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Asymmetric Dynamic Resource Management Problem with Different Regimes 不同制度下的不对称动态资源管理问题
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601003
V. V. Mazalov, A. N. Rettieva
{"title":"Asymmetric Dynamic Resource Management Problem with Different Regimes","authors":"V. V. Mazalov,&nbsp;A. N. Rettieva","doi":"10.1134/S1064562425601003","DOIUrl":"10.1134/S1064562425601003","url":null,"abstract":"<p>A dynamic game related to a resource management problem with asymmetric players is considered. The resource evolution depends on interchanged usage regimes: exploitation periods, where many players extract a common resource, and moratorium periods, where extraction is prohibited and the resource stock evolves according to the natural growth rule. Both noncooperative and cooperative behaviors of players are constructed and compared. To maintain sustainable resource exploitation, a certain ratio of the lengths of moratorium to extraction periods is applied. The value of exploitation horizon is determined by optimizing the price of anarchy.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 1","pages":"S119 - S126"},"PeriodicalIF":0.6,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
An Example of Two Level Cooperation for Differential Game with Pairwise Interactions in Pollution Control Problems 污染控制问题中具有两两相互作用的微分对策的两层合作例子
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601040
Y. He, L. A. Petrosyan
{"title":"An Example of Two Level Cooperation for Differential Game with Pairwise Interactions in Pollution Control Problems","authors":"Y. He,&nbsp;L. A. Petrosyan","doi":"10.1134/S1064562425601040","DOIUrl":"10.1134/S1064562425601040","url":null,"abstract":"<p>In this paper, we consider two levels of cooperation in a differential game with pairwise interactions. At the first level, the partner sets are treated as players, and the Shapley value is used to allocate the payoff among the partner sets. At the second level, this payoff is distributed among the individual players within each partner set. A new characteristic function is constructed, and its convexity is proved. The results are illustrated through a pollution control problem involving pairwise interactions.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 1","pages":"S53 - S59"},"PeriodicalIF":0.6,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Adaptive Control for Two-Agent Opinion Dynamics under Uncertainty 不确定性下双主体意见动态的自适应控制
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601143
Y. Chen, V. V. Mazalov, H. Gao
{"title":"Adaptive Control for Two-Agent Opinion Dynamics under Uncertainty","authors":"Y. Chen,&nbsp;V. V. Mazalov,&nbsp;H. Gao","doi":"10.1134/S1064562425601143","DOIUrl":"10.1134/S1064562425601143","url":null,"abstract":"<p>A model of opinion dynamics is considered, in which the trust between the agents is unknown and modeled using random variables with certain probability distributions. Additionally, there is a player whose goal is to maintain the agents’ opinions at a specific level. Initially, an optimal control is found in explicit form, assuming that the trust coefficients are known. Then this control is used at each step to obtain realizations of the random variables. Computer experiments have been conducted.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 1","pages":"S11 - S20"},"PeriodicalIF":0.6,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
European Option Superhedging as an Antagonistic Game 欧洲期权超级对冲作为一种对抗性博弈
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601015
O. V. Zverev, E. A. Shelemekh
{"title":"European Option Superhedging as an Antagonistic Game","authors":"O. V. Zverev,&nbsp;E. A. Shelemekh","doi":"10.1134/S1064562425601015","DOIUrl":"10.1134/S1064562425601015","url":null,"abstract":"<p>In the article, the European option superhedging problem is identified with a dynamic stochastic zero-sum game between the market and the contract seller. The seller manages a portfolio of underlying assets in order to minimize her expected exponential risk. The market determines a probability distribution for discounted prices of traded assets: absolutely continuous with respect to a given underlying distribution and maximazing seller’s expected risk. Recurrence relations for the upper and lower values of the game are obtained. It is shown that the absence of arbitrage opportunities in the market is a necessary and sufficient condition for the existence of a self-financing portfolio, with which the lower bound in the definition of the upper value of the game is obtained. Such a portfolio is superhedging, and the upper value of the game allows one to calculate the upper hedging price. Moreover, it is shown that, in a market model without arbitrage opportunities, there is always a game equilibrium. The saddle point of the game, if it exists, determines a superhedging portfolio and a martingale probability distribution, with which an upper bound in the definition of the upper value of the game is achieved. This distribution defines the seller’s worst market in the sense that the reserve of the superhedging portfolio is fully consumed in that market model. Using examples, we provide comparison between results of option calculations based on probabilistic and trajectory-based game approaches, analyze advantages and disadvantages of the topology choice (<span>(sigma ({{L}^{1}},{{L}^{infty }}))</span> topology instead of weak topology) in the probabilistic formulation of this type of problems.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 1","pages":"S86 - S102"},"PeriodicalIF":0.6,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Bi-Criterial Approach to Optimization Problems with Uncertain Factors 不确定因素优化问题的双准则方法
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601027
I. V. Konnov
{"title":"Bi-Criterial Approach to Optimization Problems with Uncertain Factors","authors":"I. V. Konnov","doi":"10.1134/S1064562425601027","DOIUrl":"10.1134/S1064562425601027","url":null,"abstract":"<p>We propose a new approach to optimization problems with uncertain factors, which is related to transformation of the initial problem into a bi-criteria optimization problem. This problem is solved by combining the successive concessions method and linear convolution of the criteria. An application of the method to the simplest extremal graph problems is described.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 1","pages":"S80 - S85"},"PeriodicalIF":0.6,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Opinion Formation in the Presence of Hidden Internal Opinions and Possibility of Influencing Them 内在隐性意见存在下的意见形成及其影响的可能性
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S106456242560112X
K. O. Urtyakova, E. M. Parilina
{"title":"Opinion Formation in the Presence of Hidden Internal Opinions and Possibility of Influencing Them","authors":"K. O. Urtyakova,&nbsp;E. M. Parilina","doi":"10.1134/S106456242560112X","DOIUrl":"10.1134/S106456242560112X","url":null,"abstract":"<p>The paper proposes a modified concealed voter model MCVM in which each agent in the network is represented by two nodes corresponding to her external (public) and internal (hidden) opinion. Agents exchange opinions in the external layer and copy the internal opinion into the external layer and vice versa. In our work, one more action has been added—transmitting the external opinion of an agent to another agent in the internal layer. We find a formula to calculate the average time to reach consensus and compare them for MCVM and CVM. The results of numerical simulations of opinion dynamics according to the proposed MCVM model are presented.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 1","pages":"S32 - S41"},"PeriodicalIF":0.6,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
The Price of Anarchy in the Congestion Game with Flow Constraints 具有流量约束的拥堵博弈中无政府状态的代价
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601131
A. Yu. Krylatov, T. Qiao
{"title":"The Price of Anarchy in the Congestion Game with Flow Constraints","authors":"A. Yu. Krylatov,&nbsp;T. Qiao","doi":"10.1134/S1064562425601131","DOIUrl":"10.1134/S1064562425601131","url":null,"abstract":"<p>This paper considers the congestion game with flow constraints. While the total number of players in the congestion game is usually specified and the flow of players assigned to each of the alternatives is, generally speaking, unlimited, in the formulation considered in this paper, the flow of players can be limited for each of the available alternatives and in total. The paper provides a general formulation of the congestion game with flow constraints and studies its solution space. We estimate the price of anarchy for different numbers of players, which helps us determine when the game’s equilibrium assignment is close to the social optimum and when it deviates. Finally, we consider examples of practical problems and cases that can be modeled and described using the corresponding game.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 1","pages":"S21 - S31"},"PeriodicalIF":0.6,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Comparative Analysis of Incentive-Based and Structural Control in Games on Networks with Linear Best Response 线性最优网络博弈中基于激励控制与结构控制的比较分析
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425600988
I. V. Petrov
{"title":"Comparative Analysis of Incentive-Based and Structural Control in Games on Networks with Linear Best Response","authors":"I. V. Petrov","doi":"10.1134/S1064562425600988","DOIUrl":"10.1134/S1064562425600988","url":null,"abstract":"<p>This paper examines games on networks with linear best responses, which allow for the analysis of how interaction structures influence agents’ strategic behavior. Special attention is given to intervention issues in such models, particularly in selecting optimal intervention strategies aimed at maximizing the central planner’s objective function. Two main control policies are analyzed: individual agent incentives and modifications of the interaction structure. The concept of a representative agent is introduced to simplify equilibrium analysis and control problems in games on networks. Both aggregate outcome maximization problems and adversarial scenarios between competing central planners are considered. Analytical conditions are derived to determine whether controlling the interaction structure is more effective than influencing individual incentives. Numerical experiments confirm the theoretical results and demonstrate their applicability to different types of network structures.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 1","pages":"S103 - S110"},"PeriodicalIF":0.6,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 One Differential Game with Payoff Functions of the Germeier Convolution Type 一类具有Germeier卷积型收益函数的微分对策
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S106456242560099X
V. A. Gorelik, T. V. Zolotova
{"title":"On One Differential Game with Payoff Functions of the Germeier Convolution Type","authors":"V. A. Gorelik,&nbsp;T. V. Zolotova","doi":"10.1134/S106456242560099X","DOIUrl":"10.1134/S106456242560099X","url":null,"abstract":"<p>The paper considers a differential game model with functionals represented by a convolution in the form of the minimum of two criteria, one of which describes the competition of players in a common (external) sphere of activity and the other describes the personal achievements of each player (in the internal sphere). The player’s control is the resource redistribution between the external and internal spheres. It is shown that, under some natural assumptions of monotonicity of criteria in such games, Nash and Stackelberg equilibria exist and coincide, possessing the properties of stability and Pareto optimality. </p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 1","pages":"S111 - S118"},"PeriodicalIF":0.6,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Conflict Triangles and Hexamatrix Games 冲突三角形和六边形游戏
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601088
A. V. Orlov
{"title":"Conflict Triangles and Hexamatrix Games","authors":"A. V. Orlov","doi":"10.1134/S1064562425601088","DOIUrl":"10.1134/S1064562425601088","url":null,"abstract":"<p>The paper considers one class of finite non-cooperative games (with a finite number of strategies for each player)—E.B. Yanovskaya’s polymatrix games. More specifically, three-player polymatrix games, so-called hexamatrix games (HMGs), which can be completely described by six matrices, are studied. A number of model examples of three-party conflicts, describing some real-life situations, are presented and formulated as HMGs. The feasibility of using hexamatrix games to model economic relationships between three participants is demonstrated. To find the Nash equilibrium in the formulated games, an optimization approach is used, where the equilibrium problem is reduced to a nonconvex optimization problem with a bilinear structure. The latter is solved using A.S. Strekalovskii’s Global Search Theory (GST) for (d.c.) optimization problems with objective functions representable as the difference of two convex functions.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 1","pages":"S42 - S52"},"PeriodicalIF":0.6,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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