SOLUTIONS IN A NON-ANTAGONISTIC POSITIONAL DIFFERENTIAL GAME

A new approach to constructing solutions in a two-person non-antagonis tic positional differential game (NPDG) is proposed. The approach is b ased on the use of the principle of non-degradation of guaranteed resu lts [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 Pa reto-optimal states, that are best for one and for the other players a nd, 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 di fferent types of player behaviour. This paper is an extension of the i nvestigation described in [3, 4]. (C) 1998 Elsevier Science Ltd. Ail r ights reserved.