A differential investment game with unknown utility switching moment

This article presents an approach to estimate the switching moment of utility functions in non-cooperative differential games, which serves as a crucial determinant in strategic decision-making under uncertainty. Grounded on the previously established models for cooperative scenarios, this study extends the estimation methodology to non-cooperative scenarios where individual players pursue independent objectives. By formulating a minimax problem, we derive optimal estimates for the switching moment, allowing each player to maximize their individual payoff under conditions of incomplete information. An example of an investment problem illustrates the application of the model, highlighting the contrasts in optimal estimate of switching moment between non-cooperative and cooperative frameworks. Comparative analysis further demonstrates that there are significant differences between the non-cooperative and cooperative frameworks in terms of optimal estimates, strategy stability and adaptability to uncertainty.