Mathematical Game Theory and Applications

About one differential game with payment functions type of Germeier's convolution

2024-12-11T09:36:52+03:00

The paper considers a differential game model with functionals that are a convolution of the minimum type of two criteria, one of which describes the competition of players in some general (external) sphere of activity, and the other describes the personal achievements of each player (in the internal sphere). The player control is the distribution of resources 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. This work is a development of the results for the static model published by the authors in this journal in 2022.

Partial sums of antagonistic games and their applications

2024-12-11T09:36:52+03:00

An abstract algebraic approach to the formation of high-dimensional matrix games is proposed. The considered class of games includes, in particular, statistical games. A general method for constructing randomized decision rules for the problem of estimating the parameter of a discrete random variable is discussed. For economically significant tasks, the cost of additional observation is calculated.

Differential pursuit games of neutral type with integral restrictions on player controls

2024-12-11T09:36:51+03:00

In this paper, we study linear differential games described by a system of linear differential-difference equations of neutral type under integral constraints on the controls of the players. We obtain new sufficient conditions on parameters of the process guaranteeing finishing the game in a definite finite time.

Triangles of conflicts and hexamatrix games

2024-12-11T09:36:51+03:00

The paper addresses one class of finite non-cooperative games (with finite numbers of strategies for each player) – Polymatrix Games of E.B. Yanovskaya. Namely, we study in detail the 3-players Polymatrix Games, the so-called Hexamatrix Games (HMG), which can be completely described by six matrices. A number of model examples of 3-sides real-life conflicts are presented and formulated as HMG. The possibility of using hexamatrix games to model economic relationships between three participants is demonstrated. To find a Nash Equilibrium in the formulated games, we use an optimization approach, when the problem is transformed into a nonconvex optimization problem with a bilinear structure. The latter is solved by the A.S. Strekalovsky’s Global Search Theory (GST) for (d.c.) optimization problems with objective functions represented as the difference of two convex functions.

Study of computational complexity of the algorithm for finding the traffic flow Wardrop equilibrium

2024-12-11T09:36:51+03:00

The paper describes an algorithm for finding the Wardrop equilibrium and optimal distribution of traffic flows in the urban road network. Implementing this algorithm, the software has been developed. To study the computational complexity of the algorithm for finding the equilibrium distribution of traffic flows depending on the model dimension, the process of conducting and analyzing the results of computational experiments is presented.