Mathematics of Operations Research最新文献_第2页

On a Network Centrality Maximization Game 论网络中心性最大化博弈

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-08-16 DOI: 10.1287/moor.2022.0251

Costanza Catalano, Maria Castaldo, Giacomo Como, Fabio Fagnani

{"title":"On a Network Centrality Maximization Game","authors":"Costanza Catalano, Maria Castaldo, Giacomo Como, Fabio Fagnani","doi":"10.1287/moor.2022.0251","DOIUrl":"https://doi.org/10.1287/moor.2022.0251","url":null,"abstract":"We study a network formation game where n players, identified with the nodes of a directed graph to be formed, choose where to wire their outgoing links in order to maximize their PageRank centrality. Specifically, the action of every player i consists in the wiring of a predetermined number di of directed out-links, and her utility is her own PageRank centrality in the network resulting from the actions of all players. We show that this is a potential game and that the best response correspondence always exhibits a local structure in that it is never convenient for a node i to link to other nodes that are at incoming distance more than di from her. We then study the equilibria of this game determining necessary conditions for a graph to be a (strict, recurrent) Nash equilibrium. Moreover, in the homogeneous case, where players all have the same number d of out-links, we characterize the structure of the potential-maximizing equilibria, and in the special cases d = 1 and d = 2, we provide a complete classification of the set of (strict, recurrent) Nash equilibria. Our analysis shows in particular that the considered formation mechanism leads to the emergence of undirected and disconnected or loosely connected networks.Funding: This research was carried out within the framework of the Ministero dell’Università e della Ricerca (MIUR)-funded Progetto di Eccellenza of the Dipartimento di Scienze Matematiche G. L. Lagrange, Politecnico di Torino [CUP: E11G18000350001]. It received partial support from the MIUR-funded project PRIN 2017 “Advanced Network Control of Future Smart Grids” and from the Compagnia di San Paolo.","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"2 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimal Ratcheting of Dividends with Capital Injection 注资后股息的最优梯度调整

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-08-13 DOI: 10.1287/moor.2023.0102

Wenyuan Wang, Ran Xu, Kaixin Yan

{"title":"Optimal Ratcheting of Dividends with Capital Injection","authors":"Wenyuan Wang, Ran Xu, Kaixin Yan","doi":"10.1287/moor.2023.0102","DOIUrl":"https://doi.org/10.1287/moor.2023.0102","url":null,"abstract":"In this paper, we investigate the optimal dividend problem with capital injection and ratcheting constraint with nondecreasing dividend payout rate. Capital injections are introduced in order to eliminate the possibility of bankruptcy. Under the Cramér–Lundberg risk model, the problem is formulated as a two-dimensional stochastic control problem. By applying the viscosity theory, we show that the value function is the unique viscosity solution to the associated Hamilton–Jacobi–Bellman equation. In order to obtain analytical results, we further study the problem with finite ratcheting constraint, where the dividend rate takes only a finite number of available values. We show that the value function under general ratcheting can be approximated arbitrarily closely by the one with finite ratcheting. Finally, we derive the expressions of value function when the threshold-type finite ratcheting dividend strategy with capital injection is applied, and we show the optimality of such a strategy under certain conditions of concavity. Numerical examples under various scenarios are provided at the end.Funding W. Wang was supported by the National Natural Science Foundation of China [Grants 12171405, 12271066, and 11661074] and the Fundamental Research Funds for the Central Universities of China [Grant 20720220044]. R. Xu was supported by the National Natural Science Foundation of China [Grants 12201506 and 12371468], the Natural Science Foundation of the Jiangsu Higher Education Institutions of China [Grant 21KJB110024], and Xi’an Jiaotong-Liverpool University Research Development Funding [Grant RDF-20-01-02].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"38 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the Set of Balanced Games 论平衡游戏集

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-08-13 DOI: 10.1287/moor.2023.0379

Pedro Garcia-Segador, Michel Grabisch, Pedro Miranda

引用次数: 0

Compact Extended Formulations for Low-Rank Functions with Indicator Variables 带指示变量的低域函数的紧凑扩展公式

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-08-12 DOI: 10.1287/moor.2021.0281

Shaoning Han, Andrés Gómez

{"title":"Compact Extended Formulations for Low-Rank Functions with Indicator Variables","authors":"Shaoning Han, Andrés Gómez","doi":"10.1287/moor.2021.0281","DOIUrl":"https://doi.org/10.1287/moor.2021.0281","url":null,"abstract":"We study the mixed-integer epigraph of a special class of convex functions with nonconvex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are defined as compositions of low-dimensional nonlinear functions with affine functions. Extended formulations describing the convex hull of such sets can easily be constructed via disjunctive programming although a direct application of this method often yields prohibitively large formulations, whose size is exponential in the number of variables. In this paper, we propose a new disjunctive representation of the sets under study, which leads to compact formulations with size exponential in the dimension of the nonlinear function but polynomial in the number of variables. Moreover, we show how to project out the additional variables for the case of dimension one, recovering or generalizing known results for the convex hulls of such sets (in the original space of variables). Our computational results indicate that the proposed approach can significantly improve the performance of solvers in structured problems.Funding: This work was supported by the National Science Foundation Division of Computing and Communication Foundations [Grant 2006762].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"5 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Parabolic Regularity of Spectral Functions 谱函数的抛物线正则性

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-08-12 DOI: 10.1287/moor.2023.0010

Ashkan Mohammadi, Ebrahim Sarabi

引用次数: 0

Uncertainty Propagation and Dynamic Robust Risk Measures 不确定性传播与动态稳健风险度量

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-08-09 DOI: 10.1287/moor.2023.0267

Marlon R. Moresco, Mélina Mailhot, Silvana M. Pesenti

{"title":"Uncertainty Propagation and Dynamic Robust Risk Measures","authors":"Marlon R. Moresco, Mélina Mailhot, Silvana M. Pesenti","doi":"10.1287/moor.2023.0267","DOIUrl":"https://doi.org/10.1287/moor.2023.0267","url":null,"abstract":"We introduce a framework for quantifying propagation of uncertainty arising in a dynamic setting. Specifically, we define dynamic uncertainty sets designed explicitly for discrete stochastic processes over a finite time horizon. These dynamic uncertainty sets capture the uncertainty surrounding stochastic processes and models, accounting for factors such as distributional ambiguity. Examples of uncertainty sets include those induced by the Wasserstein distance and f-divergences. We further define dynamic robust risk measures as the supremum of all candidates’ risks within the uncertainty set. In an axiomatic way, we discuss conditions on the uncertainty sets that lead to well-known properties of dynamic robust risk measures, such as convexity and coherence. Furthermore, we discuss the necessary and sufficient properties of dynamic uncertainty sets that lead to time-consistencies of dynamic robust risk measures. We find that uncertainty sets stemming from f-divergences lead to strong time-consistency whereas the Wasserstein distance results in a new time-consistent notion of weak recursiveness. Moreover, we show that a dynamic robust risk measure is strong time-consistent or weak recursive if and only if it admits a recursive representation of one-step conditional robust risk measures arising from static uncertainty sets.Funding: M. Mailhot and S. M. Pesenti acknowledge support from the Canadian Statistical Sciences Institute (CANSSI) and from the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2015-05447, DGECR-2020-00333, and RGPIN-2020-04289]. M. R. Moresco thanks the Horizon Postdoctoral Fellowship for the support.","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"20 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141939658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fair Shares: Feasibility, Domination, and Incentives 公平分享：可行性、主导权和激励机制

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-30 DOI: 10.1287/moor.2022.0257

Moshe Babaioff, Uriel Feige

引用次数: 0

An Augmented Lagrangian Approach to Conically Constrained Nonmonotone Variational Inequality Problems 用增量拉格朗日法解决共轭约束非单调变分不等式问题

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-29 DOI: 10.1287/moor.2023.0167

Lei Zhao, Daoli Zhu, Shuzhong Zhang

{"title":"An Augmented Lagrangian Approach to Conically Constrained Nonmonotone Variational Inequality Problems","authors":"Lei Zhao, Daoli Zhu, Shuzhong Zhang","doi":"10.1287/moor.2023.0167","DOIUrl":"https://doi.org/10.1287/moor.2023.0167","url":null,"abstract":"In this paper we consider a nonmonotone (mixed) variational inequality (VI) model with (nonlinear) convex conic constraints. Through developing an equivalent Lagrangian function-like primal-dual saddle point system for the VI model in question, we introduce an augmented Lagrangian primal-dual method, called ALAVI (Augmented Lagrangian Approach to Variational Inequality) in the paper, for solving a general constrained VI model. Under an assumption, called the primal-dual variational coherence condition in the paper, we prove the convergence of ALAVI. Next, we show that many existing generalized monotonicity properties are sufficient—though by no means necessary—to imply the abovementioned coherence condition and thus are sufficient to ensure convergence of ALAVI. Under that assumption, we further show that ALAVI has in fact an [Formula: see text] global rate of convergence where k is the iteration count. By introducing a new gap function, this rate further improves to be [Formula: see text] if the mapping is monotone. Finally, we show that under a metric subregularity condition, even if the VI model may be nonmonotone, the local convergence rate of ALAVI improves to be linear. Numerical experiments on some randomly generated highly nonlinear and nonmonotone VI problems show the practical efficacy of the newly proposed method.Funding: L. Zhao and D. Zhu were partially supported by the Major Project of the National Natural Science Foundation of China [Grant 72293582], the National Key R&D Program of China [Grant 2023YFA0915202], and the Fundamental Research Funds for the Central Universities (the Interdisciplinary Program of Shanghai Jiao Tong University) [Grant YG2024QNA36]. L. Zhao was partially supported by the Startup Fund for Young Faculty at SJTU (SFYF at SJTU) [Grant 22X010503839].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"20 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Nonzero-Sum Optimal Stopping Game with Continuous vs. Periodic Exercise Opportunities 连续锻炼机会与定期锻炼机会的非零和最优停止博弈

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-29 DOI: 10.1287/moor.2023.0123

José Luis Pérez, Neofytos Rodosthenous, Kazutoshi Yamazaki

{"title":"Nonzero-Sum Optimal Stopping Game with Continuous vs. Periodic Exercise Opportunities","authors":"José Luis Pérez, Neofytos Rodosthenous, Kazutoshi Yamazaki","doi":"10.1287/moor.2023.0123","DOIUrl":"https://doi.org/10.1287/moor.2023.0123","url":null,"abstract":"We introduce a new nonzero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modeling the value of an asset, one player observes and can act on the process continuously, whereas the other player can act on it only periodically at independent Poisson arrival times. The first one to stop receives a reward, different for each player, whereas the other one gets nothing. We study how each player balances the maximization of gains against the maximization of the likelihood of stopping before the opponent. In such a setup driven by a Lévy process with positive jumps, we not only prove the existence but also explicitly construct a Nash equilibrium with values of the game written in terms of the scale function. Numerical illustrations with put-option payoffs are also provided to study the behavior of the players’ strategies as well as the quantification of the value of available exercise opportunities.Funding: K. Yamazaki was partly supported by The Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI) [Grants 19H01791, 20K03758, and 24K06844], Open Partnership Joint Research Projects [Grant JPJSBP120209921], and the University of Queensland [start-up grant].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"48 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exploration Noise for Learning Linear-Quadratic Mean Field Games 学习线性-二次均值场博弈的探索噪声

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-24 DOI: 10.1287/moor.2021.0157

François Delarue, Athanasios Vasileiadis

引用次数: 0