The Ultimatum Game is conventionally formulated in the context of two players. Nonetheless, real-life scenarios often entail community interactions among numerous individuals. To address this, we introduce an extended version of the Ultimatum Game, called the Multi-Proposer-Multi-Responder Ultimatum Game. In this model, multiple responders and proposers simultaneously interact in a one-shot game, introducing competition both within proposers and within responders. We derive subgame-perfect Nash equilibria for all scenarios and explore how these non-trivial values might provide insight into proposal and rejection behavior experimentally observed in the context of one vs. one Ultimatum Game scenarios. Additionally, by considering the asymptotic numbers of players, we propose two potential estimates for a "fair" threshold: either 31.8% or 36.8% of the pie (share) for the responder.
{"title":"Fairness in Multi-Proposer-Multi-Responder Ultimatum Game","authors":"Hana Krakovská, Rudolf Hanel, Mark Broom","doi":"arxiv-2408.02410","DOIUrl":"https://doi.org/arxiv-2408.02410","url":null,"abstract":"The Ultimatum Game is conventionally formulated in the context of two\u0000players. Nonetheless, real-life scenarios often entail community interactions\u0000among numerous individuals. To address this, we introduce an extended version\u0000of the Ultimatum Game, called the Multi-Proposer-Multi-Responder Ultimatum\u0000Game. In this model, multiple responders and proposers simultaneously interact\u0000in a one-shot game, introducing competition both within proposers and within\u0000responders. We derive subgame-perfect Nash equilibria for all scenarios and\u0000explore how these non-trivial values might provide insight into proposal and\u0000rejection behavior experimentally observed in the context of one vs. one\u0000Ultimatum Game scenarios. Additionally, by considering the asymptotic numbers\u0000of players, we propose two potential estimates for a \"fair\" threshold: either\u000031.8% or 36.8% of the pie (share) for the responder.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968817","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 solve the two-player bargaining problem using Weber's law in psychophysics, which is applied to the perception of utility changes. By applying this law, one of the players (or both of them) defines lower and upper utility thresholds, such that once the lower threshold is established, bargaining continues in the inter-threshold domain where the solutions are acceptable to both parties. This provides a sequential solution to the bargaining problem, and it can be implemented iteratively reaching well-defined outcomes. The solution is Pareto-optimal, symmetric, and is invariant to affine-transformations of utilities. For susceptible players, iterations are unnecessary, so they converge in one stage toward the (axiomatic) Nash solution of the bargaining problem. This situation also accounts for the asymmetric Nash solution, where the weights of each player are expressed via their Weber constants. Thus the Nash solution is reached without external arbiters and without requiring the independence of irrelevant alternatives. For non-susceptible players our approach leads to different results.
{"title":"Bargaining via Weber's law","authors":"V. G. Bardakhchyan, A. E. Allahverdyan","doi":"arxiv-2408.02492","DOIUrl":"https://doi.org/arxiv-2408.02492","url":null,"abstract":"We solve the two-player bargaining problem using Weber's law in\u0000psychophysics, which is applied to the perception of utility changes. By\u0000applying this law, one of the players (or both of them) defines lower and upper\u0000utility thresholds, such that once the lower threshold is established,\u0000bargaining continues in the inter-threshold domain where the solutions are\u0000acceptable to both parties. This provides a sequential solution to the\u0000bargaining problem, and it can be implemented iteratively reaching well-defined\u0000outcomes. The solution is Pareto-optimal, symmetric, and is invariant to\u0000affine-transformations of utilities. For susceptible players, iterations are\u0000unnecessary, so they converge in one stage toward the (axiomatic) Nash solution\u0000of the bargaining problem. This situation also accounts for the asymmetric Nash\u0000solution, where the weights of each player are expressed via their Weber\u0000constants. Thus the Nash solution is reached without external arbiters and\u0000without requiring the independence of irrelevant alternatives. For\u0000non-susceptible players our approach leads to different results.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933573","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 credibility theory was introduced by B. Liu as a new way to describe the fuzzy uncertainty. The credibility measure is the fundamental notion of the credibility theory. Recently, L.Yang and K. Iwamura extended the credibility measure by defining the parametric measure $m_{lambda}$ ($lambda$ is a real parameter in the interval $[0,1]$ and for $lambda= 1/2$ we obtain as a particular case the notion of credibility measure). By using the $m_{lambda}$-measure, we studied in this paper a risk neutral multi-item inventory problem. Our construction generalizes the credibilistic inventory model developed by Y. Li and Y. Liu in 2019. In our model, the components of demand vector are fuzzy variables and the maximization problem is formulated by using the notion of $m_{lambda}$-expected value. We shall prove a general formula for the solution of optimization problem, from which we obtained effective formulas for computing the optimal solutions in the particular cases where the demands are trapezoidal and triangular fuzzy numbers. For $lambda=1/2$ we obtain as a particular case the computation formulas of the optimal solutions of the credibilistic inventory problem of Li and Liu. These computation formulas are applied for some $m_{lambda}$-models obtained from numerical data.
可信度理论由 B. Liu 提出，是描述模糊不确定性的一种新方法。可信度度量是可信度理论的基本概念。最近，L.Yang 和 K. Iwamura 通过定义参数度量 $m_{lambda}$（$lambda$ 是区间 $[0,1]$ 中的实参数，对于 $lambda=1/2$，我们得到了可信度量的特殊概念）扩展了可信度量。通过使用 $m_{lambda}$ 度量，我们在本文中研究了一个风险中性的多项目库存问题。我们的构造概括了李一和刘一在 2019 年提出的可信库存模型。在我们的模型中，需求向量的分量是模糊变量，最大化问题通过使用 $m_{lambda}$ 预期值的概念来表述。我们将证明优化问题求解的一般公式，并从中获得计算需求为梯形模糊数和三角形模糊数的特殊情况下最优解的有效公式。对于$lambda=1/2$，我们得到了李和刘的可信库存问题最优解的计算公式。这些计算公式适用于从数字数据中得到的一些 $m_{lambda}$ 模型。
{"title":"Inventory problems and the parametric measure $m_λ$","authors":"Irina Georgescu","doi":"arxiv-2408.02700","DOIUrl":"https://doi.org/arxiv-2408.02700","url":null,"abstract":"The credibility theory was introduced by B. Liu as a new way to describe the\u0000fuzzy uncertainty. The credibility measure is the fundamental notion of the\u0000credibility theory. Recently, L.Yang and K. Iwamura extended the credibility\u0000measure by defining the parametric measure $m_{lambda}$ ($lambda$ is a real\u0000parameter in the interval $[0,1]$ and for $lambda= 1/2$ we obtain as a\u0000particular case the notion of credibility measure). By using the\u0000$m_{lambda}$-measure, we studied in this paper a risk neutral multi-item\u0000inventory problem. Our construction generalizes the credibilistic inventory\u0000model developed by Y. Li and Y. Liu in 2019. In our model, the components of\u0000demand vector are fuzzy variables and the maximization problem is formulated by\u0000using the notion of $m_{lambda}$-expected value. We shall prove a general\u0000formula for the solution of optimization problem, from which we obtained\u0000effective formulas for computing the optimal solutions in the particular cases\u0000where the demands are trapezoidal and triangular fuzzy numbers. For\u0000$lambda=1/2$ we obtain as a particular case the computation formulas of the\u0000optimal solutions of the credibilistic inventory problem of Li and Liu. These\u0000computation formulas are applied for some $m_{lambda}$-models obtained from\u0000numerical data.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968815","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}
Existing research has established that autocrats offer concessions to prevent ouster by their inner circle. This paper examines how those concessions are influenced by the relative uncertainty of an autocrat's inner circle about remaining in that favored body. I take as my starting point the formal model of political survival presented in Bueno de Mesquita et al.'s The Logic of Political Survival. I extend the model to account for variation in the relative uncertainty of an autocrat's inner circle. To make the math tractable, I dispense with convention and introduce comparative statics across two models with different formulations of uncertainty. This exercise reveals a set of conditions under which to expect an increase in the concessions offered by an autocrat, with implications for development and democracy. Those findings yield a corresponding set of logical corollaries with potential to further our understanding of authoritarian politics, including an unexamined facet of the "dictator's dilemma" (Wintrobe 1990, 1998) and related incentives for members of an inner circle to permit purges or act to destabilize their ranks. The models also identify a source of policy volatility not found outside of autocracies. Taken together, the findings suggest a need for more research on elite uncertainty in autocracies.
现有研究已经证实，专制者会做出让步，以防止其核心圈子对其施压。本文探讨了这些让步如何受到专制者核心圈子对继续留在该受宠机构的相对不确定性的影响。我以布埃诺-德-梅斯基塔等人（Bueno de Mesquita et al.我对模型进行了扩展，以考虑专制者核心圈子相对不确定性的变化。为了使数学计算变得简单易行，我不拘泥于常规，而是引入了两个对不确定性有不同表述的模型的比较统计。这项工作揭示了一系列条件，在这些条件下，可以预期专制者会增加让步，从而对发展和民主产生影响。这些发现产生了一系列相应的逻辑推论，有可能进一步加深我们对独裁政治的理解，其中包括 "独裁者困境"（Wintrobe，1990 年，1998 年）中未被研究的一个方面，以及内部成员允许清洗或采取行动动摇其队伍的相关动机。这些模型还发现了一个在专制政体之外所没有的政策波动来源。综上所述，研究结果表明，有必要对专制政体中的精英不确定性进行更多研究。
{"title":"The Logic of Political Survival Revisited: Consequences of Elite Uncertainty Under Authoritarian Rule","authors":"Tamar Zeilberger","doi":"arxiv-2408.01887","DOIUrl":"https://doi.org/arxiv-2408.01887","url":null,"abstract":"Existing research has established that autocrats offer concessions to prevent\u0000ouster by their inner circle. This paper examines how those concessions are\u0000influenced by the relative uncertainty of an autocrat's inner circle about\u0000remaining in that favored body. I take as my starting point the formal model of\u0000political survival presented in Bueno de Mesquita et al.'s The Logic of\u0000Political Survival. I extend the model to account for variation in the relative\u0000uncertainty of an autocrat's inner circle. To make the math tractable, I\u0000dispense with convention and introduce comparative statics across two models\u0000with different formulations of uncertainty. This exercise reveals a set of\u0000conditions under which to expect an increase in the concessions offered by an\u0000autocrat, with implications for development and democracy. Those findings yield\u0000a corresponding set of logical corollaries with potential to further our\u0000understanding of authoritarian politics, including an unexamined facet of the\u0000\"dictator's dilemma\" (Wintrobe 1990, 1998) and related incentives for members\u0000of an inner circle to permit purges or act to destabilize their ranks. The\u0000models also identify a source of policy volatility not found outside of\u0000autocracies. Taken together, the findings suggest a need for more research on\u0000elite uncertainty in autocracies.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933581","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}
This study examines strategic issues in fair rank-minimizing mechanisms, which choose an assignment that minimizes the average rank of object types to which agents are assigned and satisfy a fairness property called equal treatment of equals. As one of these fair mechanisms, the uniform rank-minimizing mechanism is considered. We particularly focus on the case where agents can refuse their assignment and obtain the outside option instead. Without the refusal option, if the uniform rank-minimizing mechanism is used, truth-telling is not strategically dominated by any strategies. However, if agents have the option, then an outside option demotion strategy -- revealing all object types as acceptable without changing the ranking of truly acceptable ones -- strategically dominates truth-telling. Moreover, we show that adopting this strategy may lead to inefficient assignments. To counter this, we propose the modified uniform rank-minimizing mechanism, though it may lead agents to strategically reduce the number of acceptable types.
{"title":"Strategic Analysis of Fair Rank-Minimizing Mechanisms with Agent Refusal Option","authors":"Yasunori Okumura","doi":"arxiv-2408.01673","DOIUrl":"https://doi.org/arxiv-2408.01673","url":null,"abstract":"This study examines strategic issues in fair rank-minimizing mechanisms,\u0000which choose an assignment that minimizes the average rank of object types to\u0000which agents are assigned and satisfy a fairness property called equal\u0000treatment of equals. As one of these fair mechanisms, the uniform\u0000rank-minimizing mechanism is considered. We particularly focus on the case\u0000where agents can refuse their assignment and obtain the outside option instead.\u0000Without the refusal option, if the uniform rank-minimizing mechanism is used,\u0000truth-telling is not strategically dominated by any strategies. However, if\u0000agents have the option, then an outside option demotion strategy -- revealing\u0000all object types as acceptable without changing the ranking of truly acceptable\u0000ones -- strategically dominates truth-telling. Moreover, we show that adopting\u0000this strategy may lead to inefficient assignments. To counter this, we propose\u0000the modified uniform rank-minimizing mechanism, though it may lead agents to\u0000strategically reduce the number of acceptable types.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933571","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}
I study the persuasion of a receiver who accesses information only if she exerts costly attention effort. The sender designs an experiment to persuade the receiver to take a specific action. The experiment also affects the receiver's attention effort, that is, the probability that she updates her beliefs. As a result, persuasion has two margins: extensive (effort) and intensive (action). The receiver's utility exhibits a supermodularity property in information and effort. By leveraging this property, I prove a general equivalence between experiments and persuasion mechanisms `a la Kolotilin et al. (2017). Censoring high states is an optimal strategy for the sender in applications.
我研究的是接收者的说服问题，接收者只有付出昂贵的注意力努力才能获取信息。发送者设计了一个实验来说服接收者采取特定行动。实验也会影响接受者的注意努力，即她更新信念的概率。因此，说服有两个边际：广泛（努力）和密集（行动）。接受者的效用在信息和努力方面表现出超模块化特性。通过利用这一特性，我证明了实验与说服机制之间的一般等价性（a la Kolotilin etal.(2017).审查高状态是发送者在应用中的最优策略。
{"title":"Persuading an inattentive and privately informed receiver","authors":"Pietro Dall'Ara","doi":"arxiv-2408.01250","DOIUrl":"https://doi.org/arxiv-2408.01250","url":null,"abstract":"I study the persuasion of a receiver who accesses information only if she\u0000exerts costly attention effort. The sender designs an experiment to persuade\u0000the receiver to take a specific action. The experiment also affects the\u0000receiver's attention effort, that is, the probability that she updates her\u0000beliefs. As a result, persuasion has two margins: extensive (effort) and\u0000intensive (action). The receiver's utility exhibits a supermodularity property\u0000in information and effort. By leveraging this property, I prove a general\u0000equivalence between experiments and persuasion mechanisms `a la Kolotilin et\u0000al. (2017). Censoring high states is an optimal strategy for the sender in\u0000applications.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"189 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933514","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 investigate the choice behavior of a decision maker (DM) who harms herself, by maximizing some distortion of her true preference, in which the first $i$ alternatives are moved to the bottom, in a reversed order. The deterministic declination of our pattern has no empirical power, but it allows to define a degree of self-punishment, which measures the extent of the denial of pleasure adopted by the DM in her decision. We analyze irrational choices that display the lowest degree of self-punishment, and a characterization of them is provided. Moreover, we characterize the choice behavior that exhibits the highest degree of self-punishment, and we show that it comprises almost all choices. We also characterize stochastic self-punishment, which collects all the Random Utility Models (RUMs) whose support is restricted to the harmful distortions of some preference. Full identification of the DM's preference and randomization over its harmful distortions is allowed if each alternative is selected from the ground set with probability greater than zero. Finally, the degree of self-punishment of harmful stochastic choices is characterized.
{"title":"Harmful choices","authors":"Angelo Petralia","doi":"arxiv-2408.01317","DOIUrl":"https://doi.org/arxiv-2408.01317","url":null,"abstract":"We investigate the choice behavior of a decision maker (DM) who harms\u0000herself, by maximizing some distortion of her true preference, in which the\u0000first $i$ alternatives are moved to the bottom, in a reversed order. The\u0000deterministic declination of our pattern has no empirical power, but it allows\u0000to define a degree of self-punishment, which measures the extent of the denial\u0000of pleasure adopted by the DM in her decision. We analyze irrational choices\u0000that display the lowest degree of self-punishment, and a characterization of\u0000them is provided. Moreover, we characterize the choice behavior that exhibits\u0000the highest degree of self-punishment, and we show that it comprises almost all\u0000choices. We also characterize stochastic self-punishment, which collects all\u0000the Random Utility Models (RUMs) whose support is restricted to the harmful\u0000distortions of some preference. Full identification of the DM's preference and\u0000randomization over its harmful distortions is allowed if each alternative is\u0000selected from the ground set with probability greater than zero. Finally, the\u0000degree of self-punishment of harmful stochastic choices is characterized.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"188 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933572","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 analyze the question of whether the outcome of an oligopoly exploiting a nonrenewable resource can be replicated by a related monopoly, within the framework of continuous time and Markov Perfect Nash Equilibrium. We establish necessary and sufficient conditions and find explicit solutions in some cases. Also, very simple models with externalities are shown which Nash equilibrium cannot be replicated in a monopoly.
{"title":"What does a dynamic oligopoly maximize? The continuous time Markov case","authors":"Juan Pablo Rincón-Zapatero","doi":"arxiv-2407.20810","DOIUrl":"https://doi.org/arxiv-2407.20810","url":null,"abstract":"We analyze the question of whether the outcome of an oligopoly exploiting a\u0000nonrenewable resource can be replicated by a related monopoly, within the\u0000framework of continuous time and Markov Perfect Nash Equilibrium. We establish\u0000necessary and sufficient conditions and find explicit solutions in some cases.\u0000Also, very simple models with externalities are shown which Nash equilibrium\u0000cannot be replicated in a monopoly.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862654","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}
Kangle Mu, Zongyun Xie, Igor Kadota, Randall Berry
With the increasing demand for wireless services, spectrum management agencies and service providers (SPs) are seeking more flexible mechanisms for spectrum sharing to accommodate this growth. Such mechanisms impact the market dynamics of competitive SPs. Prior market models of spectrum sharing largely focus on scenarios where competing SPs had identical coverage areas. We depart from this and consider a scenario in which two competing SPs have overlapping but distinct coverage areas. We study the resulting competition using a Cournot model. Our findings reveal that with limited shared bandwidth, SPs might avoid overlapping areas to prevent potential losses due to interference. Sometimes SPs can strategically cooperate by agreeing not to provide service in the overlapping areas and, surprisingly, customers might also benefit from such cooperation under certain circumstances. Overall, market outcomes exhibit complex behaviors that are influenced by the sizes of coverage areas and the bandwidth of the shared spectrum.
{"title":"Impact of Geographical Separation on Spectrum Sharing Markets","authors":"Kangle Mu, Zongyun Xie, Igor Kadota, Randall Berry","doi":"arxiv-2407.20909","DOIUrl":"https://doi.org/arxiv-2407.20909","url":null,"abstract":"With the increasing demand for wireless services, spectrum management\u0000agencies and service providers (SPs) are seeking more flexible mechanisms for\u0000spectrum sharing to accommodate this growth. Such mechanisms impact the market\u0000dynamics of competitive SPs. Prior market models of spectrum sharing largely\u0000focus on scenarios where competing SPs had identical coverage areas. We depart\u0000from this and consider a scenario in which two competing SPs have overlapping\u0000but distinct coverage areas. We study the resulting competition using a Cournot\u0000model. Our findings reveal that with limited shared bandwidth, SPs might avoid\u0000overlapping areas to prevent potential losses due to interference. Sometimes\u0000SPs can strategically cooperate by agreeing not to provide service in the\u0000overlapping areas and, surprisingly, customers might also benefit from such\u0000cooperation under certain circumstances. Overall, market outcomes exhibit\u0000complex behaviors that are influenced by the sizes of coverage areas and the\u0000bandwidth of the shared spectrum.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862655","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}
Agustin G. Bonifacio, Noelia Juarez, Paola B. Manasero
We compute the lattice operations for the (pairwise) stable set in two-sided matching markets where only substitutability on agents' choice functions is imposed. To do this, we use Tarski operators defined on the lattices of worker-quasi-stable and firm-quasi-stable matchings. These operators resemble lay-off and vacancy chain dynamics, respectively. First, we compute the lattice operations in the many-to-one model. Then, we extend these operations to a many-to-many model with substitutable choice functions on one side and responsive preferences on the other, via a morphism that relates many-to-one with many-to-many matchings in a natural way. Finally, we present the lattice operations in the many-to-many model with substitutable choice functions on both sides.
{"title":"Lattice operations for the stable set in substitutable matching markets via re-equilibration dynamics","authors":"Agustin G. Bonifacio, Noelia Juarez, Paola B. Manasero","doi":"arxiv-2407.21198","DOIUrl":"https://doi.org/arxiv-2407.21198","url":null,"abstract":"We compute the lattice operations for the (pairwise) stable set in two-sided\u0000matching markets where only substitutability on agents' choice functions is\u0000imposed. To do this, we use Tarski operators defined on the lattices of\u0000worker-quasi-stable and firm-quasi-stable matchings. These operators resemble\u0000lay-off and vacancy chain dynamics, respectively. First, we compute the lattice\u0000operations in the many-to-one model. Then, we extend these operations to a\u0000many-to-many model with substitutable choice functions on one side and\u0000responsive preferences on the other, via a morphism that relates many-to-one\u0000with many-to-many matchings in a natural way. Finally, we present the lattice\u0000operations in the many-to-many model with substitutable choice functions on\u0000both sides.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862653","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：