Pareto Equilibrium of Objections and Counterobjections in a Differential Three-Person Game

Automation and Remote Control - A linear-quadratic positional differential game of three persons is considered. Coefficient criteria are established under which there is no Nash equilibrium...     

Mathematical foundations of the Golden Rule. I. Static case

The Berge equilibrium concept was suggested by Russian mathematician K. Vaisman in 1994. In this paper, we suggest to use this concept as a mathematical model of the Golden Rule. The Berge–Pareto equilibrium is formalized and sufficient conditions for the existence of the equilibrium are found. As a supplement, the existence of the mixed strategy equilibrium is proved.     

Model of individual collisions for description of electron transport in matter

Distributions of electron characteristics are constructed with the use of data of elastic and nonelastic processes of interaction between electrons and matter. The data are taken from the National Nuclear Data Center, . These characteristics are used for developing the technique of modeling the electron transport in matter. The developed model does not use the well-known slowdown approximation and multiple scattering theories. The comparison of some moments of the distributions with the NIST data is carried out. The satisfactory fit of some results computed by using the developed model and MCNP results is obtained.     

Existence of Berge equilibrium in conflicts under uncertainty

The main tool for conflict resolution (equilibration) is the equilibrium strategy. Among the torrent of publications in this field, including the seven Nobel prize winners of 1994–2012, the Nash equilibrium is the fundamental one. Such equilibrium. however, does not necessarily exist. In this case, it is only natural to introduce a new notion of equilibrium, that of Berge. It was discussed in the paper which established existence of the Berge equilibrium in the mixed strategies and proposed sufficient conditions reducible to determination of the saddle point of a special Germeier convolution of the gain functions.     

Pareto-optimal Nash equilibrium: Sufficient conditions and existence in mixed strategies

This paper considers the Nash equilibrium strategy profiles that are Pareto optimal with respect to the rest Nash equilibrium strategy profiles. The sufficient conditions for the existence of such pure strategy profiles are established. These conditions employ the Germeier convolutions of the payoff functions. For the non-cooperative games with compact strategy sets and continuous payoff functions, the existence of the Pareto optimal Nash equilibria in mixed strategies is proved.     

Mathematical Foundations of the Golden Rule. II. Dynamic Case

This paper extends the earlier research of the Golden Rule in the static case [2] to the dynamic one. The main idea is to use the Germeier convolution of the payoff functions of players within the framework of antagonistic positional differential games in quasi motions and guiding control.