This article studies several variants of the location-routing problem using a cooperative game-theoretic framework. The authors derive characteristics in terms of subadditivity, convexity, and non-emptiness of the core. Moreover, for some of the game variants, it is shown that for facility opening costs substantially larger than the costs associated with routing, the core is always non-empty. The theoretical results are supported by numerical experiments aimed at illustrating the properties and deriving insights. Among others, it is observed that, while in general it is not possible to guarantee core allocations, in a huge majority of cases the core is non-empty.
{"title":"Cooperative Game-Theoretic Features of Cost Sharing in Location-Routing","authors":"Ondrej Osicka, M. Guajardo, Thibault van Oost","doi":"10.2139/ssrn.3272182","DOIUrl":"https://doi.org/10.2139/ssrn.3272182","url":null,"abstract":"This article studies several variants of the location-routing problem using a cooperative game-theoretic framework. The authors derive characteristics in terms of subadditivity, convexity, and non-emptiness of the core. Moreover, for some of the game variants, it is shown that for facility opening costs substantially larger than the costs associated with routing, the core is always non-empty. The theoretical results are supported by numerical experiments aimed at illustrating the properties and deriving insights. Among others, it is observed that, while in general it is not possible to guarantee core allocations, in a huge majority of cases the core is non-empty.","PeriodicalId":373527,"journal":{"name":"PSN: Game Theory (Topic)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121186164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present the renegotiable acceptance mechanism in the context of the multi-unit assignment problem. This mechanism combines features of the immediate and deferred acceptance mechanisms and implements the set of stable matchings in both Nash and undominated Nash equilibria under substitutable priorities. In addition, we prove that under slot-specific priorities, the immediate acceptance mechanism also implements the set of stable matchings in Nash and undominated Nash equilibria. Finally, we present modifications of both mechanisms and show that we can dramatically reduce the complexity of the message space when preferences are responsive.
{"title":"Centralized Course Allocation","authors":"Antonio Romero-Medina, M. Triossi","doi":"10.2139/ssrn.3225162","DOIUrl":"https://doi.org/10.2139/ssrn.3225162","url":null,"abstract":"We present the renegotiable acceptance mechanism in the context of the multi-unit assignment problem. This mechanism combines features of the immediate and deferred acceptance mechanisms and implements the set of stable matchings in both Nash and undominated Nash equilibria under substitutable priorities. In addition, we prove that under slot-specific priorities, the immediate acceptance mechanism also implements the set of stable matchings in Nash and undominated Nash equilibria. Finally, we present modifications of both mechanisms and show that we can dramatically reduce the complexity of the message space when preferences are responsive.","PeriodicalId":373527,"journal":{"name":"PSN: Game Theory (Topic)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121408021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a class of stochastic discounted games with increasing preferences. We first prove existence of extremal Stationary Markov Perfect Equilibria (SMPE) in pure strategies, and we characterize those equilibria as unique fixed points of well-chosen operators. We use this characterization to establish a class of monotone comparative results on those extremal equilibria, using an arbitrary parameter space.
{"title":"Monotone Comparative Statics in Stochastic Games With Increasing Preferences","authors":"P. Leoni","doi":"10.2139/ssrn.3167679","DOIUrl":"https://doi.org/10.2139/ssrn.3167679","url":null,"abstract":"We consider a class of stochastic discounted games with increasing preferences. We first prove existence of extremal Stationary Markov Perfect Equilibria (SMPE) in pure strategies, and we characterize those equilibria as unique fixed points of well-chosen operators. We use this characterization to establish a class of monotone comparative results on those extremal equilibria, using an arbitrary parameter space.","PeriodicalId":373527,"journal":{"name":"PSN: Game Theory (Topic)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132951272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Whether or not a given cooperative game with transferable utility is balanced; i.e. possesses a nonempty core, is a central question in the literature. The answer was furnished, independently, by Bondareva (In Vestnik Leningradskii Universitet, in Russian, 13:141–142, 1962) and Shapley (Nav Res Logist Q 14:453–460, 1967), who provided necessary and sufficient conditions in the form of a set of linear inequalities involving the game’s characteristic function. The purpose of this paper is to show how these inequalities arise naturally from the representation of a certain polyhedral cone as the intersection of half spaces. In the course of doing so we also show how each balanced collection of subsets corresponds to the complement of a face of the cone and how the set of coalitional excesses of a game coincides with its set of combination vectors. Finally, we utilize our framework to prove a notable result of Keane (Ph.D. Dissertation, Field of Math, Northwestern University, Evanston) concerning the L1-center of a cooperative game.
{"title":"The Face Lattice of Polyhedral Cones in the Theory of Cooperative Games","authors":"Norman L. Kleinberg","doi":"10.2139/ssrn.3197585","DOIUrl":"https://doi.org/10.2139/ssrn.3197585","url":null,"abstract":"Whether or not a given cooperative game with transferable utility is balanced; i.e. possesses a nonempty core, is a central question in the literature. The answer was furnished, independently, by Bondareva (In Vestnik Leningradskii Universitet, in Russian, 13:141–142, 1962) and Shapley (Nav Res Logist Q 14:453–460, 1967), who provided necessary and sufficient conditions in the form of a set of linear inequalities involving the game’s characteristic function. The purpose of this paper is to show how these inequalities arise naturally from the representation of a certain polyhedral cone as the intersection of half spaces. In the course of doing so we also show how each balanced collection of subsets corresponds to the complement of a face of the cone and how the set of coalitional excesses of a game coincides with its set of combination vectors. Finally, we utilize our framework to prove a notable result of Keane (Ph.D. Dissertation, Field of Math, Northwestern University, Evanston) concerning the L1-center of a cooperative game.","PeriodicalId":373527,"journal":{"name":"PSN: Game Theory (Topic)","volume":"276 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133621474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a monetarily incentivized Dictator Game we expected Dictators’ empathy towards the Recipients to cause more pro-social allocations. Empathy was experimentally induced via a commonly used perspective taking task. Dictators (N = 476) were instructed to split an endowment of 10€ between themselves and an unknown Recipient. They could split the money 8/2 (8€ for Dictator, 2€ for Recipient) or 5/5 (5€ each). Although the empathy manipulation successfully increased Dictators’ feelings of empathy towards the Recipients, Dictators’ decisions on how to split the money were not affected. We had ample statistical power (above .99) to detect a typical social psychology effect (corresponding to r around .20). Other possible determinants of generosity in the Dictator Game should be investigated.
{"title":"Experimentally Induced Empathy Does Not Affect Monetarily Incentivized Dictator Game Behavior","authors":"J. Lönnqvist, G. Walkowitz","doi":"10.2139/ssrn.3140006","DOIUrl":"https://doi.org/10.2139/ssrn.3140006","url":null,"abstract":"In a monetarily incentivized Dictator Game we expected Dictators’ empathy towards the Recipients to cause more pro-social allocations. Empathy was experimentally induced via a commonly used perspective taking task. Dictators (N = 476) were instructed to split an endowment of 10€ between themselves and an unknown Recipient. They could split the money 8/2 (8€ for Dictator, 2€ for Recipient) or 5/5 (5€ each). Although the empathy manipulation successfully increased Dictators’ feelings of empathy towards the Recipients, Dictators’ decisions on how to split the money were not affected. We had ample statistical power (above .99) to detect a typical social psychology effect (corresponding to r around .20). Other possible determinants of generosity in the Dictator Game should be investigated.","PeriodicalId":373527,"journal":{"name":"PSN: Game Theory (Topic)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132259340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For committee or multiwinner elections, the Chamberlin-Courant rule (CCR), which combines the Borda rule and the proportional representation, aims to pick the most representative committee (Chamberlin and Courant, 1983). Chamberlin and Courant (1983) have shown that if the size of the committee to be elected is k = 1 among m ≥ 3 candidates, the CCR is equivalent to the Borda rule; Kamwa and Merlin (2014) claimed that if k = m − 1, the CCR is equivalent to the k-Plurality rule. In this paper, we explore what happens for 1 < k < m − 1 by computing the probability of agreement between the CCR and four k-scoring rules: k-Plurality, k-Borda, k-Negative Plurality and Bloc. Our results show that for committees of at least two members, the CCR usually leads to a committee recommended by the k-Plurality rule. Furthermore, we evaluate the probability of the CCR to select the Condorcet committee a la Gehrlein when it exists. The Condorcet committee a la Gehrlein is a xed size subset of candidates such that every member defeats every non-member in pairwise comparisons. In this matter, our results indicate that the CCR performs less well than the k-Borda rule and the Bloc rule but better than the k-Plurality and the k-Negative Plurality rules.
对于委员会选举或多赢家选举，结合Borda规则和比例代表制的Chamberlin-Courant规则(CCR)旨在选出最具代表性的委员会(Chamberlin and Courant, 1983)。Chamberlin和Courant(1983)表明，如果在m≥3名候选人中，待选举委员会的人数为k = 1，则CCR相当于Borda规则;Kamwa和Merlin(2014)认为，如果k = m−1，则CCR相当于k- plurality规则。在本文中，我们通过计算CCR与四个k评分规则(k-Plurality, k- borda, k- negative Plurality和Bloc)之间一致的概率来探讨1 < k < m−1时会发生什么。我们的研究结果表明，对于至少有两名成员的委员会，CCR通常导致一个由k-Plurality规则推荐的委员会。此外，我们评估了CCR在存在孔多塞委员会时选择孔多塞委员会的概率。孔多塞委员会(Condorcet committee a la Gehrlein)是一个固定大小的候选人子集，这样每个成员都能在两两比较中击败每个非成员。在这个问题上，我们的结果表明，CCR的表现不如k-Borda规则和Bloc规则，但优于k-Plurality规则和k-Negative Plurality规则。
{"title":"The Chamberlin-Courant Rule and the k-Scoring Rules: Agreement and Condorcet Committee Consistency","authors":"Mostapha Diss, Eric Kamwa, A. Tlidi","doi":"10.2139/ssrn.3198184","DOIUrl":"https://doi.org/10.2139/ssrn.3198184","url":null,"abstract":"For committee or multiwinner elections, the Chamberlin-Courant rule (CCR), which combines the Borda rule and the proportional representation, aims to pick the most representative committee (Chamberlin and Courant, 1983). Chamberlin and Courant (1983) have shown that if the size of the committee to be elected is k = 1 among m ≥ 3 candidates, the CCR is equivalent to the Borda rule; Kamwa and Merlin (2014) claimed that if k = m − 1, the CCR is equivalent to the k-Plurality rule. In this paper, we explore what happens for 1 < k < m − 1 by computing the probability of agreement between the CCR and four k-scoring rules: k-Plurality, k-Borda, k-Negative Plurality and Bloc. Our results show that for committees of at least two members, the CCR usually leads to a committee recommended by the k-Plurality rule. Furthermore, we evaluate the probability of the CCR to select the Condorcet committee a la Gehrlein when it exists. The Condorcet committee a la Gehrlein is a xed size subset of candidates such that every member defeats every non-member in pairwise comparisons. In this matter, our results indicate that the CCR performs less well than the k-Borda rule and the Bloc rule but better than the k-Plurality and the k-Negative Plurality rules.","PeriodicalId":373527,"journal":{"name":"PSN: Game Theory (Topic)","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125241976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Shapley value is arguably the most well-known solution concept for cooperative, transferable utility games. In this Note we show, in contrast to its many marginal characterizations, that the Shapley value can also be viewed as a solution based on average productivity. Specifically, we show that the Shapley value can be axiomatized by means of symmetry, efficiency and a property we call coalition size neutrality. This property requires, roughly, that the payoff to each player depend only on that player’s overall relative average productivity and not on how that productivity is distributed over coalition size. In addition, we observe how a weakened version of coalition size neutrality may be used to characterize the vector space of all linear combinations of the Shapley value and the well-known equal division solution.
{"title":"The Shapley Value, Average Productivity Differentials, and Coalition Size","authors":"Norman L. Kleinberg","doi":"10.2139/ssrn.3197584","DOIUrl":"https://doi.org/10.2139/ssrn.3197584","url":null,"abstract":"The Shapley value is arguably the most well-known solution concept for cooperative, transferable utility games. In this Note we show, in contrast to its many marginal characterizations, that the Shapley value can also be viewed as a solution based on average productivity. Specifically, we show that the Shapley value can be axiomatized by means of symmetry, efficiency and a property we call coalition size neutrality. This property requires, roughly, that the payoff to each player depend only on that player’s overall relative average productivity and not on how that productivity is distributed over coalition size. In addition, we observe how a weakened version of coalition size neutrality may be used to characterize the vector space of all linear combinations of the Shapley value and the well-known equal division solution.","PeriodicalId":373527,"journal":{"name":"PSN: Game Theory (Topic)","volume":"152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116775716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Informational asymmetries have long been recognized as one of the causes of wasteful conflicts. Signaling has been found to be an effective tool for interested parties to truthfully communicate private information. Can signaling help reduce the risk of conflict? I study this question in a model in which a Sender sends a signal about his privately known cost of conflict, a Receiver makes an offer, and the Sender decides whether or not to start a conflict. I find that when the outcomes of a conflict do not depend on previous actions such as wars where the winner gains the disputed territory, signaling does not permit any information transmission. In turn, when the outcomes of a conflict depends on the Receiver's offer, signaling can help avoid war, but only under specific conditions. In all cases, the shadow of conflict looms large and renders signaling totally or relatively ineffective in preventing conflict.
{"title":"Signaling in the Shadow of Conflict","authors":"Stephane Wolton","doi":"10.2139/ssrn.3100989","DOIUrl":"https://doi.org/10.2139/ssrn.3100989","url":null,"abstract":"Informational asymmetries have long been recognized as one of the causes of wasteful conflicts. Signaling has been found to be an effective tool for interested parties to truthfully communicate private information. Can signaling help reduce the risk of conflict? I study this question in a model in which a Sender sends a signal about his privately known cost of conflict, a Receiver makes an offer, and the Sender decides whether or not to start a conflict. I find that when the outcomes of a conflict do not depend on previous actions such as wars where the winner gains the disputed territory, signaling does not permit any information transmission. In turn, when the outcomes of a conflict depends on the Receiver's offer, signaling can help avoid war, but only under specific conditions. In all cases, the shadow of conflict looms large and renders signaling totally or relatively ineffective in preventing conflict.","PeriodicalId":373527,"journal":{"name":"PSN: Game Theory (Topic)","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122505589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study competing mechanism games in which principals simultaneously design contracts to deal with several agents. We show that principals can profit from privately communicating with agents by generating incomplete information in the continuation game they play. Specifically, we construct an example of a complete information game in which none of the (multiple) equilibria in Yamashita (2010) survives against unilateral deviations to mechanisms involving private communication. This also contrasts with the robustness result established by Han (2007). The role of private communication we document may call for extending the standard construction of Epstein and Peters (1999) to incorporate this additional element.
{"title":"On Private Communication in Competing Mechanism Games","authors":"A. Attar, E. Campioni, Gwenaël Piaser","doi":"10.2139/ssrn.3088701","DOIUrl":"https://doi.org/10.2139/ssrn.3088701","url":null,"abstract":"We study competing mechanism games in which principals simultaneously design contracts to deal with several agents. We show that principals can profit from privately communicating with agents by generating incomplete information in the continuation game they play. Specifically, we construct an example of a complete information game in which none of the (multiple) equilibria in Yamashita (2010) survives against unilateral deviations to mechanisms involving private communication. This also contrasts with the robustness result established by Han (2007). The role of private communication we document may call for extending the standard construction of Epstein and Peters (1999) to incorporate this additional element.","PeriodicalId":373527,"journal":{"name":"PSN: Game Theory (Topic)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126466335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We provide an equilibrium analysis of the efficiency properties of bilateral tariff negotiations in a three-country, two-good general equilibrium model of international trade when transfers are not feasible. We consider "weak-rules" settings characterized by two cases: a no-rules case in which discriminatory tariffs are allowed, and an MFN-only case in which negotiated tariffs must be non-discriminatory (i.e., satisfy the MFN rule). We allow for a general family of political-economic country welfare functions and assess efficiency relative to these welfare functions. For the no-rules case with discriminatory tariffs, we consider simultaneous bilateral tariff negotiations and utilize the "Nash-in-Nash" solution concept of Horn and Wolinsky (1988). We establish a sense in which the resulting tariffs are inefficient and too low, so that excessive liberalization occurs from the perspective of the three countries. In the MFN-only case, we consider negotiations between two countries that are "principal suppliers" to each other and employ the Nash bargaining solution concept. Different possibilities arise. For one important situation, we establish a sense in which the resulting tariffs are inefficient and too high when evaluated relative to the unrestricted set of efficient tariffs. We also compare the negotiated tariffs under the MFN rule with the MFN-constrained efficiency frontier, finding that the negotiated tariffs are generically inefficient relative to this frontier and may lead to too little or too much liberalization. Finally, we illustrate our findings with a numerical analysis of a particular representation of the model as an endowment economy with Cobb-Douglas preferences and under the assumption that each government maximizes the indirect utility of the representative agent in its country.
{"title":"\"Nash-in-Nash\" Tariff Bargaining with and Without MFN","authors":"K. Bagwell, R. Staiger, Ali Yurukoglu","doi":"10.3386/w23894","DOIUrl":"https://doi.org/10.3386/w23894","url":null,"abstract":"We provide an equilibrium analysis of the efficiency properties of bilateral tariff negotiations in a three-country, two-good general equilibrium model of international trade when transfers are not feasible. We consider \"weak-rules\" settings characterized by two cases: a no-rules case in which discriminatory tariffs are allowed, and an MFN-only case in which negotiated tariffs must be non-discriminatory (i.e., satisfy the MFN rule). We allow for a general family of political-economic country welfare functions and assess efficiency relative to these welfare functions. For the no-rules case with discriminatory tariffs, we consider simultaneous bilateral tariff negotiations and utilize the \"Nash-in-Nash\" solution concept of Horn and Wolinsky (1988). We establish a sense in which the resulting tariffs are inefficient and too low, so that excessive liberalization occurs from the perspective of the three countries. In the MFN-only case, we consider negotiations between two countries that are \"principal suppliers\" to each other and employ the Nash bargaining solution concept. Different possibilities arise. For one important situation, we establish a sense in which the resulting tariffs are inefficient and too high when evaluated relative to the unrestricted set of efficient tariffs. We also compare the negotiated tariffs under the MFN rule with the MFN-constrained efficiency frontier, finding that the negotiated tariffs are generically inefficient relative to this frontier and may lead to too little or too much liberalization. Finally, we illustrate our findings with a numerical analysis of a particular representation of the model as an endowment economy with Cobb-Douglas preferences and under the assumption that each government maximizes the indirect utility of the representative agent in its country.","PeriodicalId":373527,"journal":{"name":"PSN: Game Theory (Topic)","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130901768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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