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On Integer Imputations of the Core of Totally Balanced Cooperative Games
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-03-28 DOI: 10.1134/S1064562424702399
V. V. Morozov, S. I. Romanov
{"title":"On Integer Imputations of the Core of Totally Balanced Cooperative Games","authors":"V. V. Morozov,&nbsp;S. I. Romanov","doi":"10.1134/S1064562424702399","DOIUrl":"10.1134/S1064562424702399","url":null,"abstract":"<p>We consider totally balanced cooperative games in which the characteristic function takes integer values. It is proved that any three- or four-person game has an integer imputation from the core. A similar result, with the exception of one degenerate case, is obtained for five-person games. An example of a five-person game is given in which the core consists of a single noninteger imputation.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S376 - S382"},"PeriodicalIF":0.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716732","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 Solvability of a Pursuit Game with Nonlinear Dynamics in Hilbert Space
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-03-28 DOI: 10.1134/S1064562424702351
A. V. Chernov
{"title":"On Solvability of a Pursuit Game with Nonlinear Dynamics in Hilbert Space","authors":"A. V. Chernov","doi":"10.1134/S1064562424702351","DOIUrl":"10.1134/S1064562424702351","url":null,"abstract":"<p>We consider a pursuit differential game in a Hilbert space. The game dynamics is described by two semilinear evolutionary equations with a not necessarily bounded operator in the Hilbert space; each of these equations is controlled by its own player. The controls appear linearly on the right-hand sides of the equations, and their norms are bounded by given constants. Sufficient conditions for the solvability of the pursuit game are established in both linear and nonlinear cases. For this purpose, we use the Minty–Browder theorem and a chain technology of successive continuation of the solution to a controlled system to intermediate states. As examples of reduction to the abstract operator equation under study, we consider Oskolkov’s system of equations and a semilinear wave equation.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S333 - S345"},"PeriodicalIF":0.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143717060","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
Model of a Two-Level Hierarchical System with Cooperative Behavior of Lower-Level Elements
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-03-28 DOI: 10.1134/S1064562424702363
M. A. Gorelov
{"title":"Model of a Two-Level Hierarchical System with Cooperative Behavior of Lower-Level Elements","authors":"M. A. Gorelov","doi":"10.1134/S1064562424702363","DOIUrl":"10.1134/S1064562424702363","url":null,"abstract":"<p>One of the possible generalizations to the case of many persons of the classical hierarchical Germeier game has been studied. It has been assumed that the lower-level players select one of the weakly efficient points. The maximal guaranteed result of the top-level player has been calculated. Two variants of formulation of the problems: games with and without feedback have been considered.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S346 - S356"},"PeriodicalIF":0.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716731","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 the Number of Pursuers That Guarantees the Capture of the Evader in a Game on the Graph of Icosahedral Edges
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-03-28 DOI: 10.1134/S1064562424602671
A. A. Azamov, A. G. Holboyev
{"title":"On the Number of Pursuers That Guarantees the Capture of the Evader in a Game on the Graph of Icosahedral Edges","authors":"A. A. Azamov,&nbsp;A. G. Holboyev","doi":"10.1134/S1064562424602671","DOIUrl":"10.1134/S1064562424602671","url":null,"abstract":"<p>We study how the optimal number of pursuers in a differential game on a graph changes when an edge is removed from the graph. It is shown that, when one edge of an icosahedron is removed, two pursuers are sufficient to capture the evader, whereas, for the icosahedron itself, this number is 3.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S463 - S467"},"PeriodicalIF":0.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716735","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
UCB Strategies and Optimization of Batch Processing in a One-Armed Bandit Problem
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-03-28 DOI: 10.1134/S1064562424602683
S. V. Garbar, A. V. Kolnogorov, A. N. Lazutchenko
{"title":"UCB Strategies and Optimization of Batch Processing in a One-Armed Bandit Problem","authors":"S. V. Garbar,&nbsp;A. V. Kolnogorov,&nbsp;A. N. Lazutchenko","doi":"10.1134/S1064562424602683","DOIUrl":"10.1134/S1064562424602683","url":null,"abstract":"<p>We consider a Gaussian one-armed bandit problem, which arises when optimizing batch data processing if there are two alternative processing methods with a priori known efficiency of the first method. During processing, it is necessary to determine a more effective method and ensure its preferential use. This optimal control problem is interpreted as a game with nature. We investigate cases of known and a priori unknown variance of income corresponding to the second method. The control goal is considered in a minimax setting, and UCB strategies are used to ensure it. In all the studied cases, invariant descriptions of control on a horizon equal to one are obtained, which depend only on the number of batches into which the data is divided, but not on their full number. These descriptions allow us to determine approximately optimal parameters of strategies using Monte Carlo simulation. Numerical results show the high efficiency of the proposed UCB strategies.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S422 - S432"},"PeriodicalIF":0.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143717062","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
Coalition Pareto-Optimal Solution in a Nontransferable Game
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-03-28 DOI: 10.1134/S1064562424702430
V. I. Zhukovskiy, L. V. Zhukovskaya, L. V. Smirnova
{"title":"Coalition Pareto-Optimal Solution in a Nontransferable Game","authors":"V. I. Zhukovskiy,&nbsp;L. V. Zhukovskaya,&nbsp;L. V. Smirnova","doi":"10.1134/S1064562424702430","DOIUrl":"10.1134/S1064562424702430","url":null,"abstract":"<p>By the end of the last century, four directions had been established in the mathematical theory of positional differential games (PDGs): a noncoalition version of PDG, a cooperative, hierarchical, and, finally, the least studied, a coalition version of PDG. In turn, within the coalition, there are usually games with transferable payoffs (with side payments, when players can share their winnings during the game) and nontransferable payoffs (games with side payments, when such redistributions are absent for one reason or another). Studies of coalition games with side payments are concentrated and actively conducted at the Faculty of Applied Mathematics and Management Processes of St. Petersburg University and Institute of Applied Mathematical Research of the Karelian Research Centre of Russian Academy of Sciences (L.A. Petrosyan, V.V. Mazalov, E.M. Parilina, A.N. Rettieva, and their numerous domestic and foreign students). However, side payments are not always present even in economic interactions; moreover, side payments may be generally prohibited by law. The studies we have undertaken in recent years on the balance of threats and counterthreats (sanctions and countersanctions) in noncoalition differential games allow, in our opinion, covering some aspects of the nontransferable version of coalition games. This article is devoted to the issues of internal and external stability of coalitions in the PDG class. It reveals the coefficient constraints in the mathematical model of the positional differential linear-quadratic game of six persons with a two-coalition structure, in which this coalition structure is internally and externally stable.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S409 - S421"},"PeriodicalIF":0.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716671","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
One-Armed Bandit Problem and the Mirror Descent Algorithm
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-03-28 DOI: 10.1134/S1064562424702429
D. N. Shiyan
{"title":"One-Armed Bandit Problem and the Mirror Descent Algorithm","authors":"D. N. Shiyan","doi":"10.1134/S1064562424702429","DOIUrl":"10.1134/S1064562424702429","url":null,"abstract":"<p>The application of the mirror descent algorithm (MDA) in the one-armed bandit problem in the minimax setting in relation to data processing has been considered. This problem has also been known as a game with nature, in which the payoff function of the player is the mathematical expectation of the total income. The player must determine the most effective method of the two available ones during the control process and ensure its preferential use. In this case, the a priori efficiency of one of the methods is known. In this paper, a modification of the MDA that makes it possible to improve the control efficiency by using additional information has been considered. The proposed strategy preserves the characteristic property of strategies for one-armed bandits: if a known action is applied once, it will be applied until the end of control. Modifications for the algorithm for single processing and for its batch version have been considered. Batch processing is interesting in that the total processing time is determined by the number of packets, and not by the original amount of data, with the possibility of providing parallel processing of data in packets. For the proposed algorithms, the optimal values of the adjustable parameters have been calculated using Monte Carlo simulation and minimax risk estimates have been obtained.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S399 - S408"},"PeriodicalIF":0.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716729","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
Approximate Equilibrium in a Finitely Repeated Prisoner’s Dilemma
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-03-28 DOI: 10.1134/S1064562424702405
A. M. Pisareva, E. M. Parilina
{"title":"Approximate Equilibrium in a Finitely Repeated Prisoner’s Dilemma","authors":"A. M. Pisareva,&nbsp;E. M. Parilina","doi":"10.1134/S1064562424702405","DOIUrl":"10.1134/S1064562424702405","url":null,"abstract":"<p>The paper studies a finitely repeated Prisoner’s Dilemma. To maintain cooperation in the game, a new profile of behavior strategies is proposed, where the deviation of a player is punished not until the end of the game, but rather for a given number of stages depending on the stage of the game. The existence of an approximate equilibrium or epsilon-equilibrium in these strategies is proven, and the maximum payoff of a player deviating from the approximate equilibrium is found.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S383 - S390"},"PeriodicalIF":0.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716733","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
Cooperative Multicriteria Dynamic Games: Application to Transportation Problems
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-03-28 DOI: 10.1134/S1064562424602567
A. N. Rettieva
{"title":"Cooperative Multicriteria Dynamic Games: Application to Transportation Problems","authors":"A. N. Rettieva","doi":"10.1134/S1064562424602567","DOIUrl":"10.1134/S1064562424602567","url":null,"abstract":"<p>Cooperation plays an important role in dynamic games related to resource allocation problems. This paper investigates a multicriteria dynamic resource management problem. Noncooperative and cooperative strategies and payoffs are obtained via bargaining schemes. To maintain cooperative behavior, the concept of incentive equilibrium, where the center controls the compliance with the cooperative agreement, is adopted. The presented approaches are applied to a multicriteria dynamic transportation problem.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S487 - S494"},"PeriodicalIF":0.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716741","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
Potential in Congestion Game with Different Types of Vehicles
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2025-03-28 DOI: 10.1134/S1064562424602580
N. N. Nikitina, V. V. Mazalov
{"title":"Potential in Congestion Game with Different Types of Vehicles","authors":"N. N. Nikitina,&nbsp;V. V. Mazalov","doi":"10.1134/S1064562424602580","DOIUrl":"10.1134/S1064562424602580","url":null,"abstract":"<p>Heterogeneous congestion games make it possible to simulate traffic situations involving multiple classes of vehicles with different preferences in choosing routes. In this work, we prove the existence of a potential in a discrete congestion game with <i>n</i> classes of players. Examples are given in which we calculate equilibria and demonstrate the emergence of the Braess paradox, as well as use the constructed congestion game to analyze the distribution of vehicles in the graph of urban roads for the city of Petrozavodsk.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S433 - S439"},"PeriodicalIF":0.5,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143716948","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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