Coordination of Long-Term and Short-Term Payoffs in Dynamic Bimatrix Games

Abstract

Dynamic optimality principles are applied to construct equilibrium solutions in evolutionary bimatrix games. The dynamics of the model can be interpreted as Kolmogorov’s differential equations in which coefficients describing flows are not fixed a priori and can be chosen on the feedback principle. Long-term payoffs of coalitions are defined on the infinite horizon by the integral functionals. A peculiarity of the model is the coordination of velocities of solutions constructed for long-term payoff integrals with directions of gradients of short-term payoffs. The notion of a dynamic Nash equilibrium is introduced in the class of control feedbacks. A solution based on the notion of guaranteeing feedbacks is proposed. Discontinuous guaranteeing feedbacks are constructed using generalized methods of characteristics and switching regimes are indicated.