The regularization ofNB-scheme in differential games

Abstract

The optimality principles in non-zero sum differential games and multicriterial control problems taken from the corresponding static (simultaneous) game theory are usually dynamic unstable (time inconsistent), thus their use becomes questionable if special regularization attempts are not made. This important aspect was first considered in [1], but also in the earlier paper of Strotz [7] this was shown for a special control problem with discount payoff. We have shown in [2] that many of the known procedures (excluding those based on scalarization of the payoff vector), of selecting of a special Pareto-optimal solution from the set of all Pareto-optimal solutions are dynamic unstable (time-inconsistent) and therefore the regularization procedures leading to the dynamic stable optimality principles are purposed [3]. It turns out that also in the Nash [4] bargaining process the regularization attempt can be made by constructng a special equation for the conflict point. The idea of the method is closely connected with the paper [5]. The special attention to the time-consistency problem is given also in the recent publications [6,8].