Solutions in a non-antagonistic positional differential game

Abstract

A new approach to constructing solutions in a two-person non-antagonistic positional differential game (NPDG) is proposed. The approach is based on the use of the principle of non-degradation of guaranteed results [1, 2] of the players along trajectories which generate solutions on the use of the rule of extremal shift [1,2] in the direction of Pareto-optimal states, that are best for one and for the other players and, finally, on the use of equilibrium solutions in special auxiliary bimatrix games. Splitting of the set of positions in NPDG is proposed. Non-antagonistic positional differential games are considered with different types of player behaviour. This paper is an extension of the investigation described in [3, 4].