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The purpose of this paper is to emphasize that it is necessary to consider possible “switches” when constructing dynamic models. We consider a class of differential games with switching utility functions.

We assume that the players do not have exact information about the switching moments. The problem is to compute the optimal estimate of the unknown such moment that minimizes the players’ losses in the worst case. Two scenarios are considered: (1) the players have the same estimate and (2) the players have different estimates of the switching moment. An example of an investment problem is given, and optimal controls and trajectories are calculated analytically using Pontryagin’s maximum principle.

The analysis provides a simple rule for choosing the optimal estimate. It is shown that the players’ optimal estimates are identical in both scenarios.

To date, no research has addressed the optimal estimation of uncertainty switching moments in a two-player differential game involving utility function switching. Our study offers detailed estimates of switching moments in the cooperative case. This allows players to thoroughly evaluate the performance of various estimated switching times and make well-informed conclusions.