Refinement of the Nash Solution for Games with Perfect Information

The n-person finite games with perfect information are considered. It is well known that the subgame perfectness assumption does not lead to the unique Nash equilibria (NE). Thus the problem arises of how to choose a unique subgame perfect NE. It is proved that by introducing the so-called "preference vector" for each player a unique subgame (in the sense of payoffs) NE can be constructed. The application of the approach to the "lifeline" simple pursuit game with one pursuer and two evaders enables us to find a unique subgame (in the sense of payoffs) NE in this differential game also.