TAURIDA JOURNAL OF COMPUTER SCIENCE THEORY AND MATHEMATICS最新文献

{"title":"Hierarchical model of competition under uncertainty","authors":"A. Bardin, J. N. Zhiteneva","doi":"10.37279/1729-3901-2020-19-4-18-29","DOIUrl":"https://doi.org/10.37279/1729-3901-2020-19-4-18-29","url":null,"abstract":"Oligopoly is a basic concept in the theory of competition. This structure is the central object of research in the economics of markets. There are many mathematical models of the market that are formalized in the form of an oligopoly in economic theory.\u0000The Cournot oligopoly is an elementary mathematical model of competition. The principle of equilibrium formalizes the non-cooperative nature of the conflict. Each player chooses the equilibrium strategy of behavior that provides the greatest profit, provided that the other competitors adhere to their equilibrium strategies.\u0000The Stackelberg model describes a two-level hierarchical model of firm competition. The top-level player (center, leader) chooses his strategy, assuming reasonable (optimal) decision-making by the lower-level players. Lower-level players (agents, followers) recognize the leadership of the center. They consider the center's strategies known. These players choose their strategies, wanting to maximize their payoff functions. This hierarchical structure is from a game point of view a case of a hierarchical game Gamma1.\u0000The indefinite uncontrolled factors (uncertainties) are the values for which only the range of possible values is known in this paper. Recently, studies of game models under uncertainty have been actively conducted. In particular, non-coalitional games under uncertainty are investigated.\u0000The concepts of risk and regret are formalized in various ways in the theory of problems with uncertainty. At the same time, the decision-maker takes into account both the expected losses and the possibility of favorable actions of factors beyond his control.nThis article examines the two-level hierarchical structure of decision-making in the problem of firm competition. A linear-quadratic model with two levels of hierarchy is considered. This model uses the concepts of Cournot and Stackelberg under uncertainty. Uncontrolled factors (uncertainties) are identified with the actions of the importing company.\u0000The Wald and Savage principles are used to formalize the solution. According to Wald's maximin criterion, game with nature is seen as a conflict with a player who wants to harm the decision-maker as much as possible.nnSavage's minimax regret criterion, when choosing the optimal strategy, focuses not on winning, but on regret. As an optimal strategy, the strategy is chosen in which the amount of regret in the worst conditions is minimal.\u0000A new approach to decision-making in the game with nature is formalized. It allows you to combine the positive features of both principles and weaken their negative properties. The concept of U-optimal solution of the problem in terms of risks and regrets is considered.nThe problems of formalization of some types of optimal solutions for a specific linear-quadratic problem with two levels of hierarchy are solved.","PeriodicalId":246257,"journal":{"name":"TAURIDA JOURNAL OF COMPUTER SCIENCE THEORY AND MATHEMATICS","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123882125","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}

{"title":"Solvability of pseudobulous conditional optimization problems of the type of many salesmen","authors":"M. S. Germanchuk","doi":"10.37279/1729-3901-2020-19-4-30-55","DOIUrl":"https://doi.org/10.37279/1729-3901-2020-19-4-30-55","url":null,"abstract":"Formalizing routing problems of many traveling salesman (mTSP) in complex networks leads to NP-complete pseudobulous conditional optimization problems. The subclasses of polynomially solvable problems are distinguished, for which the elements of the distance matrix satisfy the triangle inequality and other special representations of the original data. The polynomially solvable assignment problem can be used to determine the required number of salesmen and to construct their routes. Uses a subclass of tasks in the form of pseudobulous optimization with disjunctive normal shape (textit{DNS}) constraints to which the task is reduced mTSP. Problems in this form are polynomially solvable and allow to combine knowledge about network structure, requirements to pass routes by agents (search procedures) and efficient algorithms of logical inference on constraints in the form of textit{DNS}. This approach is the theoretical justification for the development of multi-agent system management leading to a solution mTSP. Within the framework of intellectual planning, using resources and capabilities, and taking into account the constraints for each agent on the selected clusters of the network, the construction of a common solution for the whole complex network is achieved.","PeriodicalId":246257,"journal":{"name":"TAURIDA JOURNAL OF COMPUTER SCIENCE THEORY AND MATHEMATICS","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116001038","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}

{"title":"The stability of coalitional structure in differential linear-quadratic game of four persons","authors":"V. Zhukovskiy, S. P. Samsonov, Valentyna Romanova","doi":"10.37279/1729-3901-2020-19-3-15-18","DOIUrl":"https://doi.org/10.37279/1729-3901-2020-19-3-15-18","url":null,"abstract":"In article coefficient criteria of the stability of coalitional structure in\u0000differential linear-quadratic positional game of 4 persons are established.\u0000Following the approach adopted in the article, it is possible to obtain\u0000coefficient criteria of the stability of coalitional structures both in games\u0000with a large number of players and for other coalitional structures","PeriodicalId":246257,"journal":{"name":"TAURIDA JOURNAL OF COMPUTER SCIENCE THEORY AND MATHEMATICS","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130872875","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}