only how hard to work but also how much risk to take. This paper shows that overconfidence—the tendency to overestimate one’s own ability—can lead to surprising strategic behavior in tournaments in which players make both risk and effort choices. We find two key results. First, overconfident players may adopt less risky strategies than rational ones, defying the common belief that overconfidence necessarily drives risk-taking. Second, when overconfident players adopt less risky strategies, they may exert greater effort, revealing a new mechanism by which overconfidence can enhance effort provision.
{"title":"Less risk, more effort: How overconfidence reshapes tournament strategies","authors":"Noëmi Jacober, Luís Santos-Pinto","doi":"10.1016/j.mathsocsci.2025.102477","DOIUrl":"10.1016/j.mathsocsci.2025.102477","url":null,"abstract":"<div><div>In many competitive settings, players must decide not only how hard to work but also how much risk to take. This paper shows that overconfidence—the tendency to overestimate one’s own ability—can lead to surprising strategic behavior in tournaments in which players make both risk and effort choices. We find two key results. First, overconfident players may adopt less risky strategies than rational ones, defying the common belief that overconfidence necessarily drives risk-taking. Second, when overconfident players adopt less risky strategies, they may exert greater effort, revealing a new mechanism by which overconfidence can enhance effort provision.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"139 ","pages":"Article 102477"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580298","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 : 2026-01-01Epub Date: 2025-12-03DOI: 10.1016/j.mathsocsci.2025.102488
Frederik Van De Putte, Stefan Wintein
Claim-strength problems are a distinctive class of allocation problems in which the currency of claims is different from that of the estate that is to be divided. We study mixtures (i.e. convex combinations) of three basic allocation rules for claim-strength problems: the proportional rule, the uniform allocation rule, and the plurality allocation rule. We observe that any such mixture satisfies a generalized transfer axiom in addition to a number of invariance properties. We establish a fundamental representation theorem: taken jointly, these axioms fully characterize the class of all mixtures of the three base rules. This result is tight. From it, we derive characterizations of more specific classes and the three basic rules themselves. We moreover show that within the class of mixtures, the only three rules that satisfy a familiar consistency axiom are the base rules.
{"title":"Claim-strength problems and mixtures: An axiomatic study","authors":"Frederik Van De Putte, Stefan Wintein","doi":"10.1016/j.mathsocsci.2025.102488","DOIUrl":"10.1016/j.mathsocsci.2025.102488","url":null,"abstract":"<div><div>Claim-strength problems are a distinctive class of allocation problems in which the currency of claims is different from that of the estate that is to be divided. We study mixtures (i.e. convex combinations) of three basic allocation rules for claim-strength problems: the proportional rule, the uniform allocation rule, and the plurality allocation rule. We observe that any such mixture satisfies a generalized <em>transfer</em> axiom in addition to a number of <em>invariance</em> properties. We establish a fundamental representation theorem: taken jointly, these axioms fully characterize the class of all mixtures of the three base rules. This result is tight. From it, we derive characterizations of more specific classes and the three basic rules themselves. We moreover show that within the class of mixtures, the only three rules that satisfy a familiar <em>consistency</em> axiom are the base rules.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"139 ","pages":"Article 102488"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694045","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 : 2026-01-01Epub Date: 2025-12-06DOI: 10.1016/j.mathsocsci.2025.102491
Doron Klunover
We consider a lottery contest between n risk-neutral symmetric players, who compete for a prize with a common value. Prior to exerting effort, each player chooses between an old technology, in which return on effort is certain, and a new technology, in which return on effort is uncertain but on average is equal to the return on effort in the old technology. We characterize symmetric and asymmetric equilibria and show that in equilibrium the new technology is adopted by a proper subset of the players. The results offer an explanation for endogenous emergence of asymmetric technologies in contests.
{"title":"Endogenous technology choice in contests","authors":"Doron Klunover","doi":"10.1016/j.mathsocsci.2025.102491","DOIUrl":"10.1016/j.mathsocsci.2025.102491","url":null,"abstract":"<div><div>We consider a lottery contest between <em>n</em> risk-neutral symmetric players, who compete for a prize with a common value. Prior to exerting effort, each player chooses between an old technology, in which return on effort is certain, and a new technology, in which return on effort is uncertain but on average is equal to the return on effort in the old technology. We characterize symmetric and asymmetric equilibria and show that in equilibrium the new technology is adopted by a proper subset of the players. The results offer an explanation for endogenous emergence of asymmetric technologies in contests.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"139 ","pages":"Article 102491"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145748443","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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