Doklady Mathematics最新文献

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.

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.

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.

A model of a transportation system with parallel channels and BPR latency functions with symmetric linear externalities is considered in the case where the impact of the channel loads on latency is pairwise symmetric. For this case, it is proved that the game of traffic allocation among the channels is potential, and the price of anarchy is bounded above by a value of (frac{4}{3}).

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 n 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.

The minimax game problem of approach of a conflict-controlled system in a finite-dimensional Euclidean space at a fixed time moment is studied. Issues related to the construction of solutions to the problem are discussed, namely, the calculation and approximate calculation of solvability sets and the first player’s solving feedback strategies. N.N. Krasovskii’s method of unification is further developed. A feedback strategy of the first player based on the extreme aiming of the system’s trajectory at finite systems of sets in the phase space that approximate the solvability set of the approach problem is studied. As the main result, we justify the effectiveness of the extreme aiming strategy for an approximate solution of the problem. The effectiveness of the strategy is justified using unification constructions supplementing Krasovskii’s unification method.

The phenomenon of intransitivity of trading strategies with constant levels in the stock market is studied. By using Doob’s stopping theorem and basic concepts from probability theory, accurate estimates for the strength of intransitivity are derived for the case of strategies with constant levels.

The problem of optimal organization of state inspection with an honest head and rational auditors is considered. Audit schemes are investigated in which the honest behavior of taxpayers and auditors turns out to be resistant to coalition deviations. In addition to hierarchical structures, a three-stage scheme with cross-checking is considered. It is proved that cross-checking is never optimal. The minimum audit costs for two- and three-level structures are determined. The best option is specified depending on the model parameters.

The paper examines an infinite-horizon multistage game of renewable resource extraction with two types of players differing in the discount rates of future payoffs. Using the dynamic programming method, we construct a noncooperative solution—a subgame perfect Nash equilibrium in stationary feedback strategies—and a cooperative (Pareto optimal) solution for the case of complete cooperation of all players. The resulting solutions are analyzed for sensitivity to variations in model parameters. In particular, the range of the coefficient of natural resource renewal is found in which a noncooperative solution leads to complete depletion of the resource, while a cooperative scheme allows the players to avoid this negative scenario. A numerical example is given to demonstrate the theoretical results obtained.

The article provides an overview of the practice of using large language models (LLMs) in cyberattacks. Artificial intelligence models (machine learning and deep learning) are applied across various fields, with cybersecurity being no exception. One aspect of this usage is offensive artificial intelligence, specifically in relation to LLMs. Generative models, including LLMs, have been utilized in cybersecurity for some time, primarily for generating adversarial attacks on machine learning models. The analysis focuses on how LLMs, such as ChatGPT, can be exploited by malicious actors to automate the creation of phishing emails and malware, significantly simplifying and accelerating the process of conducting cyberattacks. Key aspects of LLM usage are examined, including text generation for social engineering attacks and the creation of malicious code. The article is aimed at cybersecurity professionals, researchers, and LLM developers, providing them with insights into the risks associated with the malicious use of these technologies and recommendations for preventing their exploitation as cyber weapons. The research emphasizes the importance of recognizing potential threats and the need for active countermeasures against automated cyberattacks.