On equilibrium strategies in noncooperative dynamic games

In this paper a charactf'rization is given for equilibrium strategies in noncooperative dynamic games. These dynamic games are formulated in a very general way without any topological conditions: For a Nash-equilibrium concept, it is shown that equilibrium strategies are conserving and equalizing. Moreover, it is shown that a set of strategies with these properties satisfies the equilibrium conditions. With these characterization earlier characterizations for one-person decision processes, gambling houses and dynamic games have been generalized. Especially, this paper shows that such a characterization is basic for a very general class of dynamic games and does not depend on special structure. Of course, in dynamic games with more structure a more refined formulation of the characterization is possible.