Models of energy infrastructure and dynamical coordination games

Abstract

The paper is devoted to analysis of equilibrium trajectories in dynamical bimatrix coordination games. Control strategies are constructed basing on the feedback principle, developed in N.N. Krasovskii’s scientific school. The dynamics of the controlled system operates on the infinite time horizon, and players’ functionals are determined as the limit of the expected values of bimatrix games payoffs. The solution of the problem is implemented within the theory of generalized minimax solutions of Hamilton-Jacobi equations. The method of conjugate derivatives is used for verification of the stability property for the constructed value functions. Basing on switching lines of value functions, an algorithm is elaborated for construction of equilibrium trajectories. The proposed approach provides the solution of the dynamical game with better properties than values of competitive static Nash equilibria. The obtained result demonstrates the idea for shifting of the dynamical system from unfavorable competitive Nash equilibria to cooperative Pareto maximum points with better payoffs. Analysis of asymptotic behavior for equilibrium trajectories is applied to the problem of investments. Particularly, a case study is examined for East Siberian gas pipeline projects, in which equilibrium trajectories are constructed and investment efficiency is analyzed.